Diffusiophoresis of Colloidal Particles in the Limit of Very High Ionic Strength

Diffusiophoresis is the deterministic migration of a colloidal particle through an aqueous solution, driven by a gradient in concentration of a solute which experiences a long-range interaction with the colloidal particle.  The prefix “diffusio-“ refers to the need for the range of interaction between particle and solute to be large enough that any stress exerted along the particle surface by the concentration gradient can result in flow of the fluid relative to the particle. 

For charged colloidal particles and electrolytes, the particle-solute interaction is electrostatic and the range equals the Debye screen­ing length, which is inversely proportional to the square-root of ionic strength.  In the limit of very high ionic strengths, diffusiophoresis and electrophoresis are expected to vanish. 

We measured the rate of deposition of 320 nm anionic latex particles onto the face of a Nuclepore membrane having 100 nm pores, which separates a stirred solution having 4 M of NaCl from another stirred solution having 0.4 M of NaCl plus 5wt% latex.  The weight of deposit grew linearly with time over the 20 minutes of the experiment and corresponds to a particle speed of about 3 micron/sec.  A diffusion potential of 7 mV was also measured with the high-salt side being more positive. 

The observed dependence of the deposition speed and diffusion potential on the ratio of salt concentrations (see Fig. 1) is consistent with a mechanism in which the negatively charged latex particles undergo electrophoresis in the electric field induced by the salt gradient.  Given that the Debye length is only 0.15 nm (less than one water molecule) at 4 M, it is astonishing that the particle moves at all.  Indeed the measured electrophoretic mobility of the latex decreases monotonic­ally to zero at about 5 M of NaCl (see Fig. 2). 

One likely reason for our astonishment is that the equation used for calculating Debye length for a given salt concentration (as well as nearly all the models for electrophoresis and diffusio­phoresis) is based on the assumption that the electrolyte solutions are thermodynamically ideal.  But at these high salt concentration, steric repulsion between ions of finite size makes the solution highly nonideal. 

The observed persistence of diffusiophoretic transport of particles in high salinity gradients bodes well for the application of functionalized nanoparticles in enhanced oil recovery during which medium-salinity flood waters contact connate brines in reservoirs.* 

      

                                   Fig. 1                                                                               Fig. 2

 

---

* A. Kar et al., ACS Nano 9, 746-753 (2015).