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1 [CT142]

[CT142]

[00095] Low Reynolds number hydrodynamics of a slip-stick sphere

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : Low Reynolds number hydrodynamics of spherical particles with non-uniform surface roughness show potential applications in microfluidic situations like swimming micro-organisms and emulsions. In this work, we study the hydrodynamics of spherical slip-stick particle models; namely, i) axisymmetric cap/strip model and ii) non-axisymmetric patch model, suspended in an unbounded arbitrary Stokes flow whose surface is partitioned into two different slip regions. We evaluate the optimum configurations for migrational and rotational motion of the slip-stick spherical particle.
Classification : 76D07, 35A25
Author(s) :
- Shiba Biswas (Indian Institute of Technology Kharagpur, India-721302)
- Poornachandra Sekhar Burada (Indian Institute of Technology Kharagpur, India-721302)
- Raja Sekhar G P (Indian Institute of Technology Kharagpur, India-721302)

[00261] Translational motion of a slightly deformed viscous spherical droplet in Stokes flow

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : The problem of steady translational motion of a slightly deformed spherical droplet immersed in an immiscible viscous fluid is studied analytically under the consideration of vanishing Reynolds number. The flow fields in both the regions i.e. in the interior of droplet and exterior of droplet are governed by steady Stokes equations that are solved asymptotically using a method of perturbed expansions undersuitable boundary conditions. The deformation from spherical shape is characterized by a small parameter called deformation parameter, therefore, we have solved the problem up to the second order of the deformation parameter by neglecting the higher orders. The effect of deformation parameter is observed by means of force expression. The explicit expressions for the hydrodynamic drag force exerted on the droplet surface are obtained for the special cases of prolate and oblate spheroids. Our results are in good agreement with the exisitng results in literature for deformed solid sphere up to first and second order.
Classification : 76D07, 76T06, Transport Phenomena, Motion of bubbles and drops
Author(s) :
- Jai Prakash (Mahindra University, Hyderabad)
- Huan J. Keh (National Taiwan University, Taipei)

[00518] Unsteady Stokes flow past a sphere with mixed slip-stick boundary conditions

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : A general solution to unsteady Stokes equations for an incompressible, viscous flow past a sphere with mixed slip-stick boundary conditions is given. Faxén’s laws for drag and torque exerted on the sphere are derived, and the results have been compared in special cases of no-slip and shear-free boundary conditions with the existing literature. We extend this work to bodies of arbitrary shape under the same boundary conditions.
Classification : 76D07, 76D05
Author(s) :
- Dimple Satya Sree Dadi (University of Hyderabad)
- Dimple Satya Sree Dadi (University of Hyderabad)
- Sri Padmavati B (University of Hyderabad)

[01119] Miscible Flows Based On Darcy-Stokes-Brinkman Model: Existence and Uniqueness

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : Flows in a porous or vuggy medium are encountered in several physical phenomena, including oil recovery. A vast literature use the unsteady Brinkman and continuity equations for numerical modeling of such flow systems. We couple these equations with a convection-diffusion equation for the solute concentration to take the miscibility of fluids into account. For the first time, we show the well-posedness of this problem by employing regularized Galerkin method and hemivaritional inequalities.
Classification : 76Dxx, 76Sxx, 35Qxx, 35Dxx
Author(s) :
- Sahil Kundu (Indian Institute of Technology Ropar,Ropar, India)
- Manoranjan Mishra (Indian Institute of Technology Ropar, India)
- Surya Narayan Maharana (Indian Institute of Technology Ropar)

[02353] Finite volume coupled with finite element scheme for the chemotaxis-fluid model

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : We propose a linear decoupled positivity-preserving scheme for the chemotaxis-fluid system modeling the mutual interaction of the swimming aerobic bacteria with the surrounding fluid flow. The scheme consists of the finite element method (FEM) for the fluid equations on a regular triangulation and an upwind finite volume method (FVM) for the chemotaxis system on two types of dual mesh. The discrete cellular density and chemical concentration can be regarded as the piecewise constant functions on the dual mesh $($or equivalently, the piecewise linear functions on the triangulation in the mass-lumping sense$)$, which are obtained by the upwind finite volume approximation satisfying the positivity-preserving and mass conservation laws. The numerical velocity is computed by the finite element method in the triangulation and is utilized to define the upwind-type numerical flux in the dual mesh. We examine the $M$-property of the matrices from the discrete system and prove the well-posedness and the positivity-preserving property. By using the $L^p$-estimate of the discrete Laplace operators, semigroup analysis, and induction method, we establish the optimal error estimates for chemical concentration, cellular density and velocity field in $(l^\infty(W^{1,p}), l^\infty(L^p),l^\infty(W^{1,p}))$-norms. Several numerical examples are presented to confirm the theoretical results.
Classification : 76Dxx, 65Mxx, 76Mxx
Author(s) :
- Ping Zeng (University of Electronic Science and Technology of China)
- Guanyu Zhou (University of Electronic Science and Technology of China)