Diffusiophoresis in one-dimensional solute gradients

Abstract

The diffusiophoretic motion of suspended colloidal particles under one-dimensional solute gradients is solved using numerical and analytical techniques. Similarity solutions are developed for the injection and withdrawal dynamics of particles into semi-infinite pores. Furthermore, a method of characteristics formulation of the diffusion-free particle transport model is presented and integrated to realize particle trajectories. Analytical solutions are presented for the limit of small particle diffusiophoretic mobility Γ relative to the solute diffusivity D for particle motions in both semi-infinite and finite domains. Results confirm the build up of local maxima and minima in the propagating particle front dynamics. The method of characteristics is shown to successfully predict particle motions and the position of the particle front, although it fails to accurately predict suspended particle concentrations in the vicinity of sharp gradients, such as at the particle front peak seen in some injection cases, where particle diffusion inevitably plays an important role. Results inform the design of applications in which the use of applied solute gradients can greatly enhance particle injection into and withdrawal from pores.

Stratification of mixtures in evaporating liquid films occurs only for a range of volume fractions of the smaller component

“…3(b) converge on each other and on the yellow line marking the descending front. Similar localisation of particles due to diffusiophoresis is seen in systems where diffusiophoresis is due to salt gradients 24,26,40,41 . There this convergence is called focusing.…”

Cleaning by Surfactant Gradients: Particulate Removal from Porous Materials and the Significance of Rinsing in Laundry Detergency

“…Nevertheless, it has only recently been the subject of renewed interest due to the recognition that control of chemical gradients makes possible manipulation of colloidal particles in a wide range of circumstances [2]. For example, diffusiophoresis in salt gradients is highly efficacious at delivering micron-sized particles into dead-end pores, on time scales of minutes rather than the hours that would be required if relying on pure diffusion [3][4][5]. Electrolyte diffusiophoresis has been implicated as a mechanism for self-propelled 'active' colloids [6][7][8], and in the formation of exclusion zones around ion-exchange resins [9,10].…”

Microscale diffusiophoresis of proteins

“…This opens up the possibility to fit the peaks to extract these informations about the proteins. We can capture the physics in one dimensional space by introducing a dimensionless parameter 24 , η =…”