Inertial Memory Effects in Molecular Transport Across Nanoporous Membranes

This paper presents two extensions of Fick’s second law, enabling the formulation of causal particle transport models across nanoporous membranes that account for inertial memory effects. The proposed models have been applied to analyze the influence of inertial memory on the cumulative amount of particles delivered through the membrane. The results of the derived models were compared with each other and with those obtained from classical theory. It was demonstrated that the inertial memory of the membrane induces two distinct regimes of particle propagation, thereby increasing the time required for the cumulative particle delivery to reach steady state. These findings could have significant implications for understanding cell physiology, developing drug delivery systems, and designing nanoporous membranes for various applications.