Volumetric flux, definition

In this equation ut should be interpreted as the volumetric flux density (directional flow rate per unit total area). The indexes range from 1 to 3, and repetition of an index indicates summation over that index according to the conventional summation convention for Cartesian tensors. The term superficial velocity is often used, but it is in our opinion that it is misleading because n, is neither equal to the average velocity of the flow front nor to the local velocity in the pores. The permeability Kg is a positive definite tensor quantity and it can be determined both from unidirectional and radial flow experiments [20], Darcy s law has to be supplemented by a continuity equation to form a complete set of equations. In terms of the flux density this becomes ... 

The second process of water vapor removal down the channel can be described by the convective flux, Q(pw,Sat PvMet)KRTA), representing the maximum amount of water vapor removed with the purge gas when the exit purge gas is fully saturated with vapor. In the above definition Q is the purge gas volumetric flow rate and A the active area of the fuel cell. Both parameters defined above have the unit of mol/s per unit of the fuel cell active area. It follows that... 

Difliisivities are defined, not with respect to a stationary plane, but relative to a plane moving at the volume-average velocity Mq. By definition there is no net volumetric flow across this reference plane, although in some cases there is a net molar flow or a net mass flow. The molar flux of component A through this reference plane is a diffusion flux designated and is equal to the flux of A for a stationary plane [Eq. (21.2)] minus the flux due to the total flow at velocity Mq and concentration... 

The diffusivity (D) defined in this way is not necessarily independent of concentration. It should be noted that for diffusion in a binary fluid phase the flux (/) is defined relative to the plane of no net volumetric flow and the coefficient D is called the mutual diffusivity. The same expression can be used to characterize migration within a porous (or microporous) sohd, but in that case the flux is defined relative to the fixed frame of reference provided by the pore walls. The diffusivity is then more correctly termed the transport diffusivity. Note that the existence of a gradient of concentration (or chemical potential) is implicit in this definition. 

Helm (1979) introduced a straightforward definition of bulk flux of aggregate material within V, which when saturated holