Molecular Channel Characterization for a Rectangular Container With Reflecting and Absorbing Boundaries

The motion of molecules in a constrained fluid environment is defined by specified boundary conditions. Deriving analytical channel characterization of a bounded fluid environment is challenging as the solution must satisfy the given boundaries. In this letter, we derive the probability distribution function (PDF) of molecular motion inside a rectangular container with reflective and absorbing boundaries. Using the molecular motion's PDF, we deduce an analytical expression for the PDF of the first arrival time (FAT) of the molecules to an absorbing wall. Furthermore, we also evaluate the capacity for a temporally modulated molecular communication (MC) system in the bounded environment.