Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below. At this scale, inertia is unimportant and the Reynolds number is small. Our emphasis is on the simple physical picture and fundamental flow physics phenomena in this regime. We first give a brief overview of the mechanisms for swimming motility, and of the basic properties of flows at low Reynolds number, paying special attention to aspects most relevant for swimming such as resistance matrices for solid bodies, flow singularities and kinematic requirements for net translation. Then we review classical theoretical work on cell motility, in particular early calculations of swimming kinematics with prescribed stroke and the application of resistive force theory and slender-body theory to flagellar locomotion. After examining the physical means by which flagella are actuated, we outline areas of active research, including hydrodynamic interactions, biological locomotion in complex fluids, the design of small-scale artificial swimmers and the optimization of locomotion strategies. (Some figures in this article are in colour only in the electronic version) This article was invited by Christoph Schmidt.

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The hydrodynamics of swimming microorganisms

Differently from passive Brownian particles, active particles, also known as self-propelled Brownian particles or microswimmers and nanoswimmers, are capable of taking up energy from their environment and converting it into directed motion. Because of this constant flow of energy, their behavior can be explained and understood only within the framework of nonequilibrium physics. In the biological realm, many cells perform directed motion, for example, as a way to browse for nutrients or to avoid toxins. Inspired by these motile microorganisms, researchers have been developing artificial particles that feature similar swimming behaviors based on different mechanisms. These man-made micromachines and nanomachines hold a great potential as autonomous agents for health care, sustainability, and security applications. With a focus on the basic physical features of the interactions of self-propelled Brownian particles with a crowded and complex environment, this comprehensive review will provide a guided tour through its basic principles, the development of artificial self-propelling microparticles and nanoparticles, and their application to the study of nonequilibrium phenomena, as well as the open challenges that the field is currently facing.

/pdf/active-particles-in-complex-and-crowded-environments-4pyirdi1aj.pdf

Active Particles in Complex and Crowded Environments

1: Magnetic Particles: Preparation, Properties and Applications: M. Ozaki. 2: Maghemite (gamma-Fe2O3): A Versatile Magnetic Colloidal Material C.J. Serna, M.P. Morales. 3: Dynamics of Adsorption and Oxidation of Organic Molecules on Illuminated Titanium Dioxide Particles Immersed in Water M.A. Blesa, R.J. Candal, S.A. Bilmes. 4: Colloidal Aggregation in Two-Dimensions A. Moncho-Jorda, F. Martinez-Lopez, M.A. Cabrerizo-Vilchez, R. Hidalgo Alvarez, M. Quesada-PMerez. 5: Kinetics of Particle and Protein Adsorption Z. Adamczyk.

Surface and Colloid Science

Intermolecular And Surface Forces

Active Brownian particles, also referred to as microswimmers and nanoswimmers, are biological or manmade microscopic and nanoscopic particles that can self-propel. Because of their activity, their behavior can only be explained and understood within the framework of nonequilibrium physics. In the biological realm, many cells perform active Brownian motion, for example, when moving away from toxins or towards nutrients. Inspired by these motile microorganisms, researchers have been developing artificial active particles that feature similar swimming behaviors based on different mechanisms; these manmade micro- and nanomachines hold a great potential as autonomous agents for healthcare, sustainability, and security applications. With a focus on the basic physical features of the interactions of active Brownian particles with a crowded and complex environment, this comprehensive review will put the reader at the very forefront of the field of active Brownian motion, providing a guided tour through its basic principles, the development of artificial self-propelling micro- and nanoparticles, and their application to the study of nonequilibrium phenomena, as well as the open challenges that the field is currently facing.

/pdf/active-brownian-particles-in-complex-and-crowded-3ym4we2m8l.pdf

Active Brownian Particles in Complex and Crowded Environments

When a colloidal particle is exposed to an externally applied electric field, it acquires an electrophoretic velocity, resulting from fluid slip occurring across the Debye screening layer. When the field is uniformly applied, it is usually assumed that the net neutrality of the combined particle-layer system implies that the net electric force acting on it must vanish. This assumption of “force-free” phoretic motion has been employed extensively to describe electrophoresis in both unbounded and bounded fluid domains [J. L. Anderson, Annu. Rev. Fluid Mech. 21, 61 (1989)]. A careful inspection reveals here that this intuitive premise may fail when the fluid domain is bounded, in which case a nonzero electric force (resembling dielectrophoretic forces in nonuniformly applied fields) may actually exist. Such forces (represented via surface integrals of Maxwell stresses) result in particle motion above and beyond the one driven by the phoretic slip mechanism. A positive demonstration for the existence of a suc...

“Force-free” electrophoresis?

