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Journal articles on the topic 'Hele-Shaw Cell'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Bhadauria, B. S., Anish Kumar, Awanish Kumar, and S. N. Rai. "The Combined Effect of Gravity Modulation and Throughflow on Thermal Instability in the Hele-Shaw Cell Filled with Oldroyd-B Nanofluid." Journal of Nanofluids 12, no. 7 (2023): 1681–97. http://dx.doi.org/10.1166/jon.2023.2049.

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This paper shows the combined effect of throughflow and gravity modulation on the stability of Oldroyd-B nanofluid filled in Hele-Shaw cell. Nanofluid compared to the base fluid has higher thermal conduction. The thermal conductivity of nanofluid increased and thus increases the amount of energy transferred. The Oldroyd-B fluid model is important because of its numerous applications such as production of plastic sheet and extrusion of polymers through a slit die in polymer industry, biological solution pant tars glues, etc. In linear stability analysis, we found the expression of the critical

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2

Yadav, Dhananjay. "The effect of pulsating throughflow on the onset of magneto convection in a layer of nanofluid confined within a Hele-Shaw cell." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 233, no. 5 (2019): 1074–85. http://dx.doi.org/10.1177/0954408919836362.

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In this article, the joint effect of pulsating throughflow and magnetic field on the onset of convective instability in a nanofluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory and frozen profile approach. The model utilized for nanofluid combines the impacts of Brownian motion and thermophoresis, while for Hele-Shaw cell, Hele-Shaw model is considered. The Galerkin technique is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability framework is examined analytically. It is observed that the pulsating

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3

LU, H. W., K. GLASNER, A. L. BERTOZZI, and C. J. KIM. "A diffuse-interface model for electrowetting drops in a Hele-Shaw cell." Journal of Fluid Mechanics 590 (October 15, 2007): 411–35. http://dx.doi.org/10.1017/s0022112007008154.

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Electrowetting has recently been explored as a mechanism for moving small amounts of fluids in confined spaces. We propose a diffuse-interface model for drop motion, due to electrowetting, in a Hele-Shaw geometry. In the limit of small interface thickness, asymptotic analysis shows that the model is equivalent to Hele-Shaw flow with a voltage-modified Young–Laplace boundary condition on the free surface. We show that details of the contact angle significantly affect the time scale of motion in the model. We measure receding and advancing contact angles in the experiments and derive their influ

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4

Kumar, Awanish, and B. S. Bhadauria. "Effect of Magnetic Field on the Instability of Jeffrey Nanofluid (CuO + Blood and Cu + Blood) Filled in Hele-Shaw Cell with Rotation." Journal of Nanofluids 12, no. 8 (2023): 2203–17. http://dx.doi.org/10.1166/jon.2023.2083.

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There are so many works present in the literature with Hele-Shaw cell, Jeffrey nanofluid, magnetic field, and rotation individually, but here we carried out the combined study of these and it is important because there are so many applications of these in engineering, it may be used in energy absorption in the solar panel, because of Hele-Shaw cell is approximately similar to the solar panel. The main goal of the article is to analyse the instability of Jeffrey nanofluid filled in Hele-Shaw cell in the presence of the magnetic field and rotation. During the investigation, we obtained that the

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5

BALSA, THOMAS F. "Secondary flow in a Hele-Shaw cell." Journal of Fluid Mechanics 372 (October 10, 1998): 25–44. http://dx.doi.org/10.1017/s0022112098002171.

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We examine the flow in a horizontal Hele-Shaw cell in which the undisturbed unidirectional flow at infinity is required to stream around a vertical cylinder spanning the gap between the two (horizontal) plates of the cell. A combination of matched asymptotic expansions and numerical methods is employed to elucidate the structure of the boundary layer near the surface of the cylinder. The two length scales of the problem are the gap, h, and the length of the body, l; it is assumed that h/l<<1. The characteristic Reynolds number based on l is O(1). The length scales associated with the bou

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6

ENTOV, VLADIMIR M., and PAVEL I. ETINGOF. "Viscous flows with time-dependent free boundaries in a non-planar Hele–Shaw cell." European Journal of Applied Mathematics 8, no. 1 (1997): 23–35. http://dx.doi.org/10.1017/s0956792596002938.

