Academic literature on the topic 'Tensor driven diffusion'

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Journal articles on the topic "Tensor driven diffusion"

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Cover, Giovana, Mariana Pereira, Mariana Bento, Simone Appenzeller, and Leticia Rittner. "Data-Driven Corpus Callosum Parcellation Method Through Diffusion Tensor Imaging." IEEE Access 5 (2017): 22421–32. http://dx.doi.org/10.1109/access.2017.2761701.

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Kallehauge, Jesper Foldsted, Trine Lignell Guldberg, Anja Harbøll, Morten Bjørn Jensen, and Slávka Lukacova. "RTHP-09. DIFFUSION TENSOR IMAGING DRIVEN GROWTH MODELING FOR TARGET DEFINITION IN GLIOBLASTOMA." Neuro-Oncology 19, suppl_6 (November 2017): vi221. http://dx.doi.org/10.1093/neuonc/nox168.894.

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Jensen, Morten B., Trine L. Guldberg, Anja Harbøll, Slávka Lukacova, and Jesper F. Kallehauge. "Diffusion tensor magnetic resonance imaging driven growth modeling for radiotherapy target definition in glioblastoma." Acta Oncologica 56, no. 11 (September 12, 2017): 1639–43. http://dx.doi.org/10.1080/0284186x.2017.1374559.

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Drblíková, Olga, Angela Handlovičová, and Karol Mikula. "Error estimates of the finite volume scheme for the nonlinear tensor-driven anisotropic diffusion." Applied Numerical Mathematics 59, no. 10 (October 2009): 2548–70. http://dx.doi.org/10.1016/j.apnum.2009.05.010.

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Jia, Xiao-xiong, Yang Yu, Xiao-dong Wang, Hui Ma, Qing-hua Zhang, Xue-yin Huang, and He-chun Xia. "fMRI-Driven DTT Assessment of Corticospinal Tracts Prior to Cortex Resection." Canadian Journal of Neurological Sciences / Journal Canadien des Sciences Neurologiques 40, no. 4 (July 2013): 558–63. http://dx.doi.org/10.1017/s0317167100014669.

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Abstract:Background:The role of diffusion tensor tractography (DTT) has become increasingly important in the preoperative mapping of brain white matter. Recently, functional magnetic resonance imaging (fMRI) driven DTT has provided the ability to evaluate the spatial relationship between the corticospinal tract (CST) and motor resection tumor boundaries. The main objective of this study was improvement of the preoperative assessment of the CST in patients with gliomas involving the motor cortical areas.Methods:Seventeen patients with gliomas involving motor cortical areas underwent 3 dimensions (3D) T1-weighted imaging for anatomical referencing, using both fMRI and diffusion tensor imaging (DTI). We used the fast-marching tractography (FMT) algorithm to define the 3D connectivity maps within the whole brain using seed points selected in the white matter adjacent to the location of fMRI activation. The target region of interest (ROI) was placed in the cerebral peduncle. Karnofsky performance status (KPS) scores were evaluated for each patient before and after surgery.Results:The CST of a total seventeen patients were successfully tracked by choosing seed and target ROI on the path of the fibers. What is more, DTT can indicate preoperatively the possibility for total glioma removal or the maximum extent of surgical resection. The postoperative average KPS score for the seventeen patients enrolled increased by more than 10 points.Conclusions:Incorporation of fMRI driven DTT showed a maximum benefit in surgical treatment of gliomas. Our study of the assessment precision should enhance the accuracy of glioma operations with a resulting improvement in postoperative patient outcome.
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Kim, Jeongchul, Youngkyoo Jung, Richard Barcus, Jocelyne H. Bachevalier, Mar M. Sanchez, Michael A. Nader, and Christopher T. Whitlow. "Rhesus Macaque Brain Developmental Trajectory: A Longitudinal Analysis Using Tensor-Based Structural Morphometry and Diffusion Tensor Imaging." Cerebral Cortex 30, no. 8 (April 2, 2020): 4325–35. http://dx.doi.org/10.1093/cercor/bhaa015.