While the Taylor–Melcher electrohydrodynamic model entails ionic charge carriers, it addresses neither ionic transport within the liquids nor the formation of diffuse space-charge layers about their common interface. Moreover, as this model is hinged upon the presence of non-zero interfacial-charge density, it appears to be in contradiction with the aggregate electro-neutrality implied by ionic screening. Following a brief synopsis published by Baygents & Saville (Third International Colloquium on Drops and Bubbles, AIP Conference Proceedings, vol. 7, 1989, American Institute of Physics, pp. 7–17) we systematically derive here the macroscale description appropriate for leaky dielectric liquids, starting from the primitive electrokinetic equations and addressing the double limit of thin space-charge layers and strong fields. This derivation is accomplished through the use of matched asymptotic expansions between the narrow space-charge layers adjacent to the interface and the electro-neutral bulk domains, which are homogenized by the strong ionic advection. Electrokinetic transport within the electrical ‘triple layer’ comprising the genuine interface and the adjacent space-charge layers is embodied in effective boundary conditions; these conditions, together with the simplified transport within the bulk domains, constitute the requisite macroscale description. This description essentially coincides with the familiar equations of Melcher & Taylor (Annu. Rev. Fluid Mech., vol. 1, 1969, pp. 111–146). A key quantity in our macroscale description is the ‘apparent’ surface-charge density, provided by the transversely integrated triple-layer microscale charge. At leading order, this density vanishes due to the expected Debye-layer screening; its asymptotic correction provides the ‘interfacial’ surface-charge density appearing in the Taylor–Melcher model. Our unified electrohydrodynamic treatment provides a reinterpretation of both the Taylor–Melcher conductivity-ratio parameter and the electrical Reynolds number. The latter, expressed in terms of fundamental electrokinetic properties, becomes only for intense applied fields, comparable with the transverse field within the space-charge layers; at this limit the asymptotic scheme collapses. Surface-charge advection is accordingly absent in the macroscale description. Owing to the inevitable presence of (screened) net charge on the genuine interface, the drop also undergoes electrophoretic motion. The associated flow, however, is asymptotically smaller than that corresponding to the Taylor–Melcher circulation. Our successful matching procedure contrasts the analysis of Baygents & Saville, who considered more general electrolytes and were unable to directly match the inner and outer regions. We discuss this difference in detail.

The Taylor–Melcher leaky dielectric model as a macroscale electrokinetic description

We analyze the transport of a point-size Brownian particle under the influence of a constant and uniform force field through a slowly varying periodic channel whose cross-sectional area variations represent effective "entropy barriers." Using generalized Taylor-Aris dispersion (macrotransport) theory for spatially periodic media, we compute the mean velocity and effective diffusion coefficient (dispersivity) describing the long-time global transport of the particle. Systematic asymptotic perturbation analysis illuminates the transport process occurring in the strong-field limit, notably the role of the mean-squared channel roughness. The results thus obtained compare favorably with Brownian dynamics simulations over the full range of driving forces.

Force-driven transport through periodic entropy barriers

The electrophoretic motion of a conducting particle, driven by an induced-charge mechanism, is analyzed. The dependence of the motion upon particle shape is embodied in two tensorial coefficients that relate the particle translational and rotational velocities to the externally applied electric field. The coefficients are represented as surface integrals of the electric potential over the particle boundary, thereby eliminating the need to solve the flow field. Nonspherical particles may translate and∕or rotate in response to the imposed field, even if their net electric charge vanishes.

Induced-charge electrophoresis of nonspherical particles

The electrophoretic motion of a sphere resulting from an applied electric field directed parallel to a nearby plane wall is analysed for the case of a small sphere-wall gap width. The thin-Debye-layer approximation is employed. Using matched asymptotic expansions, the fluid domain is separated into an 'inner' (gap-scaled) region, wherein the electric field and velocity gradients are large, and an 'outer' (sphere-scaled) region, wherein field variations are moderate. Asymptotic expressions for the force and torque acting on the sphere are obtained using a reciprocal theorem, thereby avoiding the need to explicitly solve the pertinent Stokes equations. These expressions, as well as the sphere's electrophoretic mobility, become unbounded for near-contact separations. The present asymptotic solution complements existing 'exact' bipolar-coordinate eigenfunction expansions, which are numerically suitable only for O(1) gap thicknesses

Ehud Yariv

Papers

“Force-free” electrophoresis?

The Taylor–Melcher leaky dielectric model as a macroscale electrokinetic description

Force-driven transport through periodic entropy barriers

Induced-charge electrophoresis of nonspherical particles

Near-contact electrophoretic motion of a sphere parallel to a planar wall