Steady-state mass transport through

Provided hydrodynamic conditions are stationary and well-defined, the steady-state mass transport through a solution towards the adsorbing surface can always be written as... 

The mass balance is described by the divergence of the mass flux through diffusion and convection. The steady state mass transport equation can be written in the following... 

Hanebuth, M., Dittmeyer, R., Mabande, G.T.P. and Schwieger, W. (2005) On the combination of different transport mechanisms for the simulation of steady-state mass transfer through composite systems using permeation through stainless steel supported silicalite-1 membranes as a model system. Catalysis Today, 104, 352-359. 

The parameter a = kJ ID is the ratio of the rate of chemical transfer from the soil to the SC (a process that can be characterized by a mass transfer coefficient which has units of cm s ) to the rate of mass transport through the SC (i.e., DIL). Thus, when a > 1, the SC resistance is most important on the other hand, for a < 1, mass transfer from the soil to the SC limits the dermal absorption rate. When the mass transfer resistance from the vehicle is insignificant, the concentration of chemical on the skin surface (i.e., C ) is equal to (see Equation 11.2). By comparison, when the mass transfer resistance witliin the vehicle is not small relative to that in the SC (i.e., a is not very large), then at steady state is reduced relative to as specified by Equation 11.3. That is. 

Mass transport through a product layer (quasi-steady-state approximation). 

If we take a thin slice of the cylinder of thickness dx we can write an expression for the transport of mass through this slice at steady state. What goes in either comes out or reacts, i.e. 

The quantity, h, in Equation 5 is not likely to be greatly different from its value in a plane adiabatic combustion wave. Taking x as the coordinate normal to such wave, h becomes the integral of the excess enthalpy per unit volume along the x-axis, so that the differential quotient, dh/dx, represents the excess enthalpy per unit volume in any layer, dx. Assuming the layer to be fixed with respect to a reference point on the x-axis, the mass flow passes through the layer in the direction from the unbumed, w, to the burned, 6, side at a velocity, S, transporting enthalpy at the rate Sdh/dx. Because the wave is in the steady state, heat flows by conduction at the same rate in the opposite direction, so that... 

The improved neutron detector spatial resolution has been a recent advance, with user instruments first available at the end of 2006 and 2007 at NIST and PSI, respectively. The work can be classified as proof-of-principle,9,10 in situ measurement of the steady-state through-plane water content during fuel cell operation," 13 and dynamic through-plane mass transport measurements.14,15... 

The salt flux through the membrane is given by the product of the permeate volume flux. /,. and the permeate salt concentration c,p. For dilute liquids the permeate volume flux is within 1 or 2% of the volume flux on the feed side of the membrane because the densities of the two solutions are almost equal. This means that, at steady state, the net salt flux at any point within the boundary layer must also be equal to the permeate salt flux Jvcip. In the boundary layer this net salt flux is also equal to the convective salt flux towards the membrane Jvc, minus the diffusive salt flux away from the membrane expressed by Fick s law (Didcildx). So, from simple mass balance, transport of salt at any point within the boundary layer can be described by the equation... 

Because the movement of the various zones is slow relative to the rates at which mass and heat are transported through the bed, a steady-state will eventually be established. The length parameter, n, is measured from the combustion interface and moves with velocity vc. 

Rate laws that are different from simple mass action often arise in chemical and biochemical applications. Important examples in biochemistry are enzyme and transporter mediated reactions where it is often assumed that a number of discrete steps are involved in converting substrates to products. The individual steps may be governed by mass action, but the overall steady state flux through an enzyme can take a more complex form. 

---