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1
Tsekov, Roumen. "Nonuniform Slip Effect in Wetting Films." Coatings 10, no. 6 (June 25, 2020): 597. http://dx.doi.org/10.3390/coatings10060597.
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The slip effect in wetting films is theoretically studied, and a nonlinear dependence of the hydrodynamic velocity on the slip length is discovered. It is demonstrated that the hydrodynamic flow is essentially affected by the presence of a nonuniform slip length distribution, leading also to enhancement of the energy dissipation in the films. This effect could dramatically slow the usually quick hydrodynamic flows over superhydrophobic surfaces, for instance.
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DAVIS, ANTHONY M. J., and ERIC LAUGA. "Hydrodynamic friction of fakir-like superhydrophobic surfaces." Journal of Fluid Mechanics 661 (August 23, 2010): 402–11. http://dx.doi.org/10.1017/s0022112010003460.
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A fluid droplet located on a superhydrophobic surface makes contact with the surface only at small isolated regions, and is mostly in contact with the surrounding air. As a result, a fluid in motion near such a surface experiences very low friction, and superhydrophobic surfaces display strong drag reduction in the laminar regime. Here we consider theoretically a superhydrophobic surface composed of circular posts (so-called fakir geometry) located on a planar rectangular lattice. Using a superposition of point forces with suitably spatially dependent strength, we derive the effective surface-slip length for a planar shear flow on such a fakir-like surface as the solution to an infinite series of linear equations. In the asymptotic limit of small surface coverage by the posts, the series can be interpreted as Riemann sums, and the slip length can be obtained analytically. For posts on a square lattice, our analytical prediction of the dimensionless slip length, in the low surface coverage limit, is in excellent quantitative agreement with previous numerical computations.
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Michelin, Sébastien, Giacomo Gallino, François Gallaire, and Eric Lauga. "Viscous growth and rebound of a bubble near a rigid surface." Journal of Fluid Mechanics 860 (December 3, 2018): 172–99. http://dx.doi.org/10.1017/jfm.2018.876.
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Motivated by the dynamics of microbubbles near catalytic surfaces in bubble-powered microrockets, we consider theoretically the growth of a free spherical bubble near a flat no-slip surface in a Stokes flow. The flow at the bubble surface is characterised by a constant slip length allowing us to tune the hydrodynamic mobility of its surface and tackle in one formulation both clean and contaminated bubbles as well as rigid shells. Starting with a bubble of infinitesimal size, the fluid flow and hydrodynamic forces on the growing bubble are obtained analytically. We demonstrate that, depending on the value of the bubble slip length relative to the initial distance to the wall, the bubble will either monotonically drain the fluid separating it from the wall, which will exponentially thin, or it will bounce off the surface once before eventually draining the thin film. Clean bubbles are shown to be a singular limit which always monotonically get repelled from the surface. The bouncing events for bubbles with finite slip lengths are further analysed in detail in the lubrication limit. In particular, we identify the origin of the reversal of the hydrodynamic force direction as due to the change in the flow pattern in the film between the bubble and the surface and to the associated lubrication pressure. Last, the final drainage dynamics of the film is observed to follow a universal algebraic scaling for all finite slip lengths.
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Li, Da Yong, Da Lei Jing, Yun Lu Pan, Khurshid Ahmad, and Xue Zeng Zhao. "Slip Length Measurement of Water Flow on Graphite Surface Using Atomic Force Microscope." Advanced Materials Research 941-944 (June 2014): 1581–84. http://dx.doi.org/10.4028/www.scientific.net/amr.941-944.1581.
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In this paper, we present experimental measurements of slip length of deionized (DI) water flow on a silicon surface and a graphite surface by using atomic force microscope. The results show that the measured hydrodynamic drag force is higher on silicon surface than that on graphite surface, and a measured slip length about 10 nm is obtained on the later surface.
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PANZER, PETER, MARIO LIU, and DIETRICH EINZEL. "THE EFFECTS OF BOUNDARY CURVATURE ON HYDRODYNAMIC FLUID FLOW: CALCULATION OF SLIP LENGTHS." International Journal of Modern Physics B 06, no. 20 (October 20, 1992): 3251–78. http://dx.doi.org/10.1142/s0217979292001420.
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The slip description of fluid flow past solid boundaries is reconsidered. We find that the traditional picture of fluid slip as a mean free path correction to hydrodynamics has to be revised whenever the particle scattering becomes close to specular. Then the microscopic slip length may diverge and it is the boundary’s curvature which is decisive for the momentum transfer between fluid and wall. By explicitly considering surface roughness we can explain discrepancies between experimentally observed data and traditional slip theory.
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Bharti, Partha P. Gopmandal, R. K. Sinha, and H. Ohshima. "Effect of core hydrophobicity on the electrophoresis of pH-regulated soft particles." Soft Matter 17, no. 11 (2021): 3074–84. http://dx.doi.org/10.1039/d0sm02278k.
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Wang, Yun-Lei, Jiu-Hui Wu, Mu-Ming Hao, and Lu-Shuai Xu. "Improved hydrodynamic performance of liquid film seal by considering boundary slip and cavitation." Industrial Lubrication and Tribology 71, no. 9 (November 4, 2019): 1108–15. http://dx.doi.org/10.1108/ilt-03-2019-0088.
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Purpose The purpose of this paper is to investigate the effect of boundary slip on hydrodynamic performance of liquid film seal considering cavitation. Design/methodology/approach A mathematical model of liquid film seal with slip surface was established based on the Navier slip model and Jakobsson–Floberg–Olsson (JFO) boundary condition. Liquid film governing equation was discretized by the finite difference method and solved by the SOR relaxation iterative algorithm and the hydrodynamic performance parameters of liquid film seal were obtained considering boundary slip and cavitation. Findings The results indicate that the values of performance parameters are affected significantly by the slip length under the condition of high speed and low differential pressure. Originality/value The performances of liquid film seal are investigated considering slip surface and cavitation. The results presented in the study are expected to provide a theoretical basis to improve the design method of liquid film seal.
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Vidal, A., and L. Botto. "Slip flow past a gas–liquid interface with embedded solid particles." Journal of Fluid Mechanics 813 (January 17, 2017): 152–74. http://dx.doi.org/10.1017/jfm.2016.842.
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We simulate shear flow past a stationary monolayer of spherical particles embedded in a flat gas–liquid interface. This problem is relevant to the understanding of the microhydrodynamics of particle-laden interfacial structures, including particle-laden drops, bubbles and foams. The combination of the free-shear condition at the gas–liquid interface and the no-slip condition at the particle surfaces gives rise to a velocity slip at the particle-laden interface. We study the characteristics of the flow near the monolayer, focusing on slip velocity, slip length and interfacial shear stress. Two microstructures are compared: a square array, and a reticulated array mimicking a percolating network of aggregated particles. We demonstrate that the scaling laws for the dependence of the slip length on solid area fraction developed for flow past superhydrophobic microstructured surfaces apply to the case of interfacial particles. The calculated slip lengths are in general smaller that those reported for microstructured superhydrophobic surfaces. This difference, which is due to the significant protrusion of the spherical particles in the liquid, can be accounted for in the case of the square array by an approximate argument. For a given area fraction, the reticulated array yields a larger slip length than the square array. We analyse the hydrodynamic forces acting on the particles, and the corresponding tangential stress exerted by the bulk ‘subphase’.
9
Hodes, Marc, Toby L. Kirk, Georgios Karamanis, and Scott MacLachlan. "Effect of thermocapillary stress on slip length for a channel textured with parallel ridges." Journal of Fluid Mechanics 814 (February 6, 2017): 301–24. http://dx.doi.org/10.1017/jfm.2017.8.
