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# The Hydrodynamics of Active Particles Inside of a Porous Container and the Galerkin Boundary Element Discretization of Stokes Flow

## Citation

Marshall, Kevin James (2018) The Hydrodynamics of Active Particles Inside of a Porous Container and the Galerkin Boundary Element Discretization of Stokes Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9MP51G8. https://resolver.caltech.edu/CaltechTHESIS:10252017-021526235

## Abstract

In this thesis I formulate and present a novel and new framework for simulating the dynamics of arbitrarily shaped active or passive particles immersed in a Stokesian fluid and evolving under confinement by a porous container or in free space. I use a completed double layer boundary integral equation to model the particle's dynamics and combine this with a new formulation that uses a second kind integral equation for describing the motion of the porous container. This newly formulated porous container model permits fluid to pass through the container's surface at a velocity in proportion to a discontinuous jump in stress across the container's surface. This jump in stress is induced by the active particle's motion. The proposed porous container model is general in the sense that it allows fluid to pass through the membrane with finite tangential and normal velocity components. I obtain the exact analytical solution to this model when the active particle and porous container are perfectly concentric. In addition, I numerically solve this system of boundary integral equations for arbitrary particle positions, and fully characterize the particle and container dynamics by performing a vast number of trajectory studies. Both the container and particle are seen to move in complicated ways owing to their self and pairwise hydrodynamic interactions. This system is studied over a vast parameter space, for multiple container to particle size ratios, multiple types of active particles, and various permeability parameterizations. This coupled set of particle and container boundary integral equations is discretized using a novel interpretation and new extension of the Galerkin Boundary Element discretization to multi-body particle systems in Stokes flow. I also implement and extend an h-adaptive conformal mesh refinement algorithm to accurately resolve near-contact particle and container interactions. In addition, I perform all Galerkin BEM calculations on CUDA enabled GPUs, allowing for these simulations to be run on modern desktop computers in seconds. I combine all of these techniques in a modern C++ Galerkin Boundary Element Method computational framework called GPUGBEM.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Galerkin Boundary Element Method, Boundary Integral Equations, Stokes Flow, Linearized Viscous Flows, Fluid Mechanics, Blake Squirmers, Active Matter, Squirmer, Porous Container, Darcy, Active Particle, GPGPU, CUDA, Confinement
Degree Grantor:California Institute of Technology
Division:Chemistry and Chemical Engineering
Major Option:Chemical Engineering
Thesis Availability:Public (worldwide access)
Thesis Committee:
• Barr, Alan H.
• Kornfield, Julia A.
• Seinfeld, John H.
Defense Date:4 October 2017
Non-Caltech Author Email:kjmarshall89 (AT) gmail.com
Funders:
Funding AgencyGrant Number
National Science Foundation Graduate Research FellowshipDGE-1144469
Record Number:CaltechTHESIS:10252017-021526235
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:10252017-021526235
DOI:10.7907/Z9MP51G8
ORCID:
AuthorORCID
Marshall, Kevin James0000-0001-6025-7674
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10544
Collection:CaltechTHESIS
Deposited By: Kevin Marshall
Deposited On:30 Oct 2017 22:28