Boundary regularized integral equation formulation of Stokes flow

Sun, Qiang; Klaseboer, Evert; Khoo, Boo Cheong; Chan, Derek Y. C.

doi:10.1063/1.4907279

Cited by 17 publications

(15 citation statements)

References 24 publications

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“…It can be seen that when N 1 varies from 0 (no slip) to 1, the gradient of flow velocity on the lower wall increases rapidly while it reduces rapidly on the upper wall. When N 1 is larger than 1, the lower wall is nearly free slip and the increase of N 1 does not modify the flow profiles too much (Sun et al , 2015), and consequently the gradients of flow velocity on both walls do not change significantly.…”

Section: Resultsmentioning

confidence: 99%

Modeling heat transfer of nanofluid flow in microchannels with electrokinetic and slippery effects using Buongiorno’s model

Huang

et al. 2019

HFF

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Purpose This paper aims to study the heat transfer of nanofluid flow driven by the move of channel walls in a microchannel under the effects of the electrical double layer and slippery properties of channel walls. The distributions of velocity, temperature and nanoparticle volumetric concentration are analyzed under different slip-length. Also, the variation rates of flow velocity, temperature, concentration of nanoparticle, the pressure constant, the local volumetric entropy generation rate and the total cross-sectional entropy generation are analyzed. Design/methodology/approach A recently developed model is chosen which is robust and reasonable from the point of view of physics, as it does not impose nonphysical boundary conditions, for instance, the zero electrical potential in the middle plane of the channel or the artificial pressure constant. The governing equations of flow motion, energy, electrical double layer and stream potential are derived with slip boundary condition presented. The model is non-dimensionalized and solved by using the homotopy analysis method. Findings Slip-length has significant influences on the velocity, temperature and nanoparticle volumetric concentration of the nanofluid. It also has strong effects on the pressure constant. With the increase of the slip-length, the pressure constant of the nanofluid in the horizontal microchannel decreases. Both the local volumetric entropy generation rate and total cross-sectional entropy generation rate are significantly affected by both the slip-length of the lower wall and the thermal diffusion. The local volumetric entropy generation rate at the upper wall is always higher than that around the lower wall. Also, the larger the slip-length is, the lower the total cross-sectional entropy generation rate is when the thermal diffusion is moderate. Originality/value The findings in this work on the heat transfer and flow phenomena of the nanofluid in microchannel are expected to make a contribution to guide the design of micro-electro-mechanical systems.

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Section: Resultsmentioning

confidence: 99%

Modeling heat transfer of nanofluid flow in microchannels with electrokinetic and slippery effects using Buongiorno’s model

Huang

et al. 2019

HFF

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“…The method of regularized Stokeslets was introduced by Cortez in [1] to eliminate the need to integrate a singular kernel in boundary integral methods for Stokes flow. Since then, regularized Stokeslets have enjoyed widespread use in models of general fluid-structure interaction [2][3][4][5][6][7][8]. The method of regularized Stokeslets has become especially popular for modeling the dynamics of thin fibers in a three-dimensional fluid, providing an alternative way to deal with the singular integrals arising in the classical slender body theories of Lighthill [9], Keller-Rubinow [10], and Johnson [11].…”

Section: Introductionmentioning

confidence: 99%

Remarks on Regularized Stokeslets in Slender Body Theory

Ohm

2021

Fluids

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We remark on the use of regularized Stokeslets in the slender body theory (SBT) approximation of Stokes flow about a thin fiber of radius ϵ>0. Denoting the regularization parameter by δ, we consider regularized SBT based on the most common regularized Stokeslet plus a regularized doublet correction. Given sufficiently smooth force data along the filament, we derive L∞ bounds for the difference between regularized SBT and its classical counterpart in terms of δ, ϵ, and the force data. We show that the regularized and classical expressions for the velocity of the filament itself differ by a term proportional to log(δ/ϵ); in particular, δ=ϵ is necessary to avoid an O(1) discrepancy between the theories. However, the flow at the surface of the fiber differs by an expression proportional to log(1+δ2/ϵ2), and any choice of δ∝ϵ will result in an O(1) discrepancy as ϵ→0. Consequently, the flow around a slender fiber due to regularized SBT does not converge to the solution of the well-posed slender body PDE which classical SBT is known to approximate. Numerics verify this O(1) discrepancy but also indicate that the difference may have little impact in practice.

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“…In addition to that, Chan et al . have proposed a boundary regularized integral equation for Stokes flows with kernels that are completely free of singularities by performing an analytical subtraction of an auxiliary known flow field calculated very close to the singularity point. Recently, Ojala and Tornberg have presented an accurate and stable way of handling with near‐singular integrals by adopting an interpolatory quadrature approach in cases where the drops come close to each other in a Stokes flow.…”

Section: Introductionmentioning

confidence: 99%

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

Siqueira

Rebouças

Oliveira

et al. 2016

Numerical Methods in Fluids

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Summary We present a numerical methodology for the simulation of a viscous drop under simple shear flows by using the boundary integral method. The present work treats only a single drop in an unbounded fluid‐flow, but the results can be directly applied to studies on the rheology of dilute emulsions, in which the hydrodynamic interactions between two or more drops can be neglected. Singular and non‐singular integral representations of the velocity field are considered. Several aspects of the method are presented, including a new mesh relaxation approach and an automatic time‐step control method. The relaxation strategy is used in order to contain the distortion of the mesh and is performed by using relaxation iterations in a virtual temporal march between each physical time step of the simulation and monitoring the standard deviation of the areas of the elements. The automatic time‐step control method uses a global quantity related to the drop deformation in order to automatically set the temporal integration time step. It is carried out in a way to keep the local integration error less than a given tolerance. This strategy reduces the computational cost of the simulation by dramatically reducing the number of time steps in the temporal integration process. Copyright © 2016 John Wiley & Sons, Ltd.

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Boundary regularized integral equation formulation of Stokes flow

Cited by 17 publications

References 24 publications

Modeling heat transfer of nanofluid flow in microchannels with electrokinetic and slippery effects using Buongiorno’s model

Modeling heat transfer of nanofluid flow in microchannels with electrokinetic and slippery effects using Buongiorno’s model

Remarks on Regularized Stokeslets in Slender Body Theory

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

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