Diffusiophoretic migration of colloidal particles in sucrose gradients

TL;DR

This work probes diffusiophoresis (DP) of neutral solutes in concentrated sucrose gradients using a dead-end microfluidic geometry to suppress parasitic flows. By tracking individual colloids and mapping sucrose concentration with Raman spectroscopy, the authors demonstrate DP-driven migration toward low solute concentration at speeds up to a few micrometers per second and show that a steric-exclusion mechanism with an exclusion length around 5 Å quantitatively accounts for the observed trajectories. The concentration dependence of the osmotic pressure Pi(C) and interdiffusion coefficient D(C) is shown to be essential for accurate modeling, and a comprehensive analysis separates DP from buoyancy- and diffusioosmotic contributions. The study provides a quantitative framework for neutral solute DP in concentrated regimes, with potential implications for biomolecule transport and industrial processing in high-sugar solutions.

Abstract

Diffusiophoresis (DP) refers to the migration of particles driven by a solute concentration gradient in a liquid. Observations in the case of molecular neutral solutes are rather scarce, due to the low drift velocities in dilute solutions, and the difficulty in distinguishing DP from other phenomena in concentrated solutions. We investigated experimentally DP of dispersed colloids driven by concentration gradients of sucrose in water at relatively high concentrations, $C \simeq 1$ mol L$^{-1}$. More precisely, we designed a microfluidic chip to impose a time-dependent sucrose gradient in dead-end microchannels with minimized parasitic flows. Significant migration of the particles toward the regions of low sucrose concentration has been observed, with velocities up to a few $μ$m s$^{-1}$. Particle tracking and Raman confocal spectroscopy were used to measure individual trajectories and the unsteady sucrose concentration profile respectively. The latter is correctly described by a diffusion equation, but with an interdiffusion coefficient that significantly depends on $C$ in the range of concentrations investigated. We then showed that a model of DP based on a steric exclusion of sucrose molecules from the particle surface with an exclusion length $R_i = 5 \pm 0.9$ angstrom (close to the characteristic size of the sucrose molecule), accounts for the observed trajectories. Possible sources for the observed scattering of our experimental data are finally discussed: Brownian motion and advection of the particles by bulk flows driven by diffusioosmosis at the channel walls and buoyancy.

Figures (9)

• Figure 1: DP migration of colloidal particles driven by a sucrose gradient in a dead-end microchannel. (a) Schematic 3D view of the dead-end pore geometry. (b) Sequence of experiments. The channels are initially filled with water and dispersed colloids ($t < 0$). At $t = 0$, a flow of sucrose at a concentration of $C_0$ is imposed in the main channel. The sucrose concentration gradient in the channel for $t > 0$ leads to colloid migration. (c) Schematic section view showing the drift of particles by the superimposition of DP at velocity $v_\mathrm{DP}$, advection by DO at velocity $v_\mathrm{DO}$, and advection by the buoyancy-driven velocity field $v_B$. $v_s$ is the DO slip velocity at the channel walls and $\mathbf{g}$ indicates the gravity field.
• Figure 2: Physical properties of aqueous sucrose solutions at $T=20\celsius$. (a) Specific volume $\nu$ vs. mass fraction $w_s$SucroseDataHandbook. The continuous line is the fit by eq \ref{['eq:volumespec']}. (b) Osmotic pressure $\Pi$ vs. molar concentration $C$. Black dots: literature data Starzak1997; dashed line: van't Hoff law; dashed-dotted line: ideal solution; red line: fit by eq \ref{['eq:Pivirial']}. (c) Viscosity $\eta$ against $C$Telis2007. The dotted line is a second-order polynomial fit.
• Figure 3: Design of the microfluidic chip. (a) Top view: $N=32$ dead-end channels of length $L=1$ mm and width $w=50µm$ connected to a main channel. The distance between adjacent channels is $50\um$. The width of the inlet channel is $200\um$. (b) Side view evidencing the different heights: $h=55\um$ for the Raman experiments shown in Figure \ref{['fig:RamanMap']}, and $h=9\um$ for the DP transport of particles. In both cases, $H_i=90\um$, $H \simeq 1\mm$ and the chip is immersed in a water bath.
• Figure 4: Calibration of the Raman measurements. Normalized Raman spectra for different aqueous sucrose solutions in the concentration range $C=0$--$1\mol\per L$ (blue to yellow). The inset shows the relative intensity $r$ of the Raman peak at $\tilde{\nu}=2920$--$2950\per\cm$ due to sucrose. The dotted line is a second-order polynomial fit.
• Figure 5: Particles trajectories from superimposed images from $t=0$ to $t=465s$, see Video S2 in Supporting Information (particle radius $a = 250nm$). Sucrose at a concentration $C_0 = 0.99\mol\per L$ is imposed in the main channel at $t=0$.