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We compute the apparent hydrodynamic slip length for (laminar and fully developed) Poiseuille flow of liquid through a heated parallel-plate channel. One side of the channel is textured with parallel (streamwise) ridges and the opposite one is smooth. On the textured side of the channel, the liquid is in the Cassie state. No-slip and constant heat flux boundary conditions are imposed at the solid–liquid interfaces along the tips of the ridges, and the menisci between ridges are considered to be flat and adiabatic. The smooth side of the channel is subjected to no-slip and adiabatic boundary conditions. We account for the streamwise and transverse thermocapillary stresses along menisci. When the latter is sufficiently small, Stokes flow may be assumed. Then, our solution is based upon a conformal map. When, additionally, the ratio of channel height to half of the ridge pitch is of order 1 or larger, an accurate but less cumbersome solution follows from a matched asymptotic expansion. When inertial effects are relevant, the slip length is numerically computed. Setting the thermocapillary stress equal to zero yields the slip length for an adiabatic flow.
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BAHGA, SUPREET S., OLGA I. VINOGRADOVA, and MARTIN Z. BAZANT. "Anisotropic electro-osmotic flow over super-hydrophobic surfaces." Journal of Fluid Mechanics 644 (February 10, 2010): 245–55. http://dx.doi.org/10.1017/s0022112009992771.
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Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to greatly enhance electrokinetic phenomena. Existing theories assume either homogeneous flat surfaces or patterned surfaces with thin double layers (compared with the texture correlation length) and thus predict simple surface-averaged, isotropic flows (independent of orientation). By analysing electro-osmotic flows over striped slip-stick surfaces with arbitrary double-layer thickness, we show that surface anisotropy generally leads to a tensorial electro-osmotic mobility and subtle, nonlinear averaging of surface properties. Interestingly, the electro-osmotic mobility tensor is not simply related to the hydrodynamic slip tensor, except in special cases. Our results imply that significantly enhanced electro-osmotic flows over super-hydrophobic surfaces are possible, but only with charged liquid–gas interfaces.
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Tian, Porui, and Yifan Li. "Effect of pH on Effective Slip Length and Surface Charge at Solid–Oil Interfaces of Roughness-Induced Surfaces." Micromachines 12, no. 7 (June 26, 2021): 752. http://dx.doi.org/10.3390/mi12070752.
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In the development of micro/nano fluid control systems, fluid resistance has always been one of the key factors restricting its development. According to previous studies, it is found that the boundary slip effect of the solid-liquid interface can effectively reduce the resistance of the microfluid and improve the transport efficiency of the microfluid. The boundary slip length is mainly affected by surface wettability, roughness, and surface charge density. Among them, the influence mechanism of surface charge density on the boundary slip is the most complicated, and there is a lack of relevant research, and further investigation is needed. In this paper, we present research on quantification of effective slip length and surface charge density, where the roughness effect is considered. The electrostatic and hydrodynamic force data obtained from atomic force microscopy (AFM) measurements were fitted and processed for comparative analysis. We obtained the variation of surface charge density and effective slip length when different oleophobic surface samples were immersed in ethylene glycol with different pH values. The effect of pH on the surface charge density and effective slip length was investigated by their variations. The mechanism of the effect of pH on the surface charge density was discussed. The experimental results show that in the ethylene glycol solution, no matter whether the pH value of the solution increases or decreases, the charge density of the surface with the same properties decreases, and the effective boundary slip length also shows a downward trend. In deionized water, the surface charge density and effective boundary slip length decreases with the decrease of PH value.
12
Muchammad, M., Mohammad Tauviqirrahman, J. Jamari, and D. J. Schipper. "Analysis of the Effect of the Slip-Pocket in Single and Double Parallel Bearing Considering Cavitation: A Theoretical Approach." Lubricants 9, no. 1 (December 28, 2020): 3. http://dx.doi.org/10.3390/lubricants9010003.
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In this paper, based on an analytical approach, the effect of pockets and boundary slip on the hydrodynamic performance of parallel sliding surfaces considering cavitation is investigated. A modified Reynolds theory is developed for solving two kinds of bearings: a single and a double pocket bearing. The performance is compared with respect to the variation of the pocket depth, pocket length, slip, and no-slip situation. The results show that the maximum pressure and load support increases with the reduction in pocket length. The main finding is that the pocket depth reduces the cavitation area. However, in the case of a single pocket, the role of pocket depth is more significant in reducing the cavitation effect than that in the case of a double pocket bearing.
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Crowdy, Darren G. "Perturbation analysis of subphase gas and meniscus curvature effects for longitudinal flows over superhydrophobic surfaces." Journal of Fluid Mechanics 822 (June 1, 2017): 307–26. http://dx.doi.org/10.1017/jfm.2017.274.
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Integral expressions for the first-order correction to the effective slip length for longitudinal flows over a unidirectional superhydrophobic surface with rectangular grooves are determined under the assumptions that the meniscus curvature is small and the viscosity contrast between the groove-trapped subphase gas and the working fluid is significant. Both pressure-driven channel flows and semi-infinite shear flows are considered. Reciprocity ideas, based on use of Green’s second identity, provide the integral expressions with integrands dependent on known flat-meniscus solutions found by Philip (Z. Angew. Math. Phys., vol. 23, 1972, pp. 353–372). The results extend earlier work by Sbragaglia & Prosperetti (Phys. Fluids, vol. 19, 2007, 043603) on how weak meniscus curvature affects hydrodynamic slip. In particular, we derive a new integral expression for the first-order slip length correction due to weak meniscus curvature.
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Savio, Daniele, Lars Pastewka, and Peter Gumbsch. "Boundary lubrication of heterogeneous surfaces and the onset of cavitation in frictional contacts." Science Advances 2, no. 3 (March 2016): e1501585. http://dx.doi.org/10.1126/sciadv.1501585.
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Surfaces can be slippery or sticky depending on surface chemistry and roughness. We demonstrate in atomistic simulations that regular and random slip patterns on a surface lead to pressure excursions within a lubricated contact that increase quadratically with decreasing contact separation. This is captured well by a simple hydrodynamic model including wall slip. We predict with this model that pressure changes for larger length scales and realistic frictional conditions can easily reach cavitation thresholds and significantly change the load-bearing capacity of a contact. Cavitation may therefore be the norm, not the exception, under boundary lubrication conditions.
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Tauviqirrahman, Mohammad, J. Jamari, Bayu Siswo Wibowo, Hilmy Muhammad Fauzan, and M. Muchammad. "Multiphase Computational Fluid Dynamics Analysis of Hydrodynamic Journal Bearing Under the Combined Influence of Texture and Slip." Lubricants 7, no. 11 (October 30, 2019): 97. http://dx.doi.org/10.3390/lubricants7110097.
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The drive to maintain the environmental sustainability and save the global energy consumption is urgent, making every powertrain system component a candidate to enhance efficiency. In this work, the combined effects of the slip boundary and textured surface in hydrodynamic journal bearing as one of the critical components in industrial powertrain and engine systems are assessed using a multiphase computational fluid dynamic analysis that allows for phase change in a cavitation process and arbitrary textured geometry. The texture studied consists of regularly spaced rectangular dimples through two-dimensional (infinitely long) journal bearing. The modified Navier–slip model is employed to describe the slip boundary condition. A systematic comparison is made for various textured configurations varying the texture depth and the length of the texturing zone with respect to the performance of a smooth (untextured) bearing for several eccentricity ratios. The effectiveness of the texture with or without slip at enhancing the load support over a corresponding smooth bearing is investigated with the parameters. The detrimental or beneficial effect of surface texturing as well as the slip promotion is explained in terms of the mechanisms of pressure generation for several eccentricity ratios. The results of the present work indicate that journal bearing textured by a proper texturing zone and dimple depth are characterized by substantial load support levels. However, in the range of high eccentricity ratios, the promotion of texturing and slip can significantly degrade the performance of the load support.
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Solomentsev, Yuri, and John L. Anderson. "Electrophoresis of slender particles." Journal of Fluid Mechanics 279 (November 25, 1994): 197–215. http://dx.doi.org/10.1017/s0022112094003885.
