Simple shear flow mass transfer

An exclusively analytical treatment of heat and mass transfer in turbulent flow in pipes fails because to date the turbulent shear stress Tl j = —Qw w p heat flux q = —Qcpw, T and also the turbulent diffusional flux j Ai = —gwcannot be investigated in a purely theoretical manner. Rather, we have to rely on experiments. In contrast to laminar flow, turbulent flow in pipes is both hydrodynamically and thermally fully developed after only a short distance x/d > 10 to 60, due to the intensive momentum exchange. This simplifies the representation of the heat and mass transfer coefficients by equations. Simple correlations, which are sufficiently accurate for the description of fully developed turbulent flow, can be found by... 

Mass transfer between a circular cylinder of radius a and a simple shear flow (G 2 = 1, the other Gkm = 0) was studied in [132]. For the dimensionless total diffusion flux per unit length of the cylinder, the following expression was obtained as Pe 0 ... 

Two situations involviag tmasport of a species lo a liquid in laminar flow can he mudeled by the system in Fig, 2.3-16. One might represent absorption (tom a gas stream into liquid Rowing over pieces of packing in a column, The other geometry could represent dissolution of a solid into a flowing liquid film or the transport from a membrane surface into a solution in laminar flow over the membrane. Both these simple systems illustrate die efleet of velocity profiles or shear rales on mass transfer to a fluid. 

Unlike creeping flow about a solid sphere, the r9 component of the rate-of-strain tensor vanishes at the gas-liquid interface, as expected for zero shear, but the simple velocity gradient (dvg/dr)r R is not zero. The fluid dynamics boundary conditions require that [(Sy/dt)rg]r=R = 0- The leading term in the polynomial expansion for vg, given by (11-126), is most important for flow around a bubble, but this term vanishes for a no-slip interface when the solid sphere is stationary. For creeping flow around a gas bubble, the tangential velocity component within the mass transfer boundary layer is approximated as... 

---