ANALYTICAL SOLUTION OF MICROPLASIC POLLUTANT TRANSFER THROUGH AQUIFER IN THE PRESENCE OF SOURCE/SINK

An exact analytical solution is developed for the governing one-dimensional advection–dispersion–reaction equation by first separating the steady-state contribution associated with the source/sink term from the transient concentration. The governing advection–dispersion–reaction equation is solved analytically by decomposing the solution into steady-state and transient components, followed by an exponential transformation to eliminate the advective first-derivative term and separation of variables to obtain an eigenfunction expansion for the transient concentration. Finally, we have found the analytical concentration distribution of microplastic pollutants as a function of space and time.This procedure yields an analytical series solution that explicitly describes the transient concentration field.The proposed solution also enables the source and sink cases to be examined within the same mathematical formulation. A positive source term represents continuous addition of microplastics to the aquifer, whereas a negative term represents removal. Consequently, the model can be used to investigate how external loading or removal modifies pollutant persistence, concentration levels, and spatial migration. The analytical expression additionally provides a benchmark for numerical simulations and facilitates sensitivity analysis without requiring repeated numerical discretization.