eduKateSG · How Science Works
Choose your reading route
A dissolved-solute gradient can interact with the thin liquid region around a particle and make the particle drift relative to the surrounding water. The direction and speed depend on the solute, particle surface and solution conditions.
Contents
Understand the mechanism · Chapters 1–3
1. Watch the particles and the water separately
Work the calculation · Chapters 4–5
Test the explanation · Chapters 6–8
6. The walls can move the liquid too
A tiny suspended particle can move through water even when no pump is pushing a bulk stream through the observation region. One possible driver is a spatial change in dissolved-solute concentration. Motion arising from that gradient through interfacial interactions is called diffusiophoresis.
The defining comparison is particle velocity relative to the surrounding liquid. If a current simply carries the particle, that is advection. If random thermal motion spreads a population without a directional mean drift, that is Brownian diffusion. Real measurements may contain all three contributions.
Shin and colleagues’ dead-end-channel experiments showed that solute gradients could enhance or inhibit colloid entry under different conditions. A closed end prevents steady throughflow through that end; it does not prohibit diffusion, particle migration or local recirculation.
A particle surface changes the nearby distribution of dissolved species. With a concentration gradient along the surface, those interactions are no longer spatially balanced in the same way. The resulting interfacial stresses and liquid motion can produce migration of the particle.
For electrolytes, both electrical and nonelectrical contributions can matter. Positive and negative ions may diffuse at different rates, producing a diffusion electric field that couples to a charged particle. Concentration-dependent stresses in the interfacial ionic layer also contribute.
There is therefore no universal rule that every particle moves towards more salt. Surface charge, ion properties and solution chemistry affect the mobility. Experimental and theoretical work on pH-dependent diffusiophoresis demonstrates why surface potential should not be treated as an unchanging label attached to a material.
This guide considers externally imposed gradients. A particle that creates its own chemical gradient through a reaction introduces an additional source-and-transport problem.
For a commonly used dilute-electrolyte approximation, write the relative drift velocity as v = DDP ∇ln c. Here c is a positive salt concentration and DDP is a signed diffusiophoretic mobility with dimensions of diffusivity.
The notation ∇ln c means ∇c/c, or equivalently the gradient of ln(c/cref) for a fixed reference concentration. The logarithm does not require taking the logarithm of an unexplained dimensional quantity.
A positive mobility gives drift towards increasing concentration in this convention. A negative mobility reverses it. The model assumes that the appropriate mobility can be treated as known over the conditions considered; it is not a universal law for all solutes and concentrations.
Keep the mobility distinct from the particle’s Brownian diffusion coefficient. Both can have units m²/s, but one relates directed drift to a solute gradient while the other describes random spreading.
Original teaching example. Across a 100-micrometre region, suppose concentration follows an exponential profile rising from c₀ to 2c₀. Then the logarithmic gradient is constant: ln 2 divided by 100 micrometres, or approximately 6931 m−1.
Assign DDP = 2.0 × 10−10 m²/s. The predicted relative speed is 1.386 × 10−6 m/s, or 1.386 micrometres per second. Over ten seconds it gives a 13.86-micrometre displacement if the gradient and mobility remain constant along the path.
The exponential profile was chosen deliberately. A linear concentration profile has constant ∇c but a varying ∇ln c. Using the same end concentrations does not make the local drift identical everywhere.
If the endpoint ratio becomes four rather than two over the same length, the speed doubles because ln 4 = 2 ln 2. If every concentration is doubled while the ratio stays fixed, this constant-mobility model predicts unchanged speed. A real mobility may change with concentration, so that last comparison is a model test.
| Concentration ratio across 100 micrometres | Assigned mobility | Predicted relative speed |
|---|---|---|
| 2 | 2.0 × 10⁻¹⁰ m²/s | 1.386 micrometres/s |
| 4 | 2.0 × 10⁻¹⁰ m²/s | 2.773 micrometres/s |
Give the particle a hypothetical one-dimensional Brownian diffusion coefficient D = 0.50 micrometres squared per second. Over ten seconds its root-mean-square random displacement about the mean is √(2Dt) = √10 ≈ 3.16 micrometres.
That spread is smaller than the 13.86-micrometre mean drift in our example, but individual paths remain irregular. At very short times, drift displacement scales as t while diffusive spread scales as √t. A convincing directional trend may require a population of trajectories rather than one apparently purposeful particle.
The solute gradient also evolves by diffusion unless maintained. A rough solute diffusion time across length L is L²/Ds. With L = 100 micrometres and assigned Ds = 1000 micrometres squared per second, this scale is ten seconds.
Thus our constant-gradient ten-second displacement needs a maintained profile or a suitably justified approximation. A calculated velocity is not automatically a long-time trajectory.
Solute gradients can interact with channel walls and drive diffusioosmotic liquid motion. A particle then experiences both the surrounding flow and its own relative phoretic drift. The measured laboratory velocity must include both.
Original work on merging solute streams investigated wall-driven recirculation and three-dimensional particle dynamics. It illustrates why a visually simple concentration arrangement can produce a complicated trajectory field.
Measure or constrain background flow, compare particle types, and reverse the gradient where the chemistry allows a meaningful comparison. A result that changes with surface chemistry can help distinguish interfacial drift from a common current.
Neither an immobile-looking liquid nor a closed channel end is sufficient proof that fluid velocity vanishes everywhere. Local return paths can exist even when the net volumetric flow through a cross-section is zero.
A useful experiment records the imposed solute history, particle concentration profiles and trajectories over time. Controls include a uniform-concentration case and a case with a reversed or altered gradient. Temperature, pH and changes in particle aggregation must be considered.
Research on time-variable inlet concentrations explores how the history of the imposed boundary condition affects dead-end-pore transport. A single final salt difference is not a full account of the driving experienced by particles.
A pore-scale entrainment study connects individual colloid motion to trapping in dead-end regions. Entry, persistence and eventual removal are separate outcomes; improved entry is not automatically improved clearance.
For a classroom analysis, compare two invented drift histories with equal peak speed but different duration. Integrating speed over time immediately shows why peak gradient alone need not determine the total displacement.
Does a particle moving towards salt prove diffusiophoresis? No. Bulk flow or other forces may move it in the same direction. The relevant evidence separates relative drift from the liquid motion.
Does a negative mobility violate diffusion? No. It specifies a direction of particle drift in response to the solute gradient; it is not a negative Brownian diffusion coefficient.
Can the constant-gradient calculation run forever? Not in a finite, relaxing system without maintaining the gradient. Geometry, gradient evolution and boundaries eventually matter.
Continue to Fluid Dynamics for advection and transport. The habit to retain is to name what moves, relative to what, and which gradient supplies the driving.