Effect of fluid velocity and particle size on the hydrodynamic diffusion layer thickness

Estimation of the concentration boundary layer adjacent to a flat surface using computational fluid dynamics

Dissolution-permeation (D/P) experiments are widely used during preclinical development due to producing results with better predictability than traditional monophasic experiments. However, it is difficult to compare absorption across in vitro setups given the propensity to only report apparent permeability. We therefore developed an approach to predict the concentration boundary layer for any D/P device by using computational fluid dynamics (CFD). The Navier-Stokes and continuity equation in 2D were solved numerically in MATLAB and by finite element methods in COMSOL v6.1 to predict the momentum [Formula: see text] and concentration ηg boundary layer for a flow over a flat plate, i.e. the classical Blasius boundary layer flow. A MATLAB algorithm was developed to calculate the edge of either boundary layer. The methodology to determine the concentration boundary layer based on Blasius's analysis provided an accurate estimate for both [Formula: see text] and ηg, resulting in, [Formula: see text] , at high Schmidt numbers (Sc ∼ 1000) within 14 % of the Blasius solution and 6.6 % of the accepted Schmidt number correlation ( [Formula: see text] ). The methodology based on the Blasius analysis of the concentration boundary layer using velocity and concentration profiles computed using CFD presented herein will enable characterization/analysis of complex D/P apparatuses used in preclinical development, where an analytical solution may not be available.

Particle Size, Dose, and Confinement Affect Passive Diffusion Flux through the Membrane Concentration Boundary Layer

The authors present a steady-state-, particle-size-, and dose-dependent dissolution-permeation model that describes particle dissolution within the concentration boundary layer (CBL) adjacent to a semipermeable surface. It is critical to understand how particle size and dose affect the behavior of dissolving particles in the presence of a CBL adjacent to a semipermeable surface both in vivo and in vitro. Control of particle size is ubiquitous in the pharmaceutical industry; however, traditional pharmaceutical assumptions of particle dissolution typically ignore particle dissolution within the length scale of the CBL. The CBL does not physically prevent particles from traveling to the semipermeable surface (mucus, epithelial barrier, synthetic membrane, etc.), and particle dissolution can occur within the CBL thickness (δC) if the particle is sufficiently small (∼dparticle ≤ δC). The total flux (the time rate transport of molecules across the membrane surface per unit area) was chosen as a surrogate parameter for measuring the additional mass generated by particles dissolving within the donor CBL. Mass transfer experiments aimed to measure the total flux of drug using an ultrathin large-area membrane diffusion cell described by Sinko et al. with a silicone-based membrane ( Mol. Pharmaceutics 2020, 17, (7) 2319-2328, DOI: 10.1021/acs.molpharmaceut.0c00040). Suspensions of ibuprofen, a model weak-acid drug, with three different particle-size distributions with average particle diameters of 6.6, 37.4, and 240 μm at multiple doses corresponding to a range of suspension concentrations with dimensionless dose numbers of 2.94, 14.7, 147, and 588 were used to test the model. Experimentally measured total flux across the semipermeable membrane/CBL region agreed with the predictions from the proposed model, and at a range of relatively low suspension concentrations, dependent on the average particle size, there was a measurable effect on the flux due to the difference in δC that formed at the membrane surface. Additionally, the dose-dependent total flux across the membrane was up to 10% higher than the flux predicted by the standard Higuchi-Hiestand dissolution model where the effects of confinement were ignored as described by Wang et al. ( Mol. Pharmaceutics 2012, 9 (5), 1052-1066, DOI: 10.1021/mp2002818).

A new modelling approach for dissolution of polydisperse powders

A new modelling approach for dissolution of polydisperse powders is developed within the framework of the classical Noyes-Whitney/Nernst-Brunner analysis. Its distinguishing feature is that the underlying continuous particle-size distribution is retained. Two different but related dependencies of the diffusion-layer thickness on particle size are considered. First, a power-law dependence that interpolates between a thickness that is proportional to (or equals) the particle radius (obtained when the exponent equals 1) and a constant thickness (obtained when the exponent is 0). Second, a piecewise linear function such that the thickness equals the particle radius for sufficiently small particles and is constant for larger ones. The modelling approach is exemplified by consideration of a lognormal particle-size distribution. Highly accurate closed-form expressions for the fraction of dissolved drug are obtained for dissolution under sink conditions (which are exact if the diffusion-layer thickness is radius-independent). Moreover, it is demonstrated that any result derived under sink conditions can be reused to determine the fraction of dissolved/absorbed drug under non-sink conditions, using the concept of a retarded time. Comparison with literature data and experiments are used to validate the modelling approach and to demonstrate its usefulness in a practical context.