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The dynamics of blobs of viscous fluid in a non-planar Hele–Shaw cell is considered. The general approach developed by Richardson and some of the resulting analytic techniques are extended to flows in non-planar cells, including cells shaped as surfaces of revolution and helical surfaces. An example related to the development and coalescence of two initially separated blobs in a cell on a spherical surface is presented. Some applications to mathematically equivalent problems dealing with planar Hele–Shaw cells with a non-uniform gap and flows through porous media are also discussed.

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7

FERNANDEZ, J., P. KUROWSKI, P. PETITJEANS, and E. MEIBURG. "Density-driven unstable flows of miscible fluids in a Hele-Shaw cell." Journal of Fluid Mechanics 451 (January 25, 2002): 239–60. http://dx.doi.org/10.1017/s0022112001006504.

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Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are investigated by means of experimental measurements, as well as two- and three-dimensional numerical simulations. The experiments focus on the early stages of the instability growth, and they provide detailed information regarding the growth rates and most amplified wavenumbers as a function of the governing Rayleigh number Ra. They identify two clearly distinct parameter regimes: a low-Ra, ‘Hele-Shaw’ regime in which the dominant wavelength scales as Ra−1, and a high-Ra ‘gap’ regime in which the length scale

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8

Paşa, Gelu. "Some models for immiscible displacements in Hele-Shaw cells." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 2 (2018): 193–207. http://dx.doi.org/10.2478/auom-2018-0025.

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Abstract We study the linear stability of the immiscible displacement of some fluids in 2D and 3D Hele-Shaw cell. We give a method for avoiding the singularities phenomenons which appears in previous papers. In the case of a non - Newtonian fluid displaced by air in a 3D Hele-Shaw cell, we give a growth constant σ of perturbations, which contains two new terms compared with the Saffman-Taylor formula. Our σ has a very high growth as a parameter appearing in the constitutive relations approaches a critical value.

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9

GRAF, F., E. MEIBURG, and C. HÄRTEL. "Density-driven instabilities of miscible fluids in a Hele-Shaw cell: linear stability analysis of the three-dimensional Stokes equations." Journal of Fluid Mechanics 451 (January 25, 2002): 261–82. http://dx.doi.org/10.1017/s0022112001006516.

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We consider the situation of a heavier fluid placed above a lighter one in a vertically arranged Hele-Shaw cell. The two fluids are miscible in all proportions. For this configuration, experiments and nonlinear simulations recently reported by Fernandez et al. (2002) indicate the existence of a low-Rayleigh-number (Ra) ‘Hele-Shaw’ instability mode, along with a high-Ra ‘gap’ mode whose dominant wavelength is on the order of five times the gap width. These findings are in disagreement with linear stability results based on the gap-averaged Hele-Shaw approach, which predict much smaller waveleng

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10

CEBERS, A. "HEXAGON-STRIPE TRANSITION AT THE MAGNETIC FIELD INDUCED PHASE TRANSFORMATIONS OF THE MAGNETORHEOLOGICAL SUSPENSIONS." International Journal of Modern Physics B 16, no. 17n18 (2002): 2345–51. http://dx.doi.org/10.1142/s0217979202012347.

