This work has come about as a result of our investigation on the ocular fluid dynamics and transport process in a partially liquefied vitreous humor. The liquid is modeled as a sphere with Stokes flow while the surrounding infinite porous region is described by Brinkman flow and it is compared with the Darcy-Darcy model in which the liquefied region is a thousands times premeable.
First figure, shows the isobars and the streamlines for the Stokes-Brinkman model and the one below is the same results for Darcy-Darcy model. In the Stokes-Brinkman model streamlines are slightly curved when enterning the liquid region while in the Darcy-Darcy model they are completely straight.
To check the validity of the Darcy-Darcy model, the volumetric flow rates entering the liquid sphere have been calculated for both Stokes-Brinkman and Darcy-Darcy models.
As it is depicted above, when the ratio of permeabilty is higher than 1000 the results in both models agree which validates the Darcy-Darcy model to some extent.