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The hydrodynamic theory of slender bodies is used to model electrophoretic motion of a slender particle having a charge (zeta potential) that varies with position along its length. The theory is limited to systems where the Debye screening length of the solution is much less than the typical cross-sectional dimension of the particle. A stokeslet representation of the hydrodynamic force is combined with the Lorentz reciprocal theorem for Stokes flow to develop a set of linear equations which must be solved for the components of the translational and angular velocities of the particle. Sample calculations are presented for the electrophoretic motion of straight spheroids and cylinders and a torus in a uniform electric field. The theory is also applied to a straight uniformly charged particle in a spatially varying electric field. The uniformly charged particle rotates into alignment with the principal axes of ∇E∞; we suggest that such alignment can lead to electrophoretic transport of particles through a small aperture in an otherwise impermeable wall. The theory developed here is more general than just for electrophoresis, since the final result is expressed in terms of a general 'slip velocity’ at the surface of the particle. Thus, the results are applicable to diffusiophoresis of slender particles if the proper slip-velocity coefficient is used.
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Kirk, Toby L., Marc Hodes, and Demetrios T. Papageorgiou. "Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature." Journal of Fluid Mechanics 811 (December 7, 2016): 315–49. http://dx.doi.org/10.1017/jfm.2016.760.
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We investigate forced convection in a parallel-plate-geometry microchannel with superhydrophobic walls consisting of a periodic array of ridges aligned parallel to the direction of a Poiseuille flow. In the dewetted (Cassie) state, the liquid contacts the channel walls only at the tips of the ridges, where we apply a constant-heat-flux boundary condition. The subsequent hydrodynamic and thermal problems within the liquid are then analysed accounting for curvature of the liquid–gas interface (meniscus) using boundary perturbation, assuming a small deflection from flat. The effects of this surface deformation on both the effective hydrodynamic slip length and the Nusselt number are computed analytically in the form of eigenfunction expansions, reducing the problem to a set of dual series equations for the expansion coefficients which must, in general, be solved numerically. The Nusselt number quantifies the convective heat transfer, the results for which are completely captured in a single figure, presented as a function of channel geometry at each order in the perturbation. Asymptotic solutions for channel heights large compared with the ridge period are compared with numerical solutions of the dual series equations. The asymptotic slip length expressions are shown to consist of only two terms, with all other terms exponentially small. As a result, these expressions are accurate even for heights as low as half the ridge period, and hence are useful for engineering applications.
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Costa, Jarlon Conceição da, Luiz Mário Nelson de Góis, and Silvana Mattedi e. Silva. "Holdup and characteristic velocity in a pulsed packed extraction column." Research, Society and Development 9, no. 8 (July 28, 2020): e674982543. http://dx.doi.org/10.33448/rsd-v9i8.2543.
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The present work aims to evaluate the hydrodynamics of a pulsed packed extractor, with an internal diameter of 0.026m and a length of 1.0m, using the liquid butanol-water system. Thus, the basic parameters obtained for the hydrodynamic study of the extraction column in question as dispersed phase, slip velocity, characteristic velocity and flooding point. The methodology used in the work consisted of determining the holdup fraction of the dispersed phase, obtained through tests of simultaneous interruptions in the column feedings. The effects of frequency pulsation, dispersed phase flow rate and continuous phase flow rate investigated in the analysis of these parameters. New empirical correlations derived from the predictions of the parameters studied obtained in terms of operating variables and physical properties of the liquid system involved. The average absolute value of the relative error (AARE) was always below 5.6%. Good agreement between calculated and experimental results observed for all investigated operating conditions.
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Deng, Mingge, Xuejin Li, Haojun Liang, Bruce Caswell, and George Em Karniadakis. "Simulation and modelling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres." Journal of Fluid Mechanics 711 (September 3, 2012): 192–211. http://dx.doi.org/10.1017/jfm.2012.387.
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AbstractFabrication of functionalized surfaces using polymer brushes is a relatively simple process and parallels the presence of glycocalyx filaments coating the luminal surface of our vasculature. In this paper, we perform atomistic-like simulations based on dissipative particle dynamics (DPD) to study both polymer brushes and glycocalyx filaments subject to shear flow, and we apply mean-field theory to extract useful scaling arguments on their response. For polymer brushes, a weak shear flow has no effect on the brush density profile or its height, while the slip length is independent of the shear rate and is of the order of the brush mesh size as a result of screening by hydrodynamic interactions. However, for strong shear flow, the polymer brush is penetrated deeper and is deformed, with a corresponding decrease of the brush height and an increase of the slip length. The transition from the weak to the strong shear regime can be described by a simple ‘blob’ argument, leading to the scaling ${\dot {\gamma } }_{0} \propto {\sigma }^{3/ 2} $, where ${\dot {\gamma } }_{0} $ is the critical transition shear rate and $\sigma $ is the grafting density. Furthermore, in the strong shear regime, we observe a cyclic dynamic motion of individual polymers, causing a reversal in the direction of surface flow. To study the glycocalyx layer, we first assume a homogeneous flow that ignores the discrete effects of blood cells, and we simulate microchannel flows at different flow rates. Surprisingly, we find that, at low Reynolds number, the slip length decreases with the mean flow velocity, unlike the behaviour of polymer brushes, for which the slip length remains constant under similar conditions. (The slip length and brush height are measured with respect to polymer mesh size and polymer contour length, respectively.) We also performed additional DPD simulations of blood flow in a tube with walls having a glycocalyx layer and with the deformable red blood cells modelled accurately at the spectrin level. In this case, a plasma cell-free layer is formed, with thickness more than three times the glycocalyx layer. We then find our scaling arguments based on the homogeneous flow assumption to be valid for this physiologically correct case as well. Taken together, our findings point to the opposing roles of conformational entropy and bending rigidity – dominant effects for the brush and glycocalyx, respectively – which, in turn, lead to different flow characteristics, despite the apparent similarity of the two systems.
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Pati, Sukumar, and Vishwanath Kumar. "Effects of temperature-dependent thermo-physical properties on hydrodynamic swirl decay in microtubes." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 233, no. 3 (January 31, 2018): 427–35. http://dx.doi.org/10.1177/0954408918755782.
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In this paper, the influence of temperature-dependent thermo-physical properties is investigated on the decay of swirl in a laminar swirling flow of liquid through a heated microtube. The conservation equations for mass, momentum, and energy are numerically solved to obtain the velocity and temperature fields. The decay of swirl is quantified by the variation of the ratio of swirl number at a section to that at the inlet ( S/ S0) along the flow. The results reveal that constant property simulations result in faster swirl decay as compared to the variable-property simulations. Further, the implications of slip length, inlet swirl number, inlet swirl velocity profile, and Reynolds number on the swirl decay are presented. The results of the present analysis bear significant technological consequences in the design of micro-heat exchangers with intrinsic rotationalities.
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Khabthani, Sondes, Antoine Sellier, and François Feuillebois. "Lubricating motion of a sphere towards a thin porous slab with Saffman slip condition." Journal of Fluid Mechanics 867 (March 28, 2019): 949–68. http://dx.doi.org/10.1017/jfm.2019.169.
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Near-contact hydrodynamic interactions between a solid sphere and a plane porous slab are investigated in the framework of lubrication theory. The size of pores in the slab is small compared with the slab thickness so that the Darcy law holds there. The slab is thin: that is, its thickness is small compared with the sphere radius. The considered problem involves a sphere translating above the slab together with a permeation flow across the slab and a uniform pressure below. The pressure is continuous across both slab interfaces and the Saffman slip condition applies on its upper interface. An extended Reynolds-like equation is derived for the pressure in the gap between the sphere and the slab. This equation is solved numerically and the drag force on the sphere is calculated therefrom for a wide range of values of the slab interface slip length and of the permeability parameter $\unicode[STIX]{x1D6FD}=24k^{\ast }R/(e\unicode[STIX]{x1D6FF}^{2})$, where $k^{\ast }$ is the permeability, $e$ is the porous slab thickness, $R$ is the sphere radius and $\unicode[STIX]{x1D6FF}$ is the gap. Moreover, asymptotics expansions for the pressure and drag are derived for high and low $\unicode[STIX]{x1D6FD}$. These expansions, which agree with the numerics, are also handy formulae for practical use. All results match with those of other authors in particular cases. The settling trajectory of a sphere towards a porous slab in a fluid at rest is calculated from these results and, as expected, the time for reaching the slab decays for increasing slab permeability and upper interface slip length.
