If you can follow their position as a function of time, the diffusivity k can be measured via = (k/2d) t, where d is the dimensionality, R is the displacement since time t=0. Obviously, this assumes that the problems is governed by Fick's law. Otherwise, a constant diffusivity does not apply.
Hello
In general, diffusion is transport resulting from concentration gradients (or, more accurately, chemical potential gradients). In the simples case, such transport can be described by the Ficks law. Also, Brownian (thermal) motion can be described as so-called self-diffusion.
However, when you have coalescence of droplets, the main driving force will be changes in the surface tension and possibly also interfacial tension. You will also have significant convection fluxes. So I do not think that your problem can be described by diffusion equations.
Yes, diffusion will contribute to the equilibration of concentrations in the coalesced droplet, but I doubt that you can obtain a reasonable estimate of the initial concentration distribution after coalescence.
Regards
Josef
If these two droplets have matters, which are in-miscible then the whole coalescent behavior can be explained by the criterion that the surface free energy minimization while keeping volumes invariant . Where the specific interface free energy between two liquids plays important role as such that it should be less than the sum over their specific surface free energies, Roughly:
4Pi fa Ra^2 + 4Pi fb Rb^2 > Xa Pi fa Rg^2 + Xb Pi fb Rg^2 + fab Pi Rab^2
where I have assumed that two spherical droplets having specific free energies fa and fb (Helmholtz) where collapse and for a spherical giant droplet with radius Rg having specific interfacial free energy fab with circular cross Section. Xa and X b volume fractions scaled by geometric factor. Rab interface radius, which is related to the Xa or Xb with geometric factor, where the sum of which is unity.
If they are miscible definitely convection and diffusion currents enter into the scenario to reach the final non-equilibrium stationary state, which involves not only surface free energies but also the bulk free energies as such that Global free energy reduction should be achieved at the end.
- Badges
- Science topic