Guiding isotropic active fluids with anisotropic friction

Abstract

Inspired by recent experiments of cells accumulating on anisotropic substrates, we study a two-dimensional, compressible, isotropic, active fluid in the presence of anisotropic friction. We find that regions of anisotropic friction that are patterned as positive topological defects may drive accumulation of an active fluid into a clump, but the robustness of this behavior depends on the initial configuration. If the initial azimuthal symmetry is sufficiently broken, we find that patterning asymmetry can instead lead to circular motion of accumulated clumps. We develop an approximate analytical model to qualitatively explain the motion. Finally, we use our simplified model to design a substrate pattern that creates directed motion of accumulated clusters along a given path.

Figures (10)

• Figure 1: (a) Density field (color) and velocity field (arrows) of a simulation of Eqs. \ref{['eqn:CEqn']} and \ref{['eqn:VEqn']} with parameters listed in Table \ref{['tbl:Params']} and $\Delta = 0$. (b) Slice across the $x$-axis of the density field from (a). (c) Slice across the $x$-axis of the $x$-component of the velocity field from (a).
• Figure 2: (a) Schematic of the effect of anisotropic friction on the velocity generated by the active force of a circular cluster. Isotropic friction yields an isotropic velocity, while anisotropy changes the velocity distribution along the cluster. (b) Simulated density field (color) and velocity field (arrows) for parameter values listed in Table \ref{['tbl:Params']} with constant anisotropic friction, $\mathbf{\hat{e}}_{\parallel}=\mathbf{\hat{x}}$. (c) Plots of the linear growth rate, Eq. \ref{['eqn:AnisotropicGrowthRate']}, for the simulation in (b). The blue curve shows $\varphi = 0$ while the orange curve shows $\varphi = \pi/2$. (d) Simulated density field and velocity field for the same parameters as in (b), except $\Delta = 10$. (e) Linear growth rate for the simulation in (d). Here $\omega(|\mathbf{k}|,\varphi=\pi/2) < 0$ for all $|\mathbf{k}|$.
• Figure 3: Visualization of easy axis patterns for topological defects with $\theta_0 = 0, \pi/4,$ and $\pi/2$.
• Figure 4: (a) Simulated steady state density field (color) and velocity field (arrows) with anisotropic friction patterned as a topological defect with $\theta_0 = \pi/4$. (b) Radial cut of steady state density fields for simulations with varying $\theta_0$. (c) Radial cut of the radial component of the steady state velocity field for simulations with varying $\theta_0$. (d) Radial cut of the azimuthal component of the steady state velocity field for simulations with varying $\theta_0$.
• Figure 5: Time snapshots of simulated density field (color) and velocity field (arrows) for anisotropic friction patterned as a topological defect with $\theta_0 = \pi/2$ initialized with a symmetric ring of high density, Eq. \ref{['eqn:RingDensity']}. The first snapshot shows the initial condition while the second snapshot shows the final, stable configuration.