Infiltration through porous media

Kozeny-Carman theory for modeling of porous granular structures saturation with emulsion during imbibition process

The issue discussed in the current publication is a process of emulsions penetration in the granular media driven by the capillary force. The research work focuses on the study of rate and height of multiphase liquids penetration in a porous bed. Changes of the medium porosity and saturation level occurring as a result of pores obstruction by the droplets of an inner phase, were considered. The surfactant-stabilized emulsions with the different dispersed phase concentrations were investigated applying a classical wicking test. The modified version of Kozeny-Carman theory was proposed in order to describe the observed imbibition process in porous structures composed of spherical grains. This approach allowed to predict transport of emulsions considering an effect of bed saturation and porosity changes. In practice, the introduced concept can be appropriable in the numerous industries and scientific fields to predict the imbibition process of the multiphase liquids in granular structures regarding variation of the investigated bed permeability.

Attachment and detachment rate distributions in deep-bed filtration

We study the transport and deposition dynamics of colloids in saturated porous media under unfavorable filtering conditions. As an alternative to traditional convection-diffusion or more detailed numerical models, we consider a mean-field description in which the attachment and detachment processes are characterized by an entire spectrum of rate constants, ranging from shallow traps which mostly account for hydrodynamic dispersivity, all the way to the permanent traps associated with physical straining. The model has an analytical solution which allows analysis of its properties including the long-time asymptotic behavior and the profile of the deposition curves. Furthermore, the model gives rise to a filtering front whose structure, stability, and propagation velocity are examined. Based on these results, we propose an experimental protocol to determine the parameters of the model.

Dissolution in a field

We study the dissolution of a solid by continuous injection of reactive "acid" particles at a single point, with the reactive particles undergoing biased diffusion in the dissolved region. When acid encounters the substrate material, both an acid particle and a unit of the material disappear. We find that the lengths of the dissolved cavity parallel and perpendicular to the bias grow as t(2/(d+1)) and t(1/(d+1)), respectively, in d dimensions, while the number of reactive particles within the cavity grows as t(2/(d+1)). We also obtain the exact density profile of the reactive particles and the relation between this profile and the motion of the dissolution boundary. The extension to variable acid strength is also discussed.