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Muchammad, Mohammad Tauviqirrahman, J. Jamari, and D. J. Schipper. "Load Support Improvement on Superhydrophobic Surface in Lubricated-MEMS Using Numerical Investigation." Advanced Materials Research 1123 (August 2015): 3–6. http://dx.doi.org/10.4028/www.scientific.net/amr.1123.3.
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The development of micro-electro-mechanical systems (MEMS) faces a great challenge in commercial application with respect to lubrication issue recently. Short life time of lubricated MEMS is primarily caused by the failure of the lubrication. In this study, the use of superhydrophobic material applied on one or both of the opposing surfaces in lubricated MEMS was introduced to reduce this type of failure. The optimum parameter of the superhydrophobic effect that provides the greatest load support in MEMS was obtained using numerical analysis. A modified Reynolds equation combined with cavitation model was derived. The slip length model was used to address the superhydrophobic effect for the hydrodynamic analysis. It was shown that in the absence of the wedge effect, load support can be obtained using the superhydrophobic surface. In addition, the numerical analysis showed that the performance of MEMS using such surface depends on cavitation.
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Kovetska, Y. Y., A. I. Skitsko, and T. V. Sorokina. "THE INSTABILITY OF SLIPPING FLOW IN A CURVILINEAR POROUS MICROCHANNEL." Industrial Heat Engineering 40, no. 3 (September 7, 2018): 20–26. http://dx.doi.org/10.31472/ihe.3.2018.03.
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The hydrodynamic instability of flow with slippage in a curvilinear porous microchannel between two stationary concentric cylinders is investigated. Unperturbed velocity profiles for a flow with slip are obtained. The problem of linear instability is solved numerically, using the collocation method. Calculations showed that an increase in the coefficient of slippage, the porosity of the medium and the width of the channel leads to an increase in the occupancy of the velocity profile of the undisturbed flow (the profile becomes more flat). This, in turn, leads to an increase in the critical values of Dean number and the critical wave length of the perturbation, which determine the instability criteria for the flow. It is also shown that for σ> 0 the dependences of the critical Dean number on the parameter η have a minimum observed at η = 0.5. With decrease in channel width and permeability, this effect is leveled.
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ROOS, P. C., and H. M. SCHUTTELAARS. "Horizontally viscous effects in a tidal basin: extending Taylor's problem." Journal of Fluid Mechanics 640 (October 27, 2009): 421–39. http://dx.doi.org/10.1017/s0022112009991327.
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The classical problem of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, pp. 148–181) of Kelvin wave reflection in a semi-enclosed rectangular basin of uniform depth is extended to account for horizontally viscous effects. To this end, we add horizontally viscous terms to the hydrodynamic model (linearized depth-averaged shallow-water equations on a rotating plane, including bottom friction) and introduce a no-slip condition at the closed boundaries.In a straight channel of infinite length, we obtain three types of wave solutions (normal modes). The first two wave types are viscous Kelvin and Poincaré modes. Compared to their inviscid counterparts, they display longitudinal boundary layers and a slight decrease in the characteristic length scales (wavelength or along-channel decay distance). For each viscous Poincaré mode, we additionally find a new mode with a nearly similar lateral structure. This third type, entirely due to viscous effects, represents evanescent waves with an along-channel decay distance bounded by the boundary-layer thickness.The solution to the viscous Taylor problem is then written as a superposition of these normal modes: an incoming Kelvin wave and a truncated sum of reflected modes. To satisfy no slip at the lateral boundary, we apply a Galerkin method. The solution displays boundary layers, the lateral one at the basin's closed end being created by the (new) modes of the third type. Amphidromic points, in the inviscid and frictionless case located on the centreline of the basin, are now found on a line making a small angle to the longitudinal direction. Using parameter values representative for the Southern Bight of the North Sea, we finally compare the modelled and observed tide propagation in this basin.
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Dhanasekaran, Johnson, and Donald L. Koch. "The hydrodynamic lift of a slender, neutrally buoyant fibre in a wall-bounded shear flow at small Reynolds number." Journal of Fluid Mechanics 879 (September 19, 2019): 121–46. http://dx.doi.org/10.1017/jfm.2019.653.
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The hydrodynamic lift velocity of a neutrally buoyant fibre in a simple shear flow near a wall is determined for small, but non-zero, fibre Reynolds number, illustrating the role of non-sphericity in lift. The rotational motion and effects of fibre orientation on lift are treated for fibre positions that induce and do not induce solid-body wall contacts. When the fibre does not contact the wall its lift velocity can be obtained in terms of the Stokes flow field by using a generalized reciprocal theorem. The Stokes velocity field is determined using slender-body theory with the no-slip velocity at the wall enforced using the method of images. To leading order the lift velocity at distances large compared with the fibre length and small compared with the Oseen length is found to be $0.0303\unicode[STIX]{x1D70C}\dot{\unicode[STIX]{x1D6FE}}^{2}l^{2}a/(\unicode[STIX]{x1D707}\ln [2l/a])$, where $l$ and $a$ are the fibre half-length and radius, $\unicode[STIX]{x1D70C}$ is the density, $\dot{\unicode[STIX]{x1D6FE}}$ is the shear rate and $\unicode[STIX]{x1D707}$ is the viscosity of the fluid. When the fibre is close enough to the wall to make solid-body contact during its rotational motion, a process known as pole vaulting coupled with inertially induced changes of fibre orientation determines the lift velocity. The order of magnitude of the lift in this case is larger by a factor of $l/a$ than when the fibre does not contact the wall and it reaches a maximum of $0.013\unicode[STIX]{x1D70C}\dot{\unicode[STIX]{x1D6FE}}^{2}l^{3}/(\unicode[STIX]{x1D707}\ln [l/a])$ for the case of a highly frictional contact and about half that value for a frictionless contact. These results are used to illustrate how particle shape can contribute to separation methods such as those in microfluidic channels or cross-flow filtration processes.
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Dukhin, A. S., and T. G. M. Van De Ven. "Trajectories of charged tracer particles around a charged sphere in a simple shear flow." Journal of Fluid Mechanics 263 (March 25, 1994): 185–206. http://dx.doi.org/10.1017/s0022112094004076.
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The trajectories of electrically charged tracer particles travelling around a charged sphere subjected to a simple shear flow have been calculated. This is a limiting case of the relative trajectories of two unequal-sized spheres when the radius ratio a1/a2 approaches zero. Until now these trajectories have been calculated by assuming the additivity of hydrodynamic and electrostatic forces, while neglecting the electroviscous coupling forces. These electroviscous forces are long range and can significantly alter the relative trajectories of spheres. When a1/a2 → 0, it is found that these trajectories depend on two parameters, α and β, which depend on the surface charge density of the tracer particle and the sphere. The relative trajectories of charged particles are qualitatively different from those of neutral particles. There exist six intervals of α-values for which the trajectories of the tracer particle show different features. Several new types of trajectory appear, besides the open and closed trajectories for neutral particles, which we refer to as uni- and bidirectional infinite length trajectories, uni- and bidirectional finite length trajectories, open returning trajectories, and prolate, oblate and circular closed trajectories. This richness of possible trajectories is the result of three electrokinetic phenomena, affecting particle motion: electro-osmotic slip, electrophoretic and diffusiophoretic motion.
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Rao, A. Subba, Seela Sainath, P. Rajendra, and G. Ramu. "Mathematical Modelling of Hydromagnetic Casson non-Newtonian Nanofluid Convection Slip Flow from an Isothermal Sphere." Nonlinear Engineering 8, no. 1 (January 28, 2019): 645–60. http://dx.doi.org/10.1515/nleng-2018-0016.
