Modeling and Simulation of Capsules and Biological Cells

C Pozrikidis (Editor)

Chapman & Hall / CRC Press, 2003

ISBN: 1584883596


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1 D. Barthes-Biesel Flow-induced capsule deformation
2 C. Pozrikidis Shell theory for capsules and cells
3 N. N'Dri, W. Shyy, H. Liu,
R. Tran-Son-Tay
Multi-scale modeling spanning from cell surface receptors to blood flow in arteries
4 T. W. Secomb Mechanics of red blood cells and blood flow in narrow tubes
5 A. Nir, O. M. Lavrenteva Capsule dynamics and interfacial transport
6 A. Borhani, N. R. Gupta Capsule motion and deformation in tube and channel flow

Excerpts from the Preface

This collection of contributed chapters addresses the mathematical modeling and numerical simulation of liquid capsules and biological cells. Capsules and cells are distinguished from common bubbles and liquid droplets in that their interfaces exhibit mechanical properties that are more involved than those described by a constant and uniform surface tension. For example, non-uniformities in temperature or interfacial concentration of an insoluble surfactant are responsible for thermocapillary and mass transfer effects that activate the interfaces, in the sense of empowering them with a driving force that contributes to the overall fluid motion, with important consequences and ramifications. The most complex types of particles considered in this book are liquid capsules and biological cells enclosed by structured interfaces with a molecular or shell-like constitution, exhibiting viscoelastic properties under direct mechanical or hydrodynamic loads.

Capsules and cells deform and evolve in two ways: passively in response to a flow and because of inter-particle interactions and mechanical stimulus; and actively by means of self-induced motion. For example, under the action of a localized interfacial tension generated by the release or injection of a surfactant, a liquid capsule may self-divide or deform to engulf ambient fluid or another cell or particle residing in its neighborhood. The active motion distinguishes capsules and cells from uncharged solid particles whose surfaces are normally impermeable and inert in the context of hydrodynamics.

Natural, artificial, and biological capsules and cells abound in nature, biology, and technology. Examples include the highly flexible, non-nucleated red blood cells, the nearly spherical white blood cells, other types of tissue cells, and various liquid globules encountered in food, cosmetics, and other industrial products. Desirable properties of capsules and cells include the ability to deform and accommodate the shapes of capillaries and microchannels, the ability to withstand the shearing action of an imposed flow, and the capacity to transport material in a protected way, and then release it in a timely fashion for the purpose of achieving a specific goal.

In the past three decades, considerable progress has been made in the mathematical analysis, mathematical modeling, and numerical simulation of the fluid dynamics of capsules and cells. Topics of active research include the modeling of interfacial mechanics and transport combined with internal and external hydrodynamics in the context of flow-structure interaction, the unified description of internal and external fluid motion, the coupling of continuum mechanics with molecular processes, and the numerical simulation of large systems accounting for strong hydrodynamic interactions. The chapters in this volume provide an overview of the state of the art on selected topics, also including the results of ongoing research by the individual authors.

This book is intended to be a stand-alone reference and a convenient starting point for students and professionals with a general interest in the mathematical and computational sciences, and a specific interest to capsule and cell dynamics and biomechanics. One deliberate restriction is that the discussion remains mostly on the level of a continuum. Molecular processes are discussed in terms of kinetics and only insofar as to provide motivation and justification for the macroscopic equations.

The first four chapters are devoted to reviewing the fundamentals of cell and membrane mechanics, and to discussing the behavior in hydrostatics and hydrodynamics. These chapters are suitable for a course in biomechanics. The last two chapters are dedicated to discussing drop and bubble dynamics associated with temperature variations and surfactant transport. These chapters are suitable for an advanced course in interfacial fluid mechanics, interfacial phenomena, and dispersed-phase dynamics.