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| Sherwood number | |
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| Name | Sherwood number |
Sherwood number The Sherwood number is a dimensionless quantity used in convective mass transfer to characterize the ratio of convective mass transport to diffusive mass transport. It appears in analogies between mass, heat, and momentum transfer and is applied across engineering problems involving transfers between phases, porous media and reactors. The concept is central to analyses in chemical engineering, mechanical engineering, and environmental engineering.
The Sherwood number is defined as the ratio of convective mass transfer to molecular diffusion, drawing a formal analogy to the Nusselt number, Reynolds number, and Schmidt number. It is commonly expressed as Sh = h_m L / D, where h_m is the convective mass transfer coefficient, L is a characteristic length such as the diameter used in studies at Imperial College London, and D is the molecular diffusivity measured in contexts like experiments at Massachusetts Institute of Technology or Lawrence Berkeley National Laboratory. Early developments tying Sherwood concepts to engineering practice can be traced through work at institutions such as University of Cambridge, University of Oxford, California Institute of Technology, and industrial research at General Electric.
Physically, the Sherwood number quantifies the relative importance of bulk transport mechanisms compared to molecular diffusion in processes studied at sites like Oak Ridge National Laboratory, Argonne National Laboratory, and National Institute of Standards and Technology. High Sherwood values indicate dominance of convective transport as seen in systems studied in Shell plc research and in pipelines analyzed by BP plc and ExxonMobil, while low Sherwood values indicate diffusion-limited regimes similar to phenomena investigated at CERN in porous media analogies. Practical contexts where Sherwood plays a role include packed bed reactors at DuPont facilities, absorption towers designed by Air Liquide, and atmospheric dispersion models developed at NASA.
Mathematically, Sh = h_m L / D links to empirical and theoretical correlations involving Reynolds number and Schmidt number. Classic correlations include forms Sh = a Re^b Sc^c derived from boundary-layer theory pioneered by researchers at Princeton University, Harvard University, and Stanford University. Specialized correlations for spheres, cylinders, and flat plates appear in texts from McGraw-Hill publishers and standards from American Society of Mechanical Engineers and International Organization for Standardization. The constants a, b, c originate from experimental regressions performed at laboratories such as Fraunhofer Society and Max Planck Institute and are tabulated in handbooks produced by Wiley.
Applications of the Sherwood number span chemical reactors, environmental remediation, and biological systems. In chemical reactor design used by BASF and Dow Chemical Company, Sh informs mass-transfer-limited reaction rate estimations. In environmental engineering projects led by United Nations Environment Programme and Environmental Protection Agency, Sherwood-based models help predict solute transport in groundwater at sites studied by US Geological Survey. Biomedical applications include modeling drug delivery in vascular flows researched at Johns Hopkins University and Mayo Clinic. In process engineering, Sh is essential for distillation, absorption, and extraction operations implemented by LyondellBasell Industries and Air Products and Chemicals.
Experimental determination of Sherwood numbers typically involves measurements of mass transfer coefficients using tracer techniques, electrochemical probes, or concentration boundary layer measurements performed at facilities like National Renewable Energy Laboratory, Sandia National Laboratories, and university labs at University of California, Berkeley. Methods include steady-state and transient techniques, rotating disk experiments first developed in classical studies at University of Manchester, and analog experiments exploiting heat-mass transfer similarity conducted at Imperial College London. Data reduction employs instrumentation standards from IEEE and calibration practices aligned with National Institutes of Health when biological systems are involved.
The Sherwood number is intrinsically related to the Nusselt number through heat–mass transfer analogies and to the Reynolds number and Schmidt number through convective flow scaling laws used in canonical studies at Massachusetts Institute of Technology, California Institute of Technology, and Texas A&M University. In porous media flows described in work at Colorado School of Mines and ETH Zurich, Sh couples with the Peclet number and the Damköhler number to characterize reaction–transport interactions. Correlations sometimes incorporate the Prandtl number when leveraging heat–mass transfer analogies in multiphase systems studied at Imperial Oil and TotalEnergies.
Category:Dimensionless numbers