Dynamical design of spatial patterns of colloidal suspensions

TL;DR

This paper investigates how time-dependent external potentials influence the formation of spatial patterns in colloidal suspensions, revealing a method to design diverse patterns through controlled potential modulation.

Contribution

It introduces a dynamical density functional theory approach to predict and design spatial patterns in colloids using arbitrary time-dependent potentials.

Findings

Spatial patterns emerge from sinusoidal external potentials with time-dependent wavelengths.

Pattern envelopes follow a Bessel function depending on oscillation amplitude.

A general design strategy for creating various spatial patterns is proposed.

Abstract

We study the collective dynamics of colloidal suspensions in the presence of a time-dependent potential, by means of dynamical density functional theory. We consider a non-linear diffusion equation for the density and show that spatial patterns emerge from a sinusoidal external potential with a time-dependent wavelength. These patterns are characterized by a sinusoidal density with the average wavelength and a Bessel-function envelope with an induced wavelength that depends only on the amplitude of the temporal oscillations. As a generalization of this result, we propose a design strategy to obtain a family of spatial patterns using time-dependent potentials of practically arbitrary shape.