Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia

Cells or bacteria carrying cilia on their surface show many striking features : alignment of cilia in an array, two-phase asymmetric beating for each cilium, coordination between cilia and existence of metachronal waves with a constant phase difference between two adjacent cilia. We give simple theoretical arguments based on hydrodynamic coupling and an internal mechanism of the cilium derived from the behavior of a collection of molecular motors, to account qualitatively for these cooperative features. Hydrodynamic interactions can lead to the alignment of an array of cilia. We study the effect of a transverse external flow and obtain a two-phase asymmetrical beating, faster along the flow and slower against the flow, proceeding around an average curved position. We show that an aligned array of cilia is able to spontaneously break the left-right symmetry and to create a global average flow. Metachronism arises as a local minimum of the beating threshold and leads to a rather constant flow

Phase separation and nucleation in mixtures of particles with different temperatures

Differences in activities in colloidal particles are sufficient to drive phase separation between active and passive (or less active) particles, even if they have only excluded volume interactions. In this paper, we study the phase separation kinetics and propose a theory of phase separation of colloidal mixtures in the diffusive limit. Our model considers a mixture of diffusing particles coupled to different thermostats, it thus has a non-equilibrium nature due to the temperature differences. However, we show that indeed the system recovers an effective equilibrium thermodynamics in the dilute limit. We obtain phase diagrams showing the asymmetry in concentrations due to activity differences. By using a more general approach, we show the equivalence of phase separation kinetics with the well known Cahn-Hilliard theory. On the other hand, higher order expansions in concentration indicate the emergence of non-equilibrium effects leading to a breakdown of the equilibrium analogy. We lay out the general theory in terms of accessible parameters which we demonstrate by several applications. In this simple formalism, we capture a positive surface tension for hard spheres}, and interesting scaling laws for interfacial properties, droplet growth dynamics, and phase segregation conditions. \rev{Several of our results are in agreement with existing numerical simulations while we also propose testable predictions.Comment: Published version, 19 pages (main text+appendix), 4 figure

A Drop of Active Matter

We study theoretically the hydrodynamics of a fluid drop containing oriented filaments endowed with active contractile or extensile stresses and placed on a solid surface. The active stresses alter qualitatively the wetting properties of the drop, leading to new spreading laws and novel static drop shapes. Candidate systems for testing our predictions include cytoskeletal extracts with motors and ATP, suspensions of bacteria or pulsatile cells, or fluids laden with artificial self-propelled colloids.Comment: submitted to J Fluid Mec

Long-time diffusion and energy transfer in polydisperse mixtures of particles with different temperatures

Evidence suggests that the transport rate of a passive particle at long timescales is enhanced due to interactions with the surrounding active ones in a size- and composition-dependent manner. Using a system of particles with different temperatures, we probe these effects in dilute solutions and derive long-time friction and self-diffusion coefficients as functions of volume fractions, sizes and temperatures of particles in $d=2$ and 3 dimensions. Thus, we model excluded-volume interactions for nonequilibrium systems but also extend the scope to short-range soft potentials and compare our results to Brownian-dynamics simulations. Remarkably, we show that both viscosity and energy flux display a nonlinear dependence on size. The simplicity of our formalism allows to discover various interesting scenarios that can be relevant for biological systems and active colloids.Comment: Published version, main text and supplemental materia

Interfacial Instability of Charged End-Group Polymer Brushes

We consider a polymer brush grafted to a surface (acting as an electrode) and bearing a charged group at its free end. Using a second distant electrode, the brush is subject to a constant electric field. Based on a coarse-grained continuum model, we calculate the average brush height and find that the brush can stretch or compress depending on the applied field and charge end-group. We further look at an undulation mode of the flat polymer brush and find that the electrostatic energy scales linearly with the undulation wavenumber, $q$. Competition with surface tension, scaling as $q^2$, tends to stabilize a lateral $q$-mode of the polymer brush with a well-defined wavelength. This wavelength depends on the brush height, surface separation, and several system parameters.Comment: 6 pages, 3 figure