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Dover Publications; 2005

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139

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[41] Ishimoto K, Gaffney EA. Squirmer dynamics near a boundary. Physical

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[43] Uspal WE. Theory of light-activated catalytic Janus particles. The Journal of Chemical Physics. 2019;150:114903

Detention times of microswimmers close to surfaces: Influence of hydrodynamic interactions and noise. Physical Review

[45] Mirkovic T, Zacharia NS, Scholes GD, Ozin GA. Nanolocomotion - Catalytic Nanomotors and Nanorotors.

[46] Ebbens SJ, Howse JR. In pursuit of propulsion at the nanoscale. Soft Matter.

[47] Lee T, Alarc'on-Correa M, Miksch C, Hahn K, Gibbs JG, Fischer P. Self-Propelling Nanomotors in the Presence of Strong Brownian Forces. Nano Letters. 2014;14:2407-2412

[48] Reigh SY, Huang M, Schofield J, Kapral R. Microscopic and continuum descriptions of Janus motor fluid flow fields. Philosophical Transactions of the

[49] de Buyl P, Mikhailov AS, Kapral R. Self-propulsion through symmetry

Royal Society A. 2016;374

breaking. EPL. 2013;103

74

[50] Dey KK, Das S, Poyton MF, Sengupta S, Butler PJ, Cremer PS, et al.

Mechanics. 2008;615:401

Review E. 2013;88:062702

Advances. 2018;4:eaao1755

[44] Schaar K, Zöttl A, Stark H.

Letters. 2015;115:038101

Small. 2010;6:159

2010;6:726

[61] Cortez R. The method of regularized Stokeslets. SIAM Journal on Scientific Computing. 2001;23:1024

[62] Aderogba K, Blake J. Action of a force near the planar surface between two semi-infinite immiscible liquids at very low Reynolds numbers. Bulletin of the Australian Mathematical Society. 1978;18:345

[63] Mathijssen AJTM, Doostmohammadi A, Yeomans JM, Shendruk TN. Hotspots of boundary accumulation: Dynamics and statistics of micro-swimmers in flowing films. Journal of the Royal Society Interface. 2016;13:20150936

[64] Delong S, Usabiaga FB, Delgado-Buscalioni R, Griffith BE, Donev A. Brownian dynamics without Green's functions. The Journal of Chemical Physics. 2014;140:134110

[65] Rapaport DC. Molecular dynamics simulation using quaternions. Journal of Computational Physics. 1985;60:306

[66] Wittkowski R, Löwen H. Selfpropelled Brownian spinning top: Dynamics of a biaxial swimmer at low Reynolds numbers. Physical Review E. 2012;85:021406

[67] Beard DA, Schlick T. Unbiased rotational moves for rigid-body dynamics. Biophysical Journal. 2003;85: 2973

[68] Jones RB, Alavi FN. Rotational diffusion of a tracer colloid particle: IV. Brownian dynamics with wall effects. Physica A. 1992;187:436-455

[69] Lisicki M, Cichocki B, Rogers SA, Dhont JKG, Lang PR. Translational and rotational near-wall diffusion of spherical colloids studied by evanescent wave scattering. Soft Matter. 2014;10:4312

[70] Fixman M. Implicit algorithm for brownian dynamics of polymers. Macromolecules. 1986;19:1195

[71] Bao Y, Rachh M, Keaveny EE, Greengard L, Donev A. A fluctuating boundary integral method for Brownian suspensions. Journal of Computational Physics. 2018;334

[72] Uspal WE, Popescu MN, Tasinkevych M, Dietrich S. Shapedependent guidance of active Janus particles by chemically patterned surfaces. New Journal of Physics. 2018; 20:015013

[73] Brady JS, Bossis G. Stokesian dynamics. Annual Review of Fluid Mechanics. 1988;20:111

[74] Kim AS, Stolzenbach KD. The Permeability of Synthetic Fractal Aggregates with Realistic Three-Dimensional Structure. Journal of Colloid and Interface Science. 2002;253: 315328

[75] Kim AS, Stolzenbach KD. Aggregate formation and collision efficiency in differential settling. Journal of Colloid and Interface Science. 2004;271:110

[76] Yan W, Brady JF. The force on a boundary in active matter. Journal of Fluid Mechanics. 2015;785:1

[77] Walter J, Salsac A-V, Barthés-Biesel D, Le Tallec P. Coupling of finite element and boundary integral methods for a capsule in a Stokes flow. International Journal for Numerical Methods in Engineering. 2010;83:829

[78] Gao T, Hu HH. Deformation of elastic particles in viscous shear flow. Journal of Computational Physics. 2009; 228:2132

Chapter 3

Transport

Albert S. Kim

transport equation

1. Introduction

77

1.1 Thermodynamic states

Abstract

Fundamentals of Irreversible

Thermodynamics for Coupled

Engineering phenomena occur in open systems undergoing irreversible, nonequilibrium processes for coupled mass, energy, and momentum transport. The momentum transport often becomes a primary or background process, on which driving forces of physical gradients govern mass and heat transfer rates. Although in the steady state no physical variables have explicit variation with time, entropy increases with time as long as the systems are open. The degree of irreversibility can be measured by the entropy-increasing rate, first proposed by L. Onsager. This book conceptually reorganizes the entropy and its rate in broader aspects. Diffusion is fully described as an irreversible, i.e., entropy increasing, phenomenon using four different physical pictures. Finally, an irreversible thermodynamic formalism using effective driving forces is established as an extension to the Onsager's reciprocal theorem, which was applied to core engineering phenomena of fundamental importance: solute diffusion and thermal flux. In addition, the osmotic and thermal

fluxes are explained in the unified theoretical framework.

component irreversible thermodynamic processes.

Keywords: irreversible thermodynamics, non-equilibrium thermodynamics, Onsager's reciprocal theorem, entropy rate, diffusion pictures, irreversible

This chapter contributes to a comprehensive explanation of the steady-state thermodynamics of irreversible processes with detailed theoretical derivations and examples. The origin and definitions of entropy are described, irreversible thermodynamics for a steady state is revisited based on Onsager's reciprocal theorem, and thermal and solute diffusion phenomena are recapitulated as examples of single-

In fundamental and applied sciences, thermodynamics (or statistical mechanics) plays an important role in understanding macroscopic behaviors of a thermodynamic system using microscopic properties of the system. Thermodynamic systems have three classifications based on their respective transport conditions at interfaces.

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