Rational Design of Two-Dimensional Colloidal Banding

Diffusiophoresis, i.e. the movement of particles in response to concentration gradient of a solute, causes particles to accumulate in regions due to a concentration gradient. This phenomenon is known as colloidal banding. Existing literature has largely focused on how particles respond to one-dimensional solute gradients. Here, we study colloidal banding in response to two-dimensional solute gradients generated by sources and sinks. First, we investigate colloidal banding in a dipole configuration, i.e., one source and one sink. We find that two timescales govern colloidal banding: the inter-dipole diffusion and the source/sink flux decay timescales. We observe that the balance of two timescales result in an optimum separation distance which maximizes particle enrichment. The optimum separation distance is governed by the partition coefficients and relative diffusivities of solute in the bulk solution and the source/sink regions. In a system with four sources and sinks, geometric asymmetry provides additional control over the attained banding structure, leading to further enriched configurations. In summary, our findings allow for rational design of two-dimensional source and sink configurations to control banding in diffusiophoretic particles.