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Abstract The typical developmental trajectory of brain structure among nonhuman primates (NHPs) remains poorly understood. In this study, we characterized the normative trajectory of developmental change among a cohort of rhesus monkeys (n = 28), ranging in age from 2 to 22 months, using structural MRI datasets that were longitudinally acquired every 3–4 months. We hypothesized that NHP-specific transient intracranial volume decreases reported during late infancy would be part of the typical developmental process, which is driven by volumetric contraction of gray matter in primary functional areas. To this end, we performed multiscale analyses from the whole brain to voxel level, characterizing regional heterogeneity, hemispheric asymmetry, and sexual dimorphism in developmental patterns. The longitudinal trajectory of brain development was explained by three different regional volumetric growth patterns (exponentially decreasing, undulating, and linearly increasing), which resulted in developmental brain volume curves with transient brain volumetric decreases. White matter (WM) fractional anisotropy increased with age, corresponding to WM volume increases, while mean diffusivity (MD) showed biphasic patterns. The longitudinal trajectory of brain development in young rhesus monkeys follows typical maturation patterns seen in humans, but regional volumetric and MD changes are more dynamic in rhesus monkeys compared with humans, with marked decreases followed by “rebound-like” increases.
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Engelbrecht, N. Eugene. "On the Effects of Pickup Ion-driven Waves on the Diffusion Tensor of Low-energy Electrons in the Heliosphere." Astrophysical Journal 849, no. 1 (October 26, 2017): L15. http://dx.doi.org/10.3847/2041-8213/aa9372.

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Hoh, N. J., and R. N. Zia. "Force-induced diffusion in suspensions of hydrodynamically interacting colloids." Journal of Fluid Mechanics 795 (April 20, 2016): 739–83. http://dx.doi.org/10.1017/jfm.2016.209.

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We study the influence of hydrodynamic, thermodynamic and interparticle forces on the diffusive motion of a Brownian probe driven by a constant external force through a dilute colloidal dispersion. The influence of these microscopic forces on equilibrium self-diffusivity (passive microrheology) is well known: all three act to hinder the short- and long-time self-diffusion. Here, via pair-Smoluchowski theory, we explore their influence on self-diffusion in a flowing suspension, where particles and fluid have been set into motion by an externally forced probe (active microrheology), giving rise to non-equilibrium flow-induced diffusion. The probe’s motion entrains background particles as it travels through the bath, deforming the equilibrium suspension microstructure. The shape and extent of microstructural distortion is set by the relative strength of the external force $F^{\mathit{ext}}$ to the entropic restoring force $kT/a_{\mathit{th}}$ of the bath particles, defining a Péclet number $\mathit{Pe}\equiv F^{\mathit{ext}}/(2kT/a_{\mathit{th}})$; and also by the strength of hydrodynamic interactions, set by the range of interparticle repulsion ${\it\kappa}=(a_{\mathit{th}}-a)/a$, where $kT$ is the thermal energy and $a_{\mathit{th}}$ and $a$ are the thermodynamic and hydrodynamic sizes of the particles, respectively. We find that in the presence of flow, the same forces that hinder equilibrium diffusion now enhance it, with diffusive anisotropy set by the range of interparticle repulsion ${\it\kappa}$. A transition from hindered to enhanced diffusion occurs when diffusive and advective forces balance, $\mathit{Pe}\sim 1$, where the exact value is a sensitive function of the strength of hydrodynamics, ${\it\kappa}$. We find that the hindered to enhanced transition straddles two transport regimes: in hindered diffusion, stochastic forces in the presence of other bath particles produce deterministic displacements (Brownian drift) at the expense of a maximal random walk. In enhanced diffusion, driving the probe with a deterministic force through an initially random suspension leads to fluctuations in the duration of probe–bath particle entrainment, giving rise to enhanced, flow-induced diffusion. The force-induced diffusion is anisotropic for all $\mathit{Pe}$, scaling as $D\sim \mathit{Pe}^{2}$ in all directions for weak forcing, regardless of the strength of hydrodynamic interactions. When probe forcing is strong, $D\sim \mathit{Pe}$ in all directions in the absence of hydrodynamic interactions, but the picture changes qualitatively as hydrodynamic interactions grow strong. In this nonlinear regime, microstructural asymmetry weakens while the anisotropy of the force-induced diffusion tensor increases dramatically. This behaviour owes its origins to the approach toward Stokes flow reversibility, where diffusion along the direction of probe force scales advectively while transverse diffusion must vanish.
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Koch, Donald L., and John F. Brady. "Dispersion in fixed beds." Journal of Fluid Mechanics 154 (May 1985): 399–427. http://dx.doi.org/10.1017/s0022112085001598.