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Abstract In this article, the combined magnetohydrodynamic heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid from an isothermal sphere surface with convective condition under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. magnetic parameter (M), Buoyancy ratio parameter (N), Casson fluid parameter (β), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr) and thermal slip (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Increasing viscoplastic (Casson) parameter decelerates the flow and also decreases thermal and nano-particle concentration. Increasing Brownian motion accelerates the flow and enhances temperatures whereas it reduces nanoparticle concentration boundary layer thickness. Increasing thermophoretic parameter increasing momentum (hydrodynamic) boundary layer thickness and nanoparticle boundary layer thickness whereas it reduces thermal boundary layer thickness. Increasing magnetohydrodynamic body force parameter decelerates the flow whereas it enhances temperature and nano-particle (species) concentrations. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.
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Gopmandal, Partha P., S. Bhattacharyya, and H. Ohshima. "Effect of hydrophobic core on the electrophoresis of a diffuse soft particle." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2199 (March 2017): 20160942. http://dx.doi.org/10.1098/rspa.2016.0942.
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Electrophoresis of a diffuse soft particle with a charged hydrophobic core is considered under the weak field and low charge density assumptions. The hydrophobic surface of the core is coated with a diffuse polyelectrolyte layer (PEL) in which a gradual transition of the polymer segment distribution from the impenetrable core to the surrounding electrolyte medium is considered. A mathematical model is adopted to analyse the impact of the core hydrophobicity on the diffuse soft particle electrophoresis. The mobility based on the present model for the limiting cases such as bare colloids with hydrophobic core and soft particles with no-slip rigid cores are in good agreement with the existing results. The presence of PEL charges produces the impact of the core hydrophobicity on the soft particle mobility different from the corresponding bare colloid with hydrophobic surface in an electrolyte medium. The impact of the core hydrophobicity is subtle when the hydrodynamic screening length of the PEL is low. Reversal in mobility can be achieved by tuning the core hydrophobicity for an oppositely charged core and PEL.
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GHISALBERTI, MARCO. "Obstructed shear flows: similarities across systems and scales." Journal of Fluid Mechanics 641 (December 10, 2009): 51–61. http://dx.doi.org/10.1017/s0022112009992175.
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In this paper, I show that a range of environmental flows are inherently dynamically similar. These flows, which are partially obstructed by a permeable medium, are here termed ‘obstructed shear flows’. Examples include aquatic flows over sediment beds, submerged vegetation canopies and coral reefs, as well as atmospheric flows over crop canopies, forests and cities (‘urban canopies’). While the density and geometry of the obstructions may vary, the drag in each system generates a velocity profile with an inflection point. This renders the flow unstable. Consequently, it is expected that (a) the dominant interfacial turbulent structure in obstructed shear flows will be a Kelvin–Helmholtz-type vortex, and (b) that this instability will engender hydrodynamic similarities among obstructed shear flows. Such similarities have been hypothesized but not yet fully explored. An extensive review of existing data confirms these dynamic similarities on scales of O(mm) to O(10 m). The extent of shear penetration into the obstruction, which is a primary determinant of residence time in the obstruction, scales upon the drag length scale. Other relationships that link the strength of turbulence and the ‘slip’ velocity at the top of the obstruction to the friction velocity (u∗) are also evident. The relationships presented here provide predictive capability for flow and transport in obstructed shear flows and suggest the possibility of a single framework to describe such flows on all scales.
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Lecampion, Brice, and Dmitry I. Garagash. "Confined flow of suspensions modelled by a frictional rheology." Journal of Fluid Mechanics 759 (October 22, 2014): 197–235. http://dx.doi.org/10.1017/jfm.2014.557.
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AbstractWe investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al. (Phys. Rev. Lett., vol. 107 (18), 2011, 188301). The friction coefficient (shear stress over particle normal stress) and solid volume fraction are taken as functions of the dimensionless viscous number $I$ defined as the ratio between the fluid shear stress and the particle normal stress. We clarify the contributions of the contact and hydrodynamic interactions on the evolution of the friction coefficient between the dilute and dense regimes reducing the phenomenological constitutive description to three physical parameters. We also propose an extension of this constitutive framework from the flowing regime (bounded by the maximum flowing solid volume fraction) to the fully jammed state (the random close packing limit). We obtain an analytical solution of the fully developed flow in channel and pipe for the frictional suspension rheology. The result can be transposed to dry granular flow upon appropriate redefinition of the dimensionless number $I$. The predictions are in excellent agreement with available experimental results for neutrally buoyant suspensions, when using the values of the constitutive parameters obtained independently from stress-controlled rheological measurements. In particular, the frictional rheology correctly predicts the transition from Poiseuille to plug flow and the associated particles migration with the increase of the entrance solid volume fraction. We also numerically solve for the axial development of the flow from the inlet of the channel/pipe toward the fully developed state. The available experimental data are in good agreement with our numerical predictions, when using an accepted phenomenological description of the relative phase slip obtained independently from batch-settlement experiments. The solution of the axial development of the flow notably provides a quantitative estimation of the entrance length effect in a pipe for suspensions when the continuum assumption is valid. Practically, the latter requires that the predicted width of the central (jammed) plug is wider than one particle diameter. A simple analytical expression for development length, inversely proportional to the gap-averaged diffusivity of a frictional suspension, is shown to encapsulate the numerical solution in the entire range of flow conditions from dilute to dense.
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SWAN, JAMES W., and ADITYA S. KHAIR. "On the hydrodynamics of ‘slip–stick’ spheres." Journal of Fluid Mechanics 606 (July 10, 2008): 115–32. http://dx.doi.org/10.1017/s0022112008001614.
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The breakdown of the no-slip condition at fluid–solid interfaces generates a host of interesting fluid-dynamical phenomena. In this paper, we consider such a scenario by investigating the low-Reynolds-number hydrodynamics of a novel ‘slip–stick’ spherical particle whose surface is partitioned into slip and no-slip regions. In the limit where the slip length is small compared to the size of the particle, we first compute the translational velocity of such a particle due to the force density on its surface. Subsequently, we compute the rotational velocity and the response to an ambient straining field of a slip–stick particle. These three Faxén-type formulae are rich in detail about the dynamics of the particles: chiefly, we find that the translational velocity of a slip–stick sphere is coupled to all of the moments of the force density on its surface; furthermore, such a particle can migrate parallel to the velocity gradient in a shear flow. Perhaps most important is the coupling we predict between torque and translation (and force and rotation), which is uncharacteristic of spherical particles in unbounded Stokes flow and originates purely from the slip–stick asymmetry.
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Puthenveettil, Baburaj A., Vijaya K. Senthilkumar, and E. J. Hopfinger. "Motion of drops on inclined surfaces in the inertial regime." Journal of Fluid Mechanics 726 (May 30, 2013): 26–61. http://dx.doi.org/10.1017/jfm.2013.209.