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The phase diagram of the magnetorheological suspension allowing for the modulated phases in the Hele-Shaw cell under the action of the normal field is calculated. The phase boundaries between the stripe, the hexagonal and the unmodulated phases in dependence on the layer thickness and the magnetic field strength are found. The existence of the transitions between the stripe and the hexagonal phases at the corresponding variation of the physical parameters is illustrated by the numerical simulation of the concentration dynamics in the Hele-Shaw cell. It is remarked that those transitions in the

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11

Morrow, Liam C., Timothy J. Moroney, Michael C. Dallaston, and Scott W. McCue. "A review of one-phase Hele-Shaw flows and a level-set method for nonstandard configurations." ANZIAM Journal 63 (November 16, 2021): 269–307. http://dx.doi.org/10.21914/anziamj.v63.16689.

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The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law. In a standard configuration with the Hele-Shaw cell made up of two flat stationary plates, the pressure is harmonic. Therefore, conformal mapping techniques and boundary integral methods can be readily applied to study the key interfacial dynamics, including the Saffman–Taylor instability and viscous fingering patterns. As well as providing a brief review of these key issues, we present a flexible numerical

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12

Rauseo, Steven N. "Fingering in a driven Hele-Shaw cell." Physical Review E 62, no. 6 (2000): 8058–63. http://dx.doi.org/10.1103/physreve.62.8058.

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13

Alimov, M. M. "Bubble growth in a Hele-Shaw cell." Fluid Dynamics 42, no. 2 (2007): 268–81. http://dx.doi.org/10.1134/s0015462807020111.

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14

Kopf‐Sill, Anne R., and G. M. Homsy. "Narrow fingers in a Hele–Shaw cell." Physics of Fluids 30, no. 9 (1987): 2607–9. http://dx.doi.org/10.1063/1.866102.

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15

Kopf‐Sill, Anne R., and G. M. Homsy. "Bubble motion in a Hele–Shaw cell." Physics of Fluids 31, no. 1 (1988): 18–26. http://dx.doi.org/10.1063/1.866566.

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16

Li, Jing, Xiaochen Li, Kaijie Chen, Bin Xie, and Shijun Liao. "Faraday waves in a Hele-Shaw cell." Physics of Fluids 30, no. 4 (2018): 042106. http://dx.doi.org/10.1063/1.5022424.

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17

Carrillo, Ll, F. X. Magdaleno, J. Casademunt, and J. Ortín. "Experiments in a rotating Hele-Shaw cell." Physical Review E 54, no. 6 (1996): 6260–67. http://dx.doi.org/10.1103/physreve.54.6260.

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18

BOOS, W., and A. THESS. "Thermocapillary flow in a Hele-Shaw cell." Journal of Fluid Mechanics 352 (December 10, 1997): 305–30. http://dx.doi.org/10.1017/s0022112097007477.

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We formulate a simple theoretical model that permits one to investigate surface-tension-driven flows with complex interface geometry. The model consists of a Hele-Shaw cell filled with two different fluids and subjected to a unidirectional temperature gradient. The shape of the interface that separates the fluids can be arbitrarily complex. If the contact line is pinned, i.e. unable to move, the problem of calculating the flow in both fluids is governed by a linear set of equations containing the characteristic aspect ratio and the viscosity ratio as the only input parameters. Analytical solut

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19

Vorontsov, S. S., A. V. Gorin, V. Ye Nakoryakov, A. G. Khoruzhenko, and V. M. Chupin. "Natural convection in a Hele-Shaw cell." International Journal of Heat and Mass Transfer 34, no. 3 (1991): 703–9. http://dx.doi.org/10.1016/0017-9310(91)90118-x.

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20

Shinozaki, Aritomo, and Yoshitsugu Oono. "Spinodal decomposition in a Hele-Shaw cell." Physical Review A 45, no. 4 (1992): R2161—R2164. http://dx.doi.org/10.1103/physreva.45.r2161.

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21

Vasconcelos, Giovani L. "Multiple bubbles in a Hele-Shaw cell." Physical Review E 50, no. 5 (1994): R3306—R3309. http://dx.doi.org/10.1103/physreve.50.r3306.

