Enhanced diffusiophoresis in dead-end pores with time-dependent boundary solute concentration

Abstract

The dead-end pore is a geometry common to studies of diffusiophoresis. In most works on diffusiophoresis in dead-end pores, the solute concentration at the pore inlet is quickly changed between two extreme values, yielding a steplike change in solute concentration. We explore - noting diffusiophoresis is inherently nonlinear and other boundary conditions are largely unexplored - the influence of a time-variable boundary solute concentration. We first define metrics for the efficiency of diffusiophoretic injection and withdrawal and characterize the steplike boundary condition. We then introduce a linear change in solute concentration over a variable timescale and comment on changes in efficiency. We find particle migration becomes linear in the limit of slow transitions relative to the timescale for solute diffusion and define an asymptotic efficiency. We further characterize oscillatory changes in the boundary solute concentration and the implications of the oscillation frequency, from slow (yielding linear particle migration) to fast (yielding nonlinear paricle migration) oscillation. The particle dynamics are distinct and can be tuned by adjusting the timescale for oscillation. Our findings are relevant to processes both in the laboratory, where they could inform the choice of timescale or oscillation frequency for changes in solute concentration, and in nature, where various events cause solute concentrations to change over distinct and disparate timescales.