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A macroscopic equation of mass conservation is obtained by ensemble-averaging the basic conservation laws in a porous medium. In the long-time limit this ‘macro-transport’ equation takes the form of a macroscopic Fick's law with a constant effective diffusivity tensor. An asymptotic analysis in low volume fraction of the effective diffusivity in a bed of fixed spheres is carried out for all values of the Péclet number ℙ = Ua/Df, where U is the average velocity through the bed. a is the particle radius and Df is the molecular diffusivity of the solute in the fluid. Several physical mechanisms causing dispersion are revealed by this analysis. The stochastic velocity fluctuations induced in the fluid by the randomly positioned bed particles give rise to a convectively driven contribution to dispersion. At high Péclet numbers, this convective dispersion mechanism is purely mechanical, and the resulting effective diffusivities are independent of molecular diffusion and grow linearly with ℙ. The region of zero velocity in and near the bed particles gives rise to non-mechanical dispersion mechanisms that dominate the longitudinal diffusivity at very high Péclet numbers. One such mechanism involves the retention of the diffusing species in permeable particles, from which it can escape only by molecular diffusion, leading to a diffusion coefficient that grows as ℙ2. Even if the bed particles are impermeable, non-mechanical contributions that grow as ℙ ln ℙ and ℙ2 at high ℙ arise from a diffusive boundary layer near the solid surfaces and from regions of closed streamlines respectively. The results for the longitudinal and transverse effective diffusivities as functions of the Péclet number are summarized in tabular form in §6. Because the same physical mechanisms promote dispersion in dilute and dense fixed beds, the predicted Péclet-number dependences of the effective diffusivities are applicable to all porous media. The theoretical predictions are compared with experiments in densely packed beds of impermeable particles, and the agreement is shown to be remarkably good.
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Emsell, L., C. Chaddock, N. Forde, W. Van Hecke, G. J. Barker, A. Leemans, S. Sunaert, et al. "White matter microstructural abnormalities in families multiply affected with bipolar I disorder: a diffusion tensor tractography study." Psychological Medicine 44, no. 10 (November 26, 2013): 2139–50. http://dx.doi.org/10.1017/s0033291713002845.

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BackgroundWhite matter (WM) abnormalities are proposed as potential endophenotypic markers of bipolar disorder (BD). In a diffusion tensor imaging (DTI) voxel-based analysis (VBA) study of families multiply affected with BD, we previously reported that widespread abnormalities of fractional anisotropy (FA) are associated with both BD and genetic liability for illness. In the present study, we further investigated the endophenotypic potential of WM abnormalities by applying DTI tractography to specifically investigate tracts implicated in the pathophysiology of BD.MethodDiffusion magnetic resonance imaging (MRI) data were acquired from 19 patients with BD type I from multiply affected families, 21 of their unaffected first-degree relatives and 18 healthy volunteers. DTI tractography was used to identify the cingulum, uncinate fasciculus (UF), arcuate portion of the superior longitudinal fasciculus (SLF), inferior longitudinal fasciculus (ILF), corpus callosum, and the anterior limb of the internal capsule (ALIC). Regression analyses were conducted to investigate the effect of participant group and genetic liability on FA and radial diffusivity (RD) in each tract.ResultsWe detected a significant effect of group on both FA and RD in the cingulum, SLF, callosal splenium and ILF driven by reduced FA and increased RD in patients compared to controls and relatives. Increasing genetic liability was associated with decreased FA and increased RD in the UF, and decreased FA in the SLF, among patients.ConclusionsWM microstructural abnormalities in limbic, temporal and callosal pathways represent microstructural abnormalities associated with BD whereas alterations in the SLF and UF may represent potential markers of endophenotypic risk.
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Dissertations / Theses on the topic "Tensor driven diffusion"

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Larsson, Karl. "Scale-Space Methods as a Means of Fingerprint Image Enhancement." Thesis, Linköping University, Department of Science and Technology, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2282.

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The usage of automatic fingerprint identification systems as a means of identification and/or verification have increased substantially during the last couple of years. It is well known that small deviations may occur within a fingerprint over time, a problem referred to as template ageing. This problem, and other reasons for deviations between two images of the same fingerprint, complicates the identification/verification process, since distinct features may appear somewhat different in the two images that are matched. Commonly used to try and minimise this type of problem are different kinds of fingerprint image enhancement algorithms. This thesis tests different methods within the scale-space framework and evaluate their performance as fingerprint image enhancement methods.