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AbstractWe present experimental results on high-Reynolds-number motion of partially non-wetting liquid drops on inclined plane surfaces using: (i) water on fluoro-alkyl silane (FAS)-coated glass; and (ii) mercury on glass. The former is a high-hysteresis ($3{5}^{\circ } $) surface while the latter is a low-hysteresis one (${6}^{\circ } $). The water drop experiments have been conducted for capillary numbers $0. 0003\lt Ca\lt 0. 0075$ and for Reynolds numbers based on drop diameter $137\lt Re\lt 3142$. The ranges for mercury on glass experiments are $0. 0002\lt Ca\lt 0. 0023$ and $3037\lt Re\lt 20\hspace{0.167em} 069$. It is shown that when $Re\gg 1{0}^{3} $ for water and $Re\gg 10$ for mercury, a boundary layer flow model accounts for the observed velocities. A general expression for the dimensionless velocity of the drop, covering the whole $Re$ range, is derived, which scales with the modified Bond number ($B{o}_{m} $). This expression shows that at low $Re$, $Ca\sim B{o}_{m} $ and at large $Re$, $Ca \sqrt{Re} \sim B{o}_{m} $. The dynamic contact angle (${\theta }_{d} $) variation scales, at least to first-order, with $Ca$; the contact angle variation in water, corrected for the hysteresis, collapses onto the low-$Re$ data of LeGrand, Daerr & Limat (J. Fluid Mech., vol. 541, 2005, pp. 293–315). The receding contact angle variation of mercury has a slope very different from that in water, but the variation is practically linear with $Ca$. We compare our dynamic contact angle data to several models available in the literature. Most models can describe the data of LeGrand et al. (2005) for high-viscosity silicon oil, but often need unexpected values of parameters to describe our water and mercury data. In particular, a purely hydrodynamic description requires unphysically small values of slip length, while the molecular-kinetic model shows asymmetry between the wetting and dewetting, which is quite strong for mercury. The model by Shikhmurzaev (Intl J. Multiphase Flow, vol. 19, 1993, pp. 589–610) is able to group the data for the three fluids around a single curve, thereby restoring a certain symmetry, by using two adjustable parameters that have reasonable values. At larger velocities, the mercury drops undergo a change at the rear from an oval to a corner shape when viewed from above; the corner transition occurs at a finite receding contact angle. Water drops do not show such a clear transition from oval to corner shape. Instead, a direct transition from an oval shape to a rivulet appears to occur.
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Sheriff, Samreen, Nazir Ahmad Mir, Shakeel Ahmad, and Naila Rafiq. "Porosity and dissipative effects in Peristalsis of hydro-magneto nanomaterial: Application of biomedical treatment." Advances in Mechanical Engineering 13, no. 4 (April 2021): 168781402110118. http://dx.doi.org/10.1177/16878140211011890.
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The non-uniformity value which currently many applications of magneto-hydrodynamics are found in medicine where drug deliverance happens through peristaltic pumping phenomena, various magnetic drugs are released to target tumor diseases and to control the drug flow movement to the desired area. Owing to these facts, the aims of this article is to examine the simultaneous influence of magneto-hydrodynamics (MHD) and slip effect on unsteady peristaltic nanofluid flow in a non-uniform porous channel of finite length. The constituent governing equations for the model have been examined under the approximation of long wave length and small Reynolds value. Keeping kerosene oil and ethylene glycol as base fluids with polystyrene chosen as nanoparticle. The current analysis is carried out for the peristaltic flow transferal which carries innumerable industrialized employments. The incompressible, viscous, electrically conducting flow is studied in wave form. Here, exact method is employed to obtained closed form solutions. We have implemented computational software packages “Mathematica” as a main tool in order to obtain explicit expressions for axial velocity, temperature, stream function, pumping phenomenon and bolus formation. Obtained solutions are used for graphical analysis against different physical parameters. It is concluded that axial velocity increments for higher Hartmann number and slip parameter near the walls. The porosity effects increases the temperature whereas the temperature field shows increasing behavior for larger Brinkman number.
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Golovatenko, V. D., and A. V. Golovatenko. "Constraining a shaped charge jet cavity in a barrier with boundary shields." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 2 (June 30, 2016): 24–29. http://dx.doi.org/10.38013/2542-0542-2016-2-24-29.
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We suggest and validate empirically an acoustic method for decelerating and halting the movement of a shaped charge jet in a barrier by means of implementing an acoustic slit in the body of the barrier, the slit being located on the opposite side of the barrier relatively to the mounted linear charge with a profiled liner. We determine the pressure range created by a linear shaped charge with a profiled liner, and provide an estimation of the hydrodynamic wave length for the penetration process.
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Chedevergne, F., G. Casalis, and J. Majdalani. "Direct numerical simulation and biglobal stability investigations of the gaseous motion in solid rocket motors." Journal of Fluid Mechanics 706 (July 13, 2012): 190–218. http://dx.doi.org/10.1017/jfm.2012.245.
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AbstractIn this article, a biglobal stability approach is used in conjunction with direct numerical simulation (DNS) to identify the instability mode coupling that may be responsible for triggering large thrust oscillations in segmented solid rocket motors (SRMs). These motors are idealized as long porous cylinders in which a Taylor–Culick type of motion may be engendered. In addition to the analytically available steady-state solution, a computed mean flow is obtained that is capable of securing all of the boundary conditions in this problem, most notably, the no-slip requirement at the chamber headwall. Two sets of unsteady simulations are performed, static and dynamic, in which the injection velocity at the chamber sidewall is either held fixed or permitted to vary with time. In these runs, both DNS and biglobal stability solutions converge in predicting the same modal dependence on the size of the domain. We find that increasing the chamber length gives rise to less stable eigenmodes. We also realize that introducing an eigenmode whose frequency is sufficiently spaced from the acoustic modes leads to a conventional linear evolution of disturbances that can be accurately predicted by the biglobal stability framework. While undergoing spatial amplification in the streamwise direction, these disturbances will tend to decay as time elapses so long as their temporal growth rate remains negative. By seeding the computations with the real part of a specific eigenfunction, the DNS outcome reproduces not only the imaginary part of the disturbance, but also the circular frequency and temporal growth rate associated with its eigenmode. For radial fluctuations in which the vorticoacoustic wave contribution is negligible in relation to the hydrodynamic stability part, excellent agreement between DNS and biglobal stability predictions is ubiquitously achieved. For axial fluctuations, however, the DNS velocity will match the corresponding stability eigenfunction only when properly augmented by the vorticoacoustic solution for axially travelling waves associated with the Taylor–Culick profile. This analytical approximation of the vorticoacoustic mode is found to be quite accurate, especially when modified using a viscous dissipation function that captures the decaying envelope of the inviscid acoustic wave amplitude. In contrast, pursuant to both static and dynamic test cases, we find that when the frequency of the introduced eigenmode falls close to (or crosses over) an acoustic mode, a nonlinear mechanism is triggered that leads to the emergence of a secondary eigenmode. Unlike the original eigenmode, the latter materializes naturally in the computed flow without being artificially seeded. This natural occurrence may be ascribed to a nonlinear modal interplay in the form of internal, eigenmode-to-eigenmode coupling instead of an external, eigenmode pairing with acoustic modes. As a result of these interactions, large amplitude oscillations are induced.
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Baños, Ruben, José Arcos, Oscar Bautista, and Federico Méndez. "Steric and Slippage Effects on Mass Transport by Using an Oscillatory Electroosmotic Flow of Power-Law Fluids." Micromachines 12, no. 5 (May 10, 2021): 539. http://dx.doi.org/10.3390/mi12050539.
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In this paper, the combined effect of the fluid rheology, finite-sized ions, and slippage toward augmenting a non-reacting solute’s mass transport due to an oscillatory electroosmotic flow (OEOF) is determined. Bikerman’s model is used to include the finite-sized ions (steric effects) in the original Poisson-Boltzmann (PB) equation. The volume fraction of ions quantifies the steric effects in the modified Poisson-Boltzmann (MPB) equation to predict the electrical potential and the ion concentration close to the charged microchannel walls. The hydrodynamics is affected by slippage, in which the slip length was used as an index for wall hydrophobicity. A conventional finite difference scheme was used to solve the momentum and species transport equations in the lubrication limit together with the MPB equation. The results suggest that the combined slippage and steric effects promote the best conditions to enhance the mass transport of species in about 90% compared with no steric effect with proper choices of the Debye length, Navier length, steric factor, Womersley number, and the tidal displacement.
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SBRAGAGLIA, M., K. SUGIYAMA, and L. BIFERALE. "Wetting failure and contact line dynamics in a Couette flow." Journal of Fluid Mechanics 614 (October 16, 2008): 471–93. http://dx.doi.org/10.1017/s0022112008003649.
