Simple models for the trapping of charged particles and macromolecules by diffusiophoresis in salt gradients

TL;DR

This work analyzes how diffusiophoresis can trap charged particles and macromolecules in salt gradients generated by a static salt source. The authors derive a simple, dimensionally agnostic framework in which the steady-state local concentration $n$ scales as $n \propto c_{\mathrm S}^{\rho}$ with $\rho = \Gamma/D_{\mathrm PART}$, and show that near the source $n(r) \sim r^{-\rho}$ for $r \ll \lambda_X$. They demonstrate that increasing $\rho$ (which grows with particle size) and the characteristic length $\lambda_X$ enhances localisation, predicting that large particles and biomacromolecules like DNA are readily trapped. The results offer a tractable model for concentrating, manipulating, and potentially inducing interactions or condensation of macromolecules in salt gradients, with applications in separation and microfluidic systems.

Abstract

We study the trapping of charged particles and macromolecules (such as DNA) in salt gradients in aqueous solutions. The source for the salt gradient can be as simple as a dissolving ionic crystal, as shown by McDermott et al. [Langmuir 28, 15491 (2012)]. Trapping is due to a competition between localisation due to diffusiophoresis in the salt gradient, and spreading out by diffusion. The size of the trap is typically 1 to 100 micrometres. We further predict that at steady state, the particle (macromolecule) number density is a power law of the salt concentration, with an exponent that is the ratio of the diffusiophoretic mobility to the diffusion coefficient of the trapped species. This ratio increases with size and typically becomes much greater than 1 for particles or macromolecules with hydrodynamic radii of hundreds of nanometres and above. Thus large particles or macromolecules are easily caught and trapped at steady state by salt gradients.

Figures (5)

• Figure 1: Schematic of our model system: a spherically symmetric salt source (blue) with particles moving towards the source (green), or away from it (red), depending on the sign of the DP mobility. The shaded rings show the concentration gradient of salt that decreases with increasing distance from the source.
• Figure 2: Plot of the DP drift speed as a function of radial position $r$, for two example values of the DP mobility$\Gamma$. The green dashed line illustrates a slope of $r^{-1}$. The system is spherically symmetric with a source of radius $r_{\rm{SOURCE}}=10µm$. The crossover length scale $\lambda_X=100µm$ and is shown by a vertical dotted line.
• Figure 3: Plot of the diffusiophoretic drift speed as a function of position $x$, for two example values of the DP mobility$\Gamma$. The system is one-dimensional, and of length $L=100µm$. The salt concentrations are held fixed at $c_1$ at $x=0$ and $c_0$ at $x=L$, with $c_1/c_0=10$.
• Figure 4: Plot of the reduced concentration as a function of radial position $r$, for systems of species that both diffuse and move due to DP. The system is spherically symmetric with a source of radius $r_{\rm{SOURCE}}=10µm$. The concentrations are reduced with respect to their values at the inner limit. In (a) the curves are for four values of $\rho$, and a common crossover length scale $\lambda_X=100µm$ --- shown by a vertical dotted line. In (b) the curves are for two values of $\lambda_X$, with a common exponent $\rho=3$. In both (a) and (b) the dashed lines are the asymptotic power laws $\sim 1/r^{\rho}$.
• Figure 5: Plot of the reduced concentration as a function of position $x/L$, for systems of species that both diffuse and move due to DP. The system is one-dimensional, and of length $L$. The salt concentrations are held fixed at $c_1$ at $x=0$ and $c_0$ at $x=L$, with $c_1/c_0=10$.