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22

Hu, Howard H., and Daniel D. Joseph. "Miscible displacement in a Hele-Shaw cell." ZAMP Zeitschrift f�r angewandte Mathematik und Physik 43, no. 4 (1992): 626–44. http://dx.doi.org/10.1007/bf00946254.

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23

Zeybek, M., and Y. C. Yortsos. "Parallel flow in Hele-Shaw cells." Journal of Fluid Mechanics 241 (August 1992): 421–42. http://dx.doi.org/10.1017/s0022112092002106.

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We consider the parallel flow of two immiscible fluids in a Hele-Shaw cell. The evolution of disturbances on the fluid interfaces is studied both theoretically and experimentally in the large-capillary-number limit. It is shown that such interfaces support wave motion, the amplitude of which for long waves is governed by a set of KdV and Airy equations. The waves are dispersive provided that the fluids have unequal viscosities and that the space occupied by the inner fluid does not pertain to the Saffman-Taylor conditions (symmetric interfaces with half-width spacing). Experiments conducted in

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24

Morrow, Liam C., Timothy J. Moroney, and Scott W. McCue. "Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations." Journal of Fluid Mechanics 877 (September 2, 2019): 1063–97. http://dx.doi.org/10.1017/jfm.2019.623.

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Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been devoted to devising strategies for controlling such patterns and reducing the growth of the interfacial fingers. We continue this research by reporting on numerical simulations, based on the level set method, of a generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is altered. First, we investigate how imposing constant and time-dependent

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25

Bere, Katalin Viktória, Emilie Nez, Edina Balog, et al. "Enhancing the yield of calcium carbonate precipitation by obstacles in laminar flow in a confined geometry." Physical Chemistry Chemical Physics 23, no. 29 (2021): 15515–21. http://dx.doi.org/10.1039/d1cp01334c.

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26

Inoue, Kai, and Susumu Inasawa. "Drying-induced back flow of colloidal suspensions confined in thin unidirectional drying cells." RSC Advances 10, no. 27 (2020): 15763–68. http://dx.doi.org/10.1039/d0ra02837a.

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27

Holubova, Renata. "Non-Newtonian fluids, viscosity and fractal dimensions." South Florida Journal of Development 5, no. 12 (2024): e4850. https://doi.org/10.46932/sfjdv5n12-068.

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The aim of the paper is to propose a laboratory task for high school students, which would enable them to investigate the properties of non-Newtonian fluids. The key problem is that the concept of viscosity which is important to characterize non-Newtonian fluids, is not part of the high school curricula. Basic information about the idea of viscosity is presented. Viscosity was measured using the Höppler viscometer. The following liquids were measured: flower honey, shower gel, soap, paint color, engine oil, propylene glycol, oil, and solution propylene glycol. The outcomes of our measurement o

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28

ALEXANDROU, ANDREAS N., and VLADIMIR ENTOV. "On the steady-state advancement of fingers and bubbles in a Hele–Shaw cell filled by a non-Newtonian fluid." European Journal of Applied Mathematics 8, no. 1 (1997): 73–87. http://dx.doi.org/10.1017/s0956792596002963.

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The problem of steady-state propagation of a finger or a bubble of inviscid fluid through a Hele–Shaw cell filled by a viscous non-Newtonian, including visco-plastic (Bingham) fluid is addressed. Only flows symmetric relative to the cell axis are considered. It is shown that, using a hodograph transform, this non-linear free boundary problem can be reduced to the solution of an elliptic system of linear partial differential equations in a fixed domain with part of the boundary being curvilinear. The resulting boundary-value problem is solved numerically using the Finite Element Method. Finger

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29

Xie, Xuming, and Sahar Almashaan. "Exact solutions to interfacial flows with kinetic undercooling in a Hele-Shaw cell of time-dependent gap." Malaya Journal of Matematik 11, S (2023): 27–42. http://dx.doi.org/10.26637/mjm11s/002.

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Hele-Shaw cells where the top plate is moving uniformly at a prescribed speed and the bottom plate is fixed have been used to study interface related problems. This paper focuses on interfacial flows with linear and nonlinear kinetic undercooling regularization in a radial Hele-Shaw cell with a time dependent gap. We obtain some exact solutions of the moving boundary problems when the initial shape is a circle, an ellipse or an annular domain. For the nonlinear case, a linear stability analysis is also presented for the circular solutions. The methodology is to use complex analysis and PDE the

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30

Entov, V. M., P. I. Etingof, and D. Ya Kleinbock. "On nonlinear interface dynamics in Hele-Shaw flows." European Journal of Applied Mathematics 6, no. 5 (1995): 399–420. http://dx.doi.org/10.1017/s0956792500001959.

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Flows with free boundaries in a Hele-Shaw cell provide a unique opportunity to study non-linear boundary dynamics using rigorous analytic approaches. While of limited direct ‘practical value’, these studies give rise to a plethora of new phenomena and insights which may serve as beacons in the turbulent ocean of moving free boundaries and pattern forming. This paper gives a brief summary of the authors' studies of Hele-Shaw flows with free boundaries and some related problems based upon Richardson's approach. Some promising directions of further research are also discussed.

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31

Kessler, Michael, Hervé Elettro, Isabelle Heimgartner, et al. "Everything in its right place: controlling the local composition of hydrogels using microfluidic traps." Lab on a Chip 20, no. 24 (2020): 4572–81. http://dx.doi.org/10.1039/d0lc00691b.

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32

Li, Jing, Xiaochen Li, and Shijun Liao. "Stability and hysteresis of Faraday waves in Hele-Shaw cells." Journal of Fluid Mechanics 871 (May 24, 2019): 694–716. http://dx.doi.org/10.1017/jfm.2019.335.

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The instability of Faraday waves in Hele-Shaw cells is investigated experimentally and theoretically. A novel hydrodynamic model involving capillary action is proposed to capture the variation of the dynamic contact line between two close walls of narrow containers. The amplitude equations are derived from the gap-averaged model. By means of Lyapunov’s first method, a good prediction of the onset threshold of forcing acceleration is obtained, which shows the model’s validity for addressing the stability problem for Faraday waves in Hele-Shaw cells. It is found that the effect of the dynamic co

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33

Saffman, P. G. "Viscous fingering in Hele-Shaw cells." Journal of Fluid Mechanics 173 (December 1986): 73–94. http://dx.doi.org/10.1017/s0022112086001088.

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The phenomenon of interfacial motion between two immiscible viscous fluids in the narrow gap between two parallel plates (Hele-Shaw cell) is considered. This flow is currently of interest because of its relation to pattern selection mechanisms and the formation of fractal, structures in a number of physical applications. Attention is concentrated on the fingers that result from the instability when a less-viscous fluid drives a more-viscous one. The status of the problem is reviewed and progress with the thirty-year-old problem of explaining the shape and stability of the fingers is described.

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34

Plouraboué, F., and E. J. Hinch. "Kelvin–Helmholtz instability in a Hele-Shaw cell." Physics of Fluids 14, no. 3 (2002): 922–29. http://dx.doi.org/10.1063/1.1446884.

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35

Tanveer, S., and P. G. Saffman. "Stability of bubbles in a Hele–Shaw cell." Physics of Fluids 30, no. 9 (1987): 2624–35. http://dx.doi.org/10.1063/1.866106.

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36

Sarkar, Subir K., and David Jasnow. "Viscous fingering in an anisotropic Hele-Shaw cell." Physical Review A 39, no. 10 (1989): 5299–307. http://dx.doi.org/10.1103/physreva.39.5299.

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37

Gavrilov, K. A., V. A. Demin, and G. F. Putin. "Convective coherent structures in a Hele-Shaw cell." Technical Physics Letters 36, no. 2 (2010): 181–84. http://dx.doi.org/10.1134/s1063785010020264.

