Mass transfer turbulent flow

One equation for turbulent-flow mass transfer to pipe walls is a modification of Eq. (1Z31) with the Nusselt and Prandtl numbers replaced by the Sherwood and Schmidt numbers. 

Illustration 5.3 Derivation of a Correlation for Turbulent Flow Mass Transfer Coefficients Using Dimensional Analysis... 

UNIT OPERATIONS FLUID FLOW PROBLEMS TURBULENT FLOW MASS TRANSFER PROBLEMS TO BE SOLVED NOMENCLATURE... 

R. B. Kinney and E. M. Sparrow, Turbulent Flow, Heat Transfer, and Mass Transfer in a Tube with Surface Suction, J. Heat Transfer (92) 117-125,1970. 

BOUNDARY-LAYER FLOW AND TURBULENCE IN MASS TRANSFER... 

Boundary-Layer Flow and Turbulence in Mass Transfer... 

Kinney, RB., Sparrow, E.M., 1970. Turbulent flow, heat transfer, and mass transfer in a tube with surface suction. ASME J. Heat Transf. 92, 117-124. 

Mass transfer processes are complicated, usually involving turbulent flow, heat transfer, multiple phases, chemical reactions, unsteady operation, as well as the influences from internal construction of the equipment and many other factors. To study such complicated system, we propose a novel scientific computing framework in which all the relevant equations on mass transfer, fluid-dynamics, heat transfer, chemical reactions, and all other influencing factors are involved and solved numerically. This is the main task and research methodology of computational mass transfer (CMT). 

Tamburrino, A. and Gulliver, J. S. 2002. Free surface turbulence and mass transfer in a channel flow, AIChEJ., 48(12), 2732. 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

The mass-transfer coefficients depend on complex functions of diffii-sivity, viscosity, density, interfacial tension, and turbulence. Similarly, the mass-transfer area of the droplets depends on complex functions of viscosity, interfacial tension, density difference, extractor geometry, agitation intensity, agitator design, flow rates, and interfacial rag deposits. Only limited success has been achieved in correlating extractor performance with these basic principles. The lumped parameter deals directly with the ultimate design criterion, which is the height of an extraction tower. 

Neglecting flow nonuniformities, the contributions of molecular diffusion and turbulent mixing arising from stream sphtting and recombination around the sorbent particles can be considered additive [Langer et al., Int. ]. Heat and Mass Transfer, 21, 751 (1978)] thus, the axial dispersion coefficient is given by ... 

Because this mass-transfer step is so vital, conventional dead-end operation of ultrafilters is veiy rare. There are many ways to depolarize a membrane. Cross-flow is by far the most common. Turbulent flow is more common than laminar flow. 

At high velocities where turbulence dominates, the main body of flowing fluid is well mixed in the direction normal to the flow, minor differences in temperature and concentration can be neglected, and the film concept can be applied. This describes the flow as if all gradients for temperature and concentration are in a narrow film along the interface with the solid (Nernst 1904), and inside the film conduction and diffusion are the transfer mechanisms. This film concept greatly simplifies the engineering calculation of heat and mass transfer. 

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