Flow Characterization in a Partially Liquefied Vitreous Humor

Abstract

The purpose of this study is to systematically examine the basic fluid dynamics associated with a fully liquid region within a porous material. 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. The development here provides basic three-dimensional axisymmetric results on flow characterization and also serves to evaluate the limits of validity of Darcy flow analysis for the same geometry. In the Darcy flow model, the liquid region is also treated as a porous region with a much higher permeability. Therefore, both liquid and porous regions are modeled by Darcy’s law. Besides the analytical results from Brinkman–Stokes model, the simpler case of Darcy–Darcy flow for the same geometry has been provided. The results of both cases are compared and the differences between the two sets of results provide the range of validity of our computational model (Khoobyar et al. in J Heat Transf 144:031208, 2022). Some interesting fluid-dynamical aspects of the system are observed through the analysis. For the Darcy–Darcy system, the liquid region velocity is uniform throughout, as expected for potential flow. With the Brinkman–Stokes model, the liquid region has a paraboloidal profile with the maximum possible peak value of six times the far-field velocity in the porous medium. With the liquid region having a lower resistance, the flow tends to converge there for both models as it seeks the path of least resistance. As for the validation of the Darcy–Darcy model, it is a good approximation as far as the exterior flow is concerned. However, the liquid region flow profiles for the two models are different as noted. The current Brinkman–Stokes model has led to explicit analytical solutions for the flow field for both regions. This has permitted an asymptotic analysis giving deeper insight into the flow characterization.