The methods tested within this thesis ranges from linear scale-space filtering, where no prior information about the images is known, to scalar and tensor driven diffusion where analysis of the images precedes and controls the diffusion process.

The linear scale-space approach is shown to improve correlation values, which was anticipated since the image structure is flattened at coarser scales. There is however no increase in the number of accurate matches, since inaccurate features also tends to get higher correlation value at large scales.

The nonlinear isotropic scale-space (scalar dependent diffusion), or the edge- preservation, approach is proven to be an ill fit method for fingerprint image enhancement. This is due to the fact that the analysis of edges may be unreliable, since edge structure is often distorted in fingerprints affected by the template ageing problem.

The nonlinear anisotropic scale-space (tensor dependent diffusion), or coherence-enhancing, method does not give any overall improvements of the number of accurate matches. It is however shown that for a certain type of template ageing problem, where the deviating structure does not significantly affect the ridge orientation, the nonlinear anisotropic diffusion is able to accurately match correlation pairs that resulted in a false match before they were enhanced.

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Book chapters on the topic "Tensor driven diffusion"

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Welk, Martin, Joachim Weickert, and Gabriele Steidl. "From Tensor-Driven Diffusion to Anisotropic Wavelet Shrinkage." In Computer Vision – ECCV 2006, 391–403. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11744023_31.

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Grigorescu, Irina, Alena Uus, Daan Christiaens, Lucilio Cordero-Grande, Jana Hutter, A. David Edwards, Joseph V. Hajnal, Marc Modat, and Maria Deprez. "Diffusion Tensor Driven Image Registration: A Deep Learning Approach." In Biomedical Image Registration, 131–40. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50120-4_13.

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Peter, Pascal, Joachim Weickert, Axel Munk, Tatyana Krivobokova, and Housen Li. "Justifying Tensor-Driven Diffusion from Structure-Adaptive Statistics of Natural Images." In Lecture Notes in Computer Science, 263–77. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14612-6_20.

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Jerome, Neil Peter, Anna Caroli, and Alexandra Ljimani. "Renal Diffusion-Weighted Imaging (DWI) for Apparent Diffusion Coefficient (ADC), Intravoxel Incoherent Motion (IVIM), and Diffusion Tensor Imaging (DTI): Basic Concepts." In Methods in Molecular Biology, 187–204. New York, NY: Springer US, 2021. http://dx.doi.org/10.1007/978-1-0716-0978-1_11.

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AbstractThe specialized function of the kidney is reflected in its unique structure, characterized by juxtaposition of disorganized and ordered elements, including renal glomerula, capillaries, and tubules. The key role of the kidney in blood filtration, and changes in filtration rate and blood flow associated with pathological conditions, make it possible to investigate kidney function using the motion of water molecules in renal tissue. Diffusion-weighted imaging (DWI) is a versatile modality that sensitizes observable signal to water motion, and can inform on the complexity of the tissue microstructure. Several DWI acquisition strategies are available, as are different analysis strategies, and models that attempt to capture not only simple diffusion effects, but also perfusion, compartmentalization, and anisotropy. This chapter introduces the basic concepts of DWI alongside common acquisition schemes and models, and gives an overview of specific DWI applications for animal models of renal disease.This chapter is based upon work from the COST Action PARENCHIMA, a community-driven network funded by the European Cooperation in Science and Technology (COST) program of the European Union, which aims to improve the reproducibility and standardization of renal MRI biomarkers. This introduction chapter is complemented by two separate chapters describing the experimental procedure and data analysis.
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Florack, Luc, Rick Sengers, Stephan Meesters, Lars Smolders, and Andrea Fuster. "Riemann-DTI Geodesic Tractography Revisited." In Mathematics and Visualization, 225–43. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56215-1_11.

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AbstractClinical tractography is a challenging problem in diffusion tensor imaging (DTI) due to persistent validation issues. Geodesic tractography, based on a shortest path principle, is conceptually appealing, but has not produced convincing results so far. A major weakness is its rigidity with respect to candidate tracts it is capable of producing given a pair of endpoints, showing a tendency to produce false positives (such as shortcuts) and false negatives (e.g. if a shortcut supplants the correct solution). We propose a new geodesic paradigm that appears to overcome these problems, making a step towards semi-automatic clinical use. To this end we couple the DTI tensor field to a family of Riemannian metrics, governed by control parameters. In practice these parameters may allow for edits by an expert through manual selection among multiple tract suggestions, or for bringing in a priori knowledge. In this paper, however, we consider an automatic, evidence-driven procedure to determine optimal controls and corresponding tentative tracts, and illustrate the role of edits to remediate erroneous defaults.
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Exner, H. E., and P. Bross. "Material Transport Rate and Stress Distribution During Grain Boundary Diffusion Driven by Surface Tension." In Sintering Key Papers, 101–10. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0741-6_7.

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Conference papers on the topic "Tensor driven diffusion"

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Becattini, G., L. S. Mattos, and D. G. Caldwell. "Diffusion tensor driven contour closing for cell microinjection targeting." In 2010 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2010). IEEE, 2010. http://dx.doi.org/10.1109/iembs.2010.5627608.

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Jin, Yu, Joseph F. JaJa, Rong Chen, and Edward H. Herskovits. "A data-driven approach to extract connectivity structures from diffusion tensor imaging data." In 2015 IEEE International Conference on Big Data (Big Data). IEEE, 2015. http://dx.doi.org/10.1109/bigdata.2015.7363843.

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Hu, Yong, Tin Yan Chan, Xiang Li, KC Mak, Keith DK Luk, and Shu-Qiang Wang. "Identify myelopathic cervical spinal cord using diffusion tensor image: A data-driven approach." In 2015 IEEE International Conference on Digital Signal Processing (DSP). IEEE, 2015. http://dx.doi.org/10.1109/icdsp.2015.7251933.

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Hai-Yun Wang and Kai-Kuang Ma. "Accurate optical flow estimation in noisy sequences by robust tensor-driven anisotropic diffusion." In rnational Conference on Image Processing. IEEE, 2005. http://dx.doi.org/10.1109/icip.2005.1530636.

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Chen, Yunmei, and Stacey Chastain. "Anisotropic diffusion driven by diffusion tensors." In International Symposium on Optical Science and Technology, edited by David C. Wilson, Hemant D. Tagare, Fred L. Bookstein, Francoise J. Preteux, and Edward R. Dougherty. SPIE, 2000. http://dx.doi.org/10.1117/12.402435.

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Kim, Y., Y. J. Chao, M. J. Pechersky, and M. J. Morgan. "Investigation of Hydrogen Transport Related Fracture in Stainless Steels." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-13823.

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Stress-assisted hydrogen diffusion analysis was performed on arc-shaped tension specimen (C-specimen) fabricated from Type 21-6-9 stainless steel. Two-dimensional finite element method was applied for the determination of elastic-plastic crack front stress fields, which was later coupled with hydrogen diffusion analyses. The extension of Fick's rule was used as the governing equation for the diffusion analysis. The distributions of hydrogen concentration were compared under various Internal Hydrogen Embrittlement (IHE) and Hydrogen Environment Embrittlement (HEE) conditions. Without any external hydrogen pressure in IHE conditions, the increment of hydrogen concentration driven by the gradient of hydrostatic stress was offset by the out-gasing driven by gradient of hydrogen concentration at the crack front region. As the hydrogen pressure increases, the hydrogen concentration at the crack front region becomes dominant and show peak value around the crack tip. Compared with the results of IHE cases, the hydrogen concentrations in HEE conditions could reach the level of steady state in a relatively short time which is attributed to the high solubility and diffusivity of the material at high temperature.
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Almutairi, Zeyad, Carolyn Ren, and David Johnson. "Effects of Hydrophobic Recovery of Plasma Treated PDMS Microchannels on Surface Tension Driven Flow." In ASME 2010 8th International Conference on Nanochannels, Microchannels, and Minichannels collocated with 3rd Joint US-European Fluids Engineering Summer Meeting. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-31243.

