The Fluid Dynamics of Cell Motility

Copyright
Contents
Preface
PART ONE FUNDAMENTALS
	1 Biological Background
		1.1 The Biological World
		1.2 Fluid Dynamics in Biology
		1.3 Biological Locomotion
		1.4 Locomotion at Low Reynolds Number
		1.5 Organelles that Confer Cell Motility
		1.6 Cellular Locomotion as a Case Study in Modelling
		Further Reading
	2 The Fluid Dynamics of Microscopic Locomotion
		2.1 Dynamics of Locomotion
		2.2 Reynolds Numbers
		2.3 The Stokes Equations
		2.4 Low Reynolds Number Dynamics
		2.5 Rate of Work and Dissipation
		2.6 Forced vs. Force-Free Motion
		2.7 Properties of Low Reynolds Number Locomotion
		Further Reading
		Exercises
	3 The Waving Sheet Model
		3.1 Biological Motivation
		3.2 Setup
		3.3 Asymptotic Solution
		3.4 Rate of Work
		3.5 Wave Optimisation
		3.6 Comparison with Experiments: Metachronal Waves of Cilia
		Further Reading
		Exercises
	4 The Squirmer Model
		4.1 Axisymmetric Squirmer
		4.2 Free-Swimmer Squirmer
		4.3 Rotating Squirmer
		4.4 Envelope Model
		4.5 Comparison with Experiments: Volvox Locomotion
		Further Reading
		Exercises
PART TWO CELLULAR LOCOMOTION
	5 Flagella and the Physics of Viscous Propulsion
		5.1 Kinematics of Flagellar Propulsion
		5.2 Forces and Torques in Stokes Flows
		5.3 Physics of Drag-Based Propulsion
		5.4 Helices and Travelling Waves Are Optimal
		Further Reading
		Exercises
	6 Hydrodynamics of Slender Filaments
		6.1 Revisiting Stokes Flow Past a Sphere
		6.2 Line Superposition of Hydrodynamic Singularities
		6.3 Local Hydrodynamics: Resistive-Force Theory (RFT)
		6.4 Nonlocal Hydrodynamics: Slender-Body Theory
		Further Reading
		Exercises
	7 Waving of Eukaryotic Flagella
		7.1 Swimming of a Periodically Waving Flagellum
		7.2 Hydrodynamically Optimal Travelling Wave
		7.3 Swimming of a Finite Flagellum
		7.4 Active Filaments
		Further Reading
		Exercises
	8 Rotation of Bacterial Flagellar Filaments
		8.1 Hydrodynamic Resistance of Helical Filaments
		8.2 Swimming of a Flagellated Bacterium
		8.3 Swimming Using Finite-Size Helical Filaments
		8.4 Optimal Helical Swimming
		Further Reading
		Exercises
	9 Flows and Stresses Induced by Cells
		9.1 Force-Free Swimming
		9.2 Force Dipoles
		9.3 Leading-Order Flow Around Cells
		9.4 Other Relevant Flow Singularities
		9.5 Average Stress Induced by Cells
		Further Reading
		Exercises
PART THREE INTERACTIONS
	10 Swimming Cells in Flows
		10.1 Spherical Swimmers in Flows
		10.2 Elongated Swimmers in Flows
		10.3 Biased Swimmers in Flows
		Further Reading
		Exercises
	11 Self-Propulsion and Surfaces
		11.1 Hydrodynamic Attraction by Surfaces
		11.2 Circular Swimming near Surfaces
		11.3 Upstream Swimming
		11.4 Impact of Surfaces on Swimming Speeds
		11.5 Wall-Bound Cilia
		Further Reading
		Exercises
	12 Hydrodynamic Synchronisation
		12.1 Synchronisation of Anchored Flagella and Cilia
		12.2 Synchronisation of Swimming Cells
		Further Reading
		Exercises
	13 Diffusion and Noisy Swimming
		13.1 Brownian Motion
		13.2 Cells vs. Noise
		13.3 Run-and-Tumble
		Further Reading
		Exercises
	14 Hydrodynamics of Collective Locomotion
		15 Locomotion and Transport in Complex Fluids
			15.1 Locomotion and Transport in Linear Viscoelastic Fluids
			15.2 Locomotion and Transport in Nonlinear Viscoelastic Fluids
			15.3 Locomotion and Transport in Heterogeneous Fluids
			Further Reading
			Exercises
		14.1 Discrete Model of Active Suspensions
		14.2 Continuum Model of Active Suspensions
		14.3 Collective Instabilities
		Further Reading
		Exercises
References
Index