A review of shaped colloidal particles in fluids: anisotropy and chirality

Abstract

This review treats asymmetric colloidal particles moving through their host fluid under the action of some form of propulsion. The propulsion can come from an external body force or from external shear flow. It may also come from externally-induced stresses at the surface, arising from imposed chemical, thermal or electrical gradients. The resulting motion arises jointly from the driven particle and the displaced fluid. If the objects are asymmetric, every aspect of their motion and interaction depends on the orientation of the objects. This orientation in turn changes in response to the driving. The objects’ shape can thus lead to a range of emergent anisotropic and chiral motion not possible with isotropic spherical particles. We first consider what aspects of a body’s asymmetry can affect its drift through a fluid, especially chiral motion. We next discuss driving by injecting external force or torque into the particles. Then we consider driving without injecting force or torque. This includes driving by shear flow and driving by surface stresses, such as electrophoresis. We consider how time-dependent driving can induce collective orientational order and coherent motion. We show how a given particle shape can be represented using an assembly of point forces called a Stokeslet object. We next consider the interactions between anisotropic propelled particles, the symmetries governing the interactions, and the possibility of bound pairs of particles. Finally we show how the collective hydrodynamics of a suspension can be qualitatively altered by the particles’ shapes. The asymmetric responses discussed here are broadly relevant also for swimming propulsion of active micron-scale objects such as microorganisms.

Odd Diffusivity of Chiral Random Motion

“…In Figure A.1 we plot the steady-state simulation average, finding the resulting flux field to be uniform while the concentration field depends linearly on x and y, in agreement with equation (29) where C 0 = 0.01 and J 0 = 0.0001.…”

“…When D ⊥ = 0, as seen from equation ( 29), asymmetric accumulation occurs along the impermeable channel walls giving rise to a linear concentration profile not only in the x-direction but in the y-direction as well. This is also visualized in Figure A.1 following numerical simulations of equations ( 15)-( 18), demonstrating agreement with the second line of (29). Diffusion in a chiral active bath.…”

“…It has separately been identified in the context of convection-diffusion processes in chiral porous media [23], and in mathematical models of chiral random walks [24,25]. Several recent studies of chiral active matter have described novel diffusive characteristics [26][27][28][29][30] as well as the drift of particles perpendicular to an applied force [25,31,32]. In this article, we suggest a unifying framework within which to understand these phenomena.…”

Taylor dispersion of elongated rods

“…Understanding the transport of particles in fluid flow has led to the development of novel particle separation techniques, mixing strategies, and lab-on-a-chip devices [1,2]. In many practical cases of interest, the geometry of the particles themselves may be complex [3], and hence it is important to understand how their shape [4] influences their bulk transport. Herein, we study how the elongated shape of passive, rod-like Brownian particles affects their dispersion in a steady, two-dimensional Poiseuille flow.…”

Symmetry properties of nonlinear hydrodynamic interactions between responsive particles

“…One of the relevant questions is whether, for a pair of particles driven by the same force, the instantaneous interaction affects only the velocity of the pair's center of mass or also their relative velocity. The latter will influence, for example, the rate of particle collisions [7] and the stability of the collective dynamics [8,9], affecting setups such as fluidized-bed chemical reactors. In the absence of relative velocity for pairs, the collective dynamics depends nonlinearly on concentration [3], whereas in its presence the dependence is linear [8], i.e., much stronger for dilute suspensions.…”