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

The aim of this study was to determine the thickness of the hydrodynamic diffusion layer (h_HDL) of three poor water-soluble compounds under laminar fluid flow using a single particle dissolution technique. The single particle dissolution experiments were performed in a flowing aqueous medium using four different fluid velocities (v), ranging from 46 to 103 mm/s. The particles used had an initial radius (r) of 18.8 to 52.3 μm. The determined h_HDL values were calculated from both dissolution experiments and computational fluid dynamics (CFD) simulation. In this study, single particle dissolution experiments gave, with one exception, h_HDL values in the range of 2.09 to 8.85 µm and corresponding simulations gave h_HDL values in the range of 2.53 to 4.38 µm. Hence, we found a semi-quantitative concordance between experimental and simulated determined h_HDL values. Also, a theoretical relation between the dependence of h_HDL on particle radius and flow velocity of the medium was established by a series of CFD simulations in a fluid velocity range of 10-100 mm/s and particle size (radius) range of 5-40 µm. The outcome suggests a power law relation of the form h_HDL∝r^3/5v^-2/5. In addition, the h_HDL seems to be independent of the solubility, while it has a diffusion coefficient dependence. In conclusion, the h_HDL values were determined under well-defined conditions; hence, this approach can be used to estimate the h_HDL under different conditions to increase the understanding of the mass transfer mechanisms during the dissolution process.