Analytical models for one-dimensional virus transport in saturated porous media

Abstract

Analytical solutions to two mathematical models for virus transport in one-dimensional homogeneous, saturated porous media are presented, for constant flux as well as constant concentration boundary conditions, accounting for first-order inactivation of suspended and adsorbed (or filtered) viruses with different inactivation constants. Two processes for virus attachment onto the solid matrix are considered. The first process is the nonequilibrium reversible adsorption, which is applicable to viruses behaving as solutes; whereas, the second is the filtration process, which is suitable for viruses behaving as colloids. Since the governing transport equations corresponding to each physical process have identical mathematical forms, only one generalized closed-form analytical solution is developed by Laplace transform techniques. The impact of the model parameters on virus transport is examined. An empirical relation between inactivation rate and subsurface temperature is employed to investigate the effect of temperature on virus transport. It is shown that the differences between the two boundary conditions are minimized at advection-dominated transport conditions.