CFD simulation of mass transfer in PermeaPad® 96-well plate
Ophthalmic drug delivery is limited by rapid precorneal clearance and short drug residence time on the ocular surface. In vitro permeation models help evaluate formulation performance and reduce reliance on animal studies, but conventional systems often neglect the influence of hydrodynamics on mass transport and membrane permeation [1]. In this work, a multiphysics computational model was developed in COMSOL Multiphysics® to investigate drug permeation across a corneal surrogate membrane in a geometry representative of a single well of a PermeaPad® 96-well plate. Based on previous studies [2] showing predominantly laminar flow in orbitally shaken 96-well plates, this assumption was adopted here. The model couples laminar fluid flow with transport of dilute species to study how rotationally induced hydrodynamics affect permeation of dexamethasone sodium phosphate (DEX) from ophthalmic solutions. Results were validated against experimental permeated mass data, supporting formulation screening and optimization of in vitro ophthalmic permeation testing. The geometry is a 3D cylindrical donor (inner cylinder) and acceptor (outer cylinder) chamber, with a membrane interface at the base of the inner compartment (Figure 1). Solute transport used the Transport of Dilute Species interface (Fick's law) with a user-controlled diffusion coefficient for sensitivity analysis, including sink conditions and permeability limits (Figure 2); initial concentration was high in the donor and near-zero in the acceptor. Hydrodynamics were introduced via the Laminar Flow interface, driven by a time-dependent angular velocity of the inner domain with a smooth startup ramp (Figure 3), coupled to species transport through convective transport. Transient simulations used an adaptive time-dependent solver with a constrained initial time step to resolve early-time gradients. Parametric sweeps evaluated chamber height, transport properties, rotational speed, and periodic operation. Cumulative permeated mass was obtained by integrating acceptor-domain concentration for comparison with experiments, alongside analyses of convection-driven mass transfer and deviations from ideal sink conditions. Species transport was dominated by diffusive flux (Figure 4). Cumulative permeated mass in the acceptor compartment (red line, Figure 2) showed periodic decreases every 25 min, reproducing the experimental sampling procedure in which the acceptor medium was partially refreshed to maintain sink conditions; this was implemented as a periodic explicit event reducing acceptor concentration to 95% of its current value. Comparing simulated static-condition permeation profiles with experiments gave a fitted effective diffusion coefficient for DEX, Dsim,DEX = 10⁻⁸ m² s⁻¹, exceeding the literature value for DEX in aqueous solution, Dexp,DEX = 4.7 · 10⁻⁹ m² s⁻¹ [3]. This discrepancy suggests the fitted coefficient captures additional effects not explicitly resolved, such as membrane porosity, underscoring the importance of accurately accounting for hydrodynamics in in vitro ophthalmic permeation systems. A CFD-based multiphysics model was developed to investigate drug permeation across a corneal-surrogate membrane in a PermeaPad® 96-well system, coupling laminar flow and dilute species transport to evaluate hydrodynamic effects on permeation. Simulated permeation agreed well with experimental observations and enabled estimation of an effective DEX diffusion coefficient under static conditions. Future work will study pulse-like shaking of the rotating frame versus continuous rotation to assess the role of blinking in ophthalmic drug delivery.