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38

Kabiraj, Subrata K., and Sujata Tarafdar. "Finger velocities in the lifting Hele–Shaw cell." Physica A: Statistical Mechanics and its Applications 328, no. 3-4 (2003): 305–14. http://dx.doi.org/10.1016/s0378-4371(03)00523-5.

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39

Miranda, José A. "Magnetic fluid in a rotating Hele–Shaw cell." Journal of Magnetism and Magnetic Materials 226-230 (May 2001): 1278–80. http://dx.doi.org/10.1016/s0304-8853(00)00829-5.

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40

Bhadauria, B. S., P. K. Bhatia, and Lokenath Debnath. "Convection in Hele–Shaw cell with parametric excitation." International Journal of Non-Linear Mechanics 40, no. 4 (2005): 475–84. http://dx.doi.org/10.1016/j.ijnonlinmec.2004.07.010.

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41

Waters, S. L., and L. J. Cummings. "Coriolis effects in a rotating Hele-Shaw cell." Physics of Fluids 17, no. 4 (2005): 048101. http://dx.doi.org/10.1063/1.1861752.

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42

Crowdy, Darren. "Multiple steady bubbles in a Hele-Shaw cell." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2102 (2008): 421–35. http://dx.doi.org/10.1098/rspa.2008.0252.

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This paper presents new solutions, in analytical form, for the shapes of an assembly of steady co-travelling bubbles in a Hele-Shaw cell. The associated velocity field is also derived. The assembly can consist of any finite number of bubbles. The solutions are expressed in terms of Schottky–Klein prime functions and are derived by exploiting results on multiply connected conformal slit mappings.

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43

Poon, Marilyn, Jessica Todd, Robert Neilson, Dustin Grace, and Jean Hertzberg. "Saffman—Taylor Instability in a Hele‐Shaw Cell." Physics of Fluids 16, no. 9 (2004): S9. http://dx.doi.org/10.1063/1.1763924.

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44

Slim, Anja C., M. M. Bandi, Joel C. Miller, and L. Mahadevan. "Dissolution-driven convection in a Hele–Shaw cell." Physics of Fluids 25, no. 2 (2013): 024101. http://dx.doi.org/10.1063/1.4790511.

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45

Hashimoto, Michinao, Piotr Garstecki, Howard A. Stone, and George M. Whitesides. "Interfacial instabilities in a microfluidic Hele-Shaw cell." Soft Matter 4, no. 7 (2008): 1403. http://dx.doi.org/10.1039/b715867j.

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46

McCloud, K. V., and J. V. Maher. "Pattern selection in an anisotropic Hele-Shaw cell." Physical Review E 51, no. 2 (1995): 1184–90. http://dx.doi.org/10.1103/physreve.51.1184.

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47

Lagrée, P. Y. "Interactive boundary layer in a Hele Shaw cell." ZAMM 87, no. 7 (2007): 486–98. http://dx.doi.org/10.1002/zamm.200610331.

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48

Chesnokov, Alexander, and Valery Liapidevskii. "Viscosity-stratified flow in a Hele–Shaw cell." International Journal of Non-Linear Mechanics 89 (March 2017): 168–76. http://dx.doi.org/10.1016/j.ijnonlinmec.2016.12.016.

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49

Anjos, Pedro H. A., and José A. Miranda. "Influence of wetting on fingering patterns in lifting Hele-Shaw flows." Soft Matter 10, no. 38 (2014): 7459–67. http://dx.doi.org/10.1039/c4sm01047g.

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50

Kashevsky, B. E., A. M. Zholud, and S. B. Kashevsky. "Hydrodynamic instability in a magnetically driven suspension of paramagnetic red blood cells." Soft Matter 11, no. 33 (2015): 6547–51. http://dx.doi.org/10.1039/c5sm01311a.

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