text: In many applications of diffusiophoresis, the motion is driven by gradients in the concentration of a salt (electrolyte) concentration, such as sodium chloride in water. Colloidal particles in water are typically charged, and there is an electrostatic potential, called a zeta potential at their surface. This charged surface of the colloidal particle interacts with a gradient in salt concentration, and this gives rise to diffusiophoretic velocity  given by
  where  is the permittivity of water,  is the viscosity of water,  is the zeta potential of the colloidal particle in the salt solution, is the reduced difference between the diffusion constant of the positively charged ion, , and the diffusion constant of the negatively charged ion, , and  is the salt concentration. is the gradient, i.e., rate of change with position, of the logarithm of the salt concentration, which is equivalent to the rate of change of the salt concentration, divided by the salt concentration – it is effectively one over the distance over which the concentration decreases by a factor of e. The above equation is approximate, and only valid for 1:1 electrolytes such as sodium chloride.
  Note that there are two contributions to diffusiophoresis of a charged particle in a salt gradient, which give rise to the two terms in the above equation for . The first is due to the fact that whenever there is a salt concentration gradient, then unless the diffusion constants of the positive and negative ions are exactly equal to each other, there is an electric field, i.e., the gradient acts a little like a capacitor. This electric filed generated by the salt gradient drives electrophoresis of the charged particle, just as an externally applied electric field does. This gives rise to the first term in the equation above, i.e., diffusiophoresis at a velocity .
  The second part is due to the surface free energy of the surface of a charged particle, decreasing with increasing salt concentration, this is a similar mechanism to that found in diffusiophoresis in gradients of neutrial substances. This gives rise to the second part of the diffusiophoretic velocity . Note that this simple theory predicts that this contribution to the diffusiophoretic motion is always up a salt concentration gradient, it always moves particles towards higher salt concentration. By contrast, the sign of the electric-field contribution to diffusiophoresis depends on the sign of . So for example, for a negatively charged particle, , and if the positively charged ions diffuse faster than the negatively charged ones, then this term will push particles down a salt gradient, but if it is the negatively charged ions that diffuse faster, then this term pushes the particles up the salt gradient.