Sherwoodnumber

The Sherwood number, often written as SherwoodNumber or abbreviated Sh, is a dimensionless quantity used in mass transfer to characterize the relative importance of convective transport to diffusive transport of a species A in a fluid B. It is defined by Sh = k L / D_AB, where k is the convective mass transfer coefficient, L is a characteristic length, and D_AB is the diffusion coefficient of A in B. Like the Nusselt number in heat transfer, the Sherwood number provides a convenient way to scale experimental data and correlations across different geometries and flow conditions.

Sh depends on geometry and flow regime. It is typically evaluated as a function of the Reynolds number Re (based on L) and the Schmidt number Sc = ν / D_AB. Common, geometry-specific correlations include: for a sphere in laminar flow, Sh = 2 + 0.6 Re^{1/2} Sc^{1/3}; for laminar flow over a flat plate, Sh ≈ 0.664 Re^{1/2} Sc^{1/3}; and for many turbulent conditions, Sh ≈ 0.037 Re^{4/5} Sc^{1/3}. More complex geometries require tailored correlations or numerical methods. These forms illustrate that Sh tends to increase with stronger convection and with higher Sc, though exact coefficients vary with setup.

Practically, once Sh is known, the mass transfer coefficient can be recovered via k = Sh D_AB / L. In diffusion-limited cases at very low Re, Sh approaches about 2, indicating minimal convective enhancement. In engineering practice, Sh is used to design and analyze processes such as drying, gas absorption, liquid-liquid extraction, electrochemical reactions, and environmental transport.