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Liquid–liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the control parameters – capillary number, viscosity ratio and separation of scale – i.e. the slip length versus the macroscopic size of the system. The transition at a critical capillary number, from a stationary to a non-stationary interface, is studied while changing the control parameters. Comparisons with similar existing analyses for other geometries, such as the Landau–Levich problem, are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation. Sharp interface and diffuse interface models are quantitatively compared, indicating the correct limit of applicability of the diffuse interface models.
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Enright, Ryan, Marc Hodes, Todd Salamon, and Yuri Muzychka. "Isoflux Nusselt Number and Slip Length Formulae for Superhydrophobic Microchannels." Journal of Heat Transfer 136, no. 1 (October 17, 2013). http://dx.doi.org/10.1115/1.4024837.
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We analytically and numerically consider the hydrodynamic and thermal transport behavior of fully developed laminar flow through a superhydrophobic (SH) parallel-plate channel. Hydrodynamic slip length, thermal slip length and heat flux are prescribed at each surface. We first develop a general expression for the Nusselt number valid for asymmetric velocity profiles. Next, we demonstrate that, in the limit of Stokes flow near the surface and an adiabatic and shear-free liquid–gas interface, both thermal and hydrodynamic slip lengths can be found by redefining existing solutions for conduction spreading resistances. Expressions for the thermal slip length for pillar and ridge surface topographies are determined. Comparison of fundamental half-space solutions for the Laplace and Stokes equations facilitate the development of expressions for hydrodynamic slip length over pillar-structured surfaces based on existing solutions for the conduction spreading resistance from an isothermal source. Numerical validation is performed and an analysis of the idealized thermal transport behavior suggests conditions under which superhydrophobic microchannels may enhance heat transfer.
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Ramos-Alvarado, Bladimir, Satish Kumar, and G. P. Peterson. "Hydrodynamic slip length as a surface property." Physical Review E 93, no. 2 (February 1, 2016). http://dx.doi.org/10.1103/physreve.93.023101.
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Maali, A., Y. Pan, B. Bhushan, and E. Charlaix. "Hydrodynamic drag-force measurement and slip length on microstructured surfaces." Physical Review E 85, no. 6 (June 14, 2012). http://dx.doi.org/10.1103/physreve.85.066310.
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Zhu, Yingxi, and Steve Granick. "Friction and the Continuum Limit – Where is the Boundary?" MRS Proceedings 651 (2000). http://dx.doi.org/10.1557/proc-651-t4.2a.1.
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AbstractThe no-slip boundary condition, believed to describe macroscopic flow of low-viscosity fluids, overestimates hydrodynamic forces starting at lengths corresponding to hundreds of molecular dimensions when water or tetradecane is placed between smooth nonwetting surfaces whose spacing varies dynamically. When hydrodynamic pressures exceed 0.1-1 atmospheres (this occurs at spacings that depend on the rate of spacing change), flow becomes easier than expected. Therefore solid-liquid surface interactions influence not just molecularly-thin confined liquids but also flow at larger length scales. This points the way to strategies for energy-saving during fluid transport and may be relevant to filtration, colloidal dynamics, and microfluidic devices, and shows a hitherto-unappreciated dependence of slip on velocity.
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Crowdy, Darren G. "Slip length formulas for longitudinal shear flow over a superhydrophobic grating with partially filled cavities." Journal of Fluid Mechanics 925 (September 1, 2021). http://dx.doi.org/10.1017/jfm.2021.709.
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Explicit formulas are given for the hydrodynamic slip lengths associated with longitudinal shear flow over a superhydrophobic grating where the menisci have partially invaded the cavities and are only weakly curved. For flat menisci that have depinned from the top of the grating and have displaced downwards into the cavities, the axial velocity is determined analytically and the slip length extracted from it. This solution is then combined with an integral identity to determine the first-order correction to the slip length when the displaced menisci bow weakly into the cavity. It is argued that the new formulas provide useful upper bounds for quantifying slip in microchannel flows involving partially filled cavities. The new solutions are natural extensions of prior results due to Philip (Z. Angew. Math. Phys., vol. 23, 1972, pp. 353–372) for shear flow over mixed no-slip/no-shear surfaces and due to Bechert & Bartenwerfer (J. Fluid Mech., vol. 206, 1989, pp. 105–129) for shear flow over blade-shaped riblets.
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Bhattacharya, A., J. K. Dutt, and R. K. Pandey. "Influence of Hydrodynamic Journal Bearings With Multiple Slip Zones on Rotordynamic Behavior." Journal of Tribology 139, no. 6 (July 10, 2017). http://dx.doi.org/10.1115/1.4036629.
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This paper mainly reports stability investigations of rotors supported on fluid film journal bearings possessing multilocational slip-no-slip zones at the bush–film interface. The coupled solution of governing equations (Reynolds equation, energy equation, heat diffusion equation, lubricant rheological relation, and thermal boundary conditions) has been used to find pressure distributions in the lubricating film followed by evaluation of bearing coefficients. These coefficients have been used to determine stability limit speed (SLS) of the system and its robustness for both short (nearly inflexible) and long (flexible) rotors. Numerical simulations show that the pattern of pressure distribution with multiple slip-no-slip zones is similar to that obtained for multilobe bearings, resulting in substantial improvement of rotor–bearing stability irrespective of eccentricity ratio. A reduction in friction force (up to Sommerfeld number 1.8) and an increase in SLS and robustness compared to conventional bearings are observed when used with short rotors. Typically, up to six pairs of slip-no-slip zones improve SLS of the rotor–shaft system and robustness for short rotors, although more pairs deteriorate both. However, for long rotors, where dynamic rotor forces also act, these bearings provide marginal improvement in stability and robustness only for a small range of slip length.
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Joshi, Yash, and B. R. Vinoth. "Entry Lengths of Laminar Pipe and Channel Flows." Journal of Fluids Engineering 140, no. 6 (February 14, 2018). http://dx.doi.org/10.1115/1.4038668.
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Numerical simulations of laminar pipe and channel flows were carried out: (i) to understand the effect of inlet conditions, viz., flat inlet and streamtube inlet, on entry lengths, and (ii) to investigate the flow development in radial/transverse locations. Results show that hydrodynamic entry lengths from the streamtube inlet simulations are significantly lower compared to the entry lengths from the flat inlet simulations for low Reynolds numbers. Moreover, results from the current study (Newtonian flow with no-slip) as well as the results from the literature (non-Newtonian flow with no-slip) showed that for many flow situations, the slowest development of axial velocity in the transverse location happens to be very near to the wall. For the above cases, the existing entry length criteria (centerline as well as global entry length) are not appropriate to define the entry length. We have proposed a new entry length criterion based on the displacement thickness which is an integral measure of the velocity profile. A new entry length correlation using the displacement thickness criterion is proposed for Newtonian flows in pipe and channel based on simulations with the streamtube inlet condition.
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Duan, Zhipeng, and Y. S. Muzychka. "Slip Flow in the Hydrodynamic Entrance Region of Circular and Noncircular Microchannels." Journal of Fluids Engineering 132, no. 1 (December 21, 2009). http://dx.doi.org/10.1115/1.4000692.
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Microscale fluid dynamics has received intensive interest due to the emergence of micro-electro-mechanical systems (MEMS) technology. When the mean free path of the gas is comparable to the channel’s characteristic dimension, the continuum assumption is no longer valid and a velocity slip may occur at the duct walls. Noncircular cross sections are common channel shapes that can be produced by microfabrication. The noncircular microchannels have extensive practical applications in MEMS. The paper deals with issues of hydrodynamic flow development. Slip flow in the entrance of circular and parallel plate microchannels is first considered by solving a linearized momentum equation. It is found that slip flow is less sensitive to analytical linearized approximations than continuum flow and the linearization method is an accurate approximation for slip flow. Also, it is found that the entrance friction factor Reynolds product is of finite value and dependent on the Kn and tangential momentum accommodation coefficient but independent of the cross-sectional geometry. Slip flow and continuum flow in the hydrodynamic entrance of noncircular microchannels has been examined and a model is proposed to predict the friction factor and Reynolds product f Re for developing slip flow and continuum flow in most noncircular microchannels. It is shown that the complete problem may be easily analyzed by combining the asymptotic results for short and long ducts. Through the selection of a characteristic length scale, the square root of cross-sectional area, the effect of duct shape has been minimized. The proposed model has an approximate accuracy of 10% for most common duct shapes.
