The diffusion coefficient of a swollen microgel particle

The drag on a permeable particle traversing through a Newtonian liquid is calculated. This is in terms of a single dimensionless group, Da, the Darcy number, which relates the particle permeability to the radius. For small values of the Darcy number the solution reverts to the well-known Stokes drag for smooth hard particles. For larger values of the Darcy number the drag is reduced. This drag allows calculation of the diffusion coefficient of such particles, again as a function of the Darcy number. The results are discussed in relation to microgel particles, which display swelling under certain conditions. The size of such particles is typically measured with dynamic light scattering, which measures the diffusion coefficient of particles and as such the analysis presented here shows the conditions under which dynamic light scattering is accurate. The Darcy number for microgel particles is estimated to be on the order of 10(-7).