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Surface tension driven flow is used in numerous microfluidic applications. It is considered a passive pumping technique which doesn’t require any external energy, aside from the interfacial surface energy between the fluid and walls. Thus, it is preferred in applications where the goal is fluid and sample transport. In many applications PDMS (Polydimethylsiloxane) is the most adapted material for chip manufacturing in microfluidics. PDMS has several aspects that make it favorable for microfluidic applications. Ease of chip fabrication, cost effectiveness, chemical stability, and good optical properties are features offered by PDMS and desirable for microfluidics. On the other hand, PDMS has some shortcomings. One of importance is that PDMS is naturally hydrophobic. For this reason it is hard to achieve surface tension flow in native PDMS for various fluids used in microfluidics. Thus, native PDMS must be treated to get hydrophilic surface properties. The most used method for altering PDMS properties to a hydrophilic state is by plasma treatment. This treatment has several aspects where it enhances the attachment of PDMS to substrates, it alters the surface from a hydrophobic to a hydrophilic state, and it increases the electrokinetic properties of PDMS. As a result, after plasma treatment surface tension pumping can be achieved in PDMS, unlike native PDMS. However, plasma treatment is not permanent due to the diffusion of non-cured PDMS species to the surface of microchannels, as is well documented in the literature. The change of plasma treated PDMS with time will affect both the electrokinetic and surface tension driven flow. To our knowledge, researchers have quantitatively documented the time effect on plasma treated PDMS microchannels (aging of PDMS) for electrokinetic flow, but not for surface tension driven flow. Therefore, a quantitative examination of the time effect on surface tension driven flow for plasma treated PDMS gives valuable information on both regaining the hydrophobic properties in PDMS and changes in the passive flow conditions. In this work a quantitative study on the hydrophobic recovery for oxygen-plasma treated PDMS and its effects on surface tension flow was examined. The study was performed with a quantitative flow visualization technique (micro particle image velocimetry). It was found that the aging of PDMS will strongly affect surface tension flow of water based solutions in PDMS microchannels. This study gives important information on the effectiveness of surface tension driven flow for oxygen plasma treated PDMS microchannels.
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Rao, Qinyang, and Barclay G. Jones. "Study of Mechanism of Initial Crud Formation on Fuel Cladding in Subcooled Boiling Region in PWR." In 10th International Conference on Nuclear Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/icone10-22558.

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A hemispherical vapor bubble model has been constructed, and thermocapillary flow driven by surface tension gradient, due to temperature difference, around bubble attached to a plane heated surface, and it has been examined using numerical methods. LiOH solute concentration distribution around the bubble has been obtained. Some parameters under PWR operating conditions have been discussed: bubble size, mass diffusion coefficient and vapor heat transfer coefficient. Effects of some important parameters, such as heat flux and bubble size, have been examined. The study shows that the thermocapillary flow around a static hemispherical vapor bubble can not generate sufficient solute concentrations to initialize crud formation under PWR operating condition.
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Rahman, M. A., and M. Z. Saghir. "Thermodiffusion, Marangoni and Gravity Driven Convections in a Liquid Layer Overlying a Porous Layer: Lateral Heating Conditions." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66129.

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In this paper, we study the onset of thermal convection in a liquid layer overlying a porous layer, where the whole system being laterally heated. The non-linear two-dimensional Navier Stokes equations, the energy equation and the mass transfer equation are solved for the liquid layer. Instead of Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. Three cases are presented in this paper. In the first case, the gravity driven buoyancy convection is studied. In the second case, the surface tension is assumed to vary linearly with temperature, therefore the existence of Marangoni convection. To analyze the Marangoni convection, we consider microgravity condition. Different aspect ratios as well as the thickness ratios are studied in detail for both the first and second cases. In the third case, diffusion and the thermodiffusion between two binary fluids with two different compositions in liquid and porous layer is studied.
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Wei, P. S., C. L. Lin, and C. N. Ting. "Scaling Thermocapillary Surface Velocity in Weld Pool." In ASME/JSME 2011 8th Thermal Engineering Joint Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajtec2011-44068.

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In this study, the peak surface velocity driven by thermocapillary force in melting or welding pool irradiated by a distributed low-power-density beam is determined from a scale analysis. In view of different distances of diffusion between momentum and energy, the effects of Prandtl number on surface velocity are of interest. A low-power-density-beam heating implies no deep and narrow cavity (or keyhole) taking place in the pool. The results find that the peak surface velocity is proportional to the first power and 2/3 power of the surface tension coefficient or Marangoni number for high and low Prandtl number, respectively. The free surface velocity is determined by Prandtl and Marangoni numbers for given dimensionless beam power and Peclet numbers. The predictions agree with numerical computations.
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