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Panahi, Majid, Ramin Jamali, Vahideh Farzam Rad, Mojtaba Khorasani, Ahamd Darudi, and Ali-Reza Moradi. "3D monitoring of the surface slippage effect on micro-particle sedimentation by digital holographic microscopy." Scientific Reports 11, no. 1 (June 21, 2021). http://dx.doi.org/10.1038/s41598-021-92498-0.
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AbstractIn several phenomena in biology and industry, it is required to understand the comprehensive behavior of sedimenting micro-particles in fluids. Here, we use the numerical refocusing feature of digital holographic microscopy (DHM) to investigate the slippage effect on micro-particle sedimentation near a flat wall. DHM provides quantitative phase contrast and three-dimensional (3D) imaging in arbitrary time scales, which suggests it as an elegant approach to investigate various phenomena, including dynamic behavior of colloids. 3D information is obtained by post-processing of the recorded digital holograms. Through analysis of 3D trajectories and velocities of multiple sedimenting micro-particles, we show that proximity to flat walls of higher slip lengths causes faster sedimentation. The effect depends on the ratio of the particle size to (1) the slip length and (2) its distance to the wall. We corroborate our experimental findings by a theoretical model which considers both the proximity and the particle interaction to a wall of different hydrophobicity in the hydrodynamic forces.
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Steigerwalt Lam, Lisa, Marc Hodes, Georgios Karamanis, Toby Kirk, and Scott MacLachlan. "Effect of Meniscus Curvature on Apparent Thermal Slip." Journal of Heat Transfer 138, no. 12 (August 16, 2016). http://dx.doi.org/10.1115/1.4034189.
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We analytically consider the effect of meniscus curvature on heat transfer to laminar flow across structured surfaces. The surfaces considered are composed of ridges. Curvature of the menisci, which separates liquid in the Cassie state and gas trapped in cavities between the ridges, results from the pressure difference between the liquid and the gas. A boundary perturbation approach is used to develop expressions that account for the change in the temperature field in the limit of small curvature of a meniscus. The meniscus is considered adiabatic and a constant heat flux boundary condition is prescribed at the tips of the ridges in a semi-infinite and periodic domain. A solution for a constant temperature ridge is also presented using existing results from a mathematically equivalent hydrodynamic problem. We provide approximate expressions for the apparent thermal slip length as function of solid fraction over a range of small meniscus protrusion angles. Numerical results show good agreement with the perturbation results for protrusion angles up to ± 20 deg.
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Maynes, D., and J. Crockett. "Apparent Temperature Jump and Thermal Transport in Channels With Streamwise Rib and Cavity Featured Superhydrophobic Walls at Constant Heat Flux." Journal of Heat Transfer 136, no. 1 (October 25, 2013). http://dx.doi.org/10.1115/1.4025045.
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This paper presents an analytical investigation of constant property, steady, fully developed, laminar thermal transport in a parallel-plate channel comprised of metal superhydrophobic (SH) walls. The superhydrophobic walls considered here exhibit microribs and cavities aligned in the streamwise direction. The cavities are assumed to be nonwetting and contain air, such that the Cassie–Baxter state is the interfacial state considered. The scenario considered is that of constant heat flux through the rib surfaces with negligible thermal transport through the air cavity interface. Closed form solutions for the local Nusselt number and local wall temperature are presented and are in the form of infinite series expansions. The analysis show the relative size of the cavity regions compared to the total rib and cavity width (cavity fraction) exercises significant influence on the aggregate thermal transport behavior. Further, the relative size of the rib and cavity module width compared to the channel hydraulic diameter (relative module width) also influences the Nusselt number. The spatially varying Nusselt number and wall temperature are presented as a function of the cavity fraction and the relative module width over the ranges 0–0.99 and 0.01–1.0, respectively. From these results, the rib/cavity module averaged Nusselt number was determined as a function of the governing parameters. The results reveal that increases in either the cavity fraction or relative module width lead to decreases in the average Nusselt number and results are presented over a wide range of conditions from which the average Nusselt number can be determined for heat transfer analysis. Further, analogous to the hydrodynamic slip length, a temperature jump length describing the apparent temperature jump at the wall is determined in terms of the cavity fraction. Remarkably, it is nearly identical to the hydrodynamic slip length for the scenario considered here and allows straightforward determination of the average Nusselt number for any cavity fraction and relative rib/cavity module width.
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Hodes, Marc, Toby Kirk, and Darren Crowdy. "Spreading and Contact Resistance Formulae Capturing Boundary Curvature and Contact Distribution Effects." Journal of Heat Transfer 140, no. 10 (June 11, 2018). http://dx.doi.org/10.1115/1.4039993.
Full textAbstract:
There is a substantial and growing body of literature which solves Laplace's equation governing the velocity field for a linear-shear flow of liquid in the unwetted (Cassie) state over a superhydrophobic surface. Usually, no-slip and shear-free boundary conditions are applied at liquid–solid interfaces and liquid–gas ones (menisci), respectively. When the menisci are curved, the liquid is said to flow over a “bubble mattress.” We show that the dimensionless apparent hydrodynamic slip length available from studies of such surfaces is equivalent to (i) the dimensionless spreading resistance for a flat, isothermal heat source flanked by arc-shaped adiabatic boundaries and (ii) the dimensionless thermal contact resistance between symmetric mating surfaces with flat contacts flanked by arc-shaped adiabatic boundaries. This is important because real surfaces are rough rather than smooth. Furthermore, we demonstrate that this observation provides a significant source of new and explicit results on spreading and contact resistances. Significantly, the results presented accommodate arbitrary solid-to-solid contact fraction and arc geometry in the contact resistance problem for the first time. We also provide formulae for the case when each period window includes a finite number of no-slip (or isothermal) and shear free (or adiabatic) regions and extend them to the case when the latter are weakly curved. Finally, we discuss other areas of mathematical physics to which our results are directly relevant.
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Chu, Henry C. W., and Chiu-On Ng. "Electroosmotic Flow Through a Circular Tube With Slip-Stick Striped Wall." Journal of Fluids Engineering 134, no. 11 (October 23, 2012). http://dx.doi.org/10.1115/1.4007690.
Full textAbstract:
This is an analytical study on electrohydrodynamic flows through a circular tube, of which the wall is micropatterned with a periodic array of longitudinal or transverse slip-stick stripes. One unit of the wall pattern comprises two stripes, one slipping and the other nonslipping, and each with a distinct ζ potential. Using the methods of eigenfunction expansion and point collocation, the electric potential and velocity fields are determined by solving the linearized Poisson–Boltzmann equation and the Stokes equation subject to the mixed electrohydrodynamic boundary conditions. The effective equations for the fluid and current fluxes are deduced as functions of the slipping area fraction of the wall, the intrinsic hydrodynamic slip length, the Debye parameter, and the ζ potentials. The theoretical limits for some particular wall patterns, which are available in the literature only for plane channels, are extended in this paper to the case of a circular channel. We confirm that some remarks made earlier for electroosmotic flow over a plane surface are also applicable to the present problem involving patterns on a circular surface. We pay particular attention to the effects of the pattern pitch on the flow in both the longitudinal and transverse configurations. When the wall is uniformly charged, the adverse effect on the electroosmotic flow enhancement due to a small fraction of area being covered by no-slip slots can be amplified if the pitch decreases. Reducing the pitch will also lead to a greater deviation from the Helmholtz–Smoluchowski limit when the slipping regions are uncharged. With oppositely charged slipping regions, local recirculation or a net reversed flow is possible, even when the wall is on the average electropositive or neutral. The flow morphology is found to be subject to the combined influence of the geometry of the tube and the electrohydrodynamic properties of the wall.