Diffusiophoresis is the spontaneous motion of colloidal particles or molecules in a fluid, induced by a concentration gradient of a different substance. In other words, it is motion of one species, A, in response to a concentration gradient in another species, B. Typically, A is colloidal particles which are in aqueous solution in which B is a dissolved salt such as sodium chloride, and so the particles of A are much larger than the ions of B. But both A and B could be polymer molecules, and B could be a small molecule. For example, concentration gradients in ethanol solutions in water move 1 μm diameter colloidal particles with diffusiophoretic velocities of order 0.1 to 1 μm/s, the movement is towards regions of the solution with lower ethanol concentration (and so higher water concentration). Both species A and B will typically be diffusing but diffusiophoresis is distinct from simple diffusion: in simple diffusion a species A moves down a gradient in its own concentration.
Diffusioosmosis, also referred to as capillary osmosis, is flow of a solution relative to a fixed wall or pore surface, where the flow is driven by a concentration gradient in the solution. This is distinct from flow relative to a surface driven by a gradient in the hydrostatic pressure in the fluid. In diffusioosmosis the hydrostatic pressure is uniform and the flow is due to a concentration gradient.
Diffusioosmosis and diffusiophoresis are essentially the same phenomenon. They are both relative motion of a surface and a solution, driven by a concentration gradient in the solution. This motion is called diffusiophoresis when the solution is considered static with particles moving in it due to relative motion of the fluid at the surface of these particles. The term diffusioosmosis is used when the surface is viewed as static, and the solution flows.
A well studied example of diffusiophoresis is the motion of colloidal particles in an aqueous solution of an electrolyte solution, where a gradient in the concentration of the electrolyte causes motion of the colloidal particles. Colloidal particles may be hundred of nanometres or larger in diameter, while the interfacial double layer region at the surface of the colloidal particle will be of order the Debye length wide, and this is typically only nanometres. So here, the interfacial width is much smaller than the size of the particle, and then the gradient in the smaller species drives diffusiophoretic motion of the colloidal particles largely through motion in the interfacial double layer.
Diffusiophoresis was first studied by Derjaguin and coworkers in 1947.
Applications of diffusiophoresis
Diffusiophoresis, by definition, moves colloidal particles, and so the applications of diffusiophoresis are to situations where we want to move colloidal particles. Colloidal particles are typically between 10 nanometres and a few micrometres in size. Simple diffusion of colloids is fast on length scales of a few micrometres, and so diffusiophoresis would not be useful, whereas on length scales larger than millimetres, diffusiophoresis may be slow as its speed decreases with decreasing size of the solute concentration gradient. Thus, typically diffusiophoresis is employed on length scales approximately in the range a micrometre to a millimetre. Applications include moving particles into or out of pores of that size, and helping or inhibiting mixing of colloidal particles.
In addition, solid surfaces that are slowly dissolving will create concentration gradients near them, and these gradients may drive movement of colloidal particles towards or away from the surface. This was studied by Prieve in the context of latex particles being pulled towards, and coating, a dissolving steel surface.
Relation to thermophoresis, multicomponent diffusion and the Marangoni effect
Diffusiophoresis is an analogous phenomenon to thermophoresis, where a species A moves in response to a temperature gradient. Both diffusiophoresis and thermophoresis are governed by Onsager reciprocal relations. Simply speaking, a gradient in any thermodynamic quantity, such as the concentration of any species, or temperature, will drive motion of all thermodynamic quantities, i.e., motion of all species present, and a temperature flux. Each gradient provides a thermodynamic force that moves the species present, and the Onsager reciprocal relations govern the relationship between the forces and the motions.