Diffusion flux mathematical formulation

Consider a gas-liquid interface, as sketched in Fig 5.16. The mathematical problem is to formulate and solve the diffusion flux equations determining the fluxes on both sides of the interface within the two films. The resulting concentration profiles and flux equations can be expressed as ... 

The fllm theory is the simplest model for interfacial mass transfer. In this case it is assumed that a stagnant fllm exists near the interface and that all resistance to the mass transfer resides in this fllm. The concentration differences occur in this film region only, whereas the rest of the bulk phase is perfectly mixed. The concentration at the depth I from the interface is equal to the bulk concentration. The mass transfer flux is thus assumed to be caused by molecular diffusion through a stagnant fllm essentially in the direction normal to the interface. It is further assumed that the interface has reached a state of thermodynamic equilibrium. The mass transfer flux across the stagnant film can thus be described as a steady diffusion flux. It can be shown that within this steady-state process the mass flux will be constant as the concentration profile is linear and independent of the diffusion coefficient. Consider a gas-liquid interface, as sketched in Fig. 5.16. The mathematical problem is to formulate and solve the diffusion flux equations determining the fluxes on both sides of the interface within the two films. The resulting concentration profiles and flux equations can be expressed as ... 

Mechanical dispersion is assumed to mathematically follow a Fickian diffusion formulation, i.e., the mechanical dispersive flux is assumed to be linearly proportional to the concentration gradient. As such the hydrodynamic dispersion is the sum of diffusive and mechanical dispersive terms, and the total dispersive flux is written as ... 

The development of the transport-diffusion al rithm consists of mathematical operations on the transport equation to obtain a relationship between the net current and flux gradient, formially designated as the. transport diffusion coefficient. The procedure is similar to that of Pomraning with the noteworthy differences that (a) no analytical approximations are required, and, (b) the analytical formulation is constrained to yield a computational algorithm that is consistent with those einpipyed in 2-D discrete ordinates and diffusion theory codes e.g., TWOTRAN (Ref. 2) and 2-DB (Ref. 3). 

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