In the present study, analytical solutions are obtained for two-dimensional advection dispersion equation for conservative solute transport in a semi-infinite heterogeneous porous medium with pulse type input point source of uniform nature. The change in dispersion parameter due to heterogeneity is considered as linear multiple of spatially dependent function and seepage velocity whereas seepag...

A novel numerical method is presented for the simulation of flow in porous media, based on a mesoscopic-scale modelling using smoothed particle hydrodynamics. The method is demonstrated to provide encouraging results for both saturated and unsaturated porous media flow. The Darcy law is confirmed for low drift velocities in a saturated medium, while nonlinear behaviour is observed for higher va...

In tissue engineering, porous biodegradable scaffolds are used as templates for regenerating required tissues. With the advances in computational tools, many modeling approaches have been considered. For example, fluid flow through porous medium can be modeled using the Brinkman equation where permeability of the porous medium has to be defined. In this review, we summarize various models recen...

Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is modeled by generalizing the porous diffusion equation with a time-dependent diffusion coefficient equivalent to a nonlinear rescaling of time.

Understanding the transport properties of a porous medium from a knowledge of its microstructure is a problem of great interest in the physical, chemical, and biological sciences. Using a first-passage time method, we compute the mean survival time tau of a Brownian particle among perfectly absorbing traps for a wide class of triply periodic porous media, including minimal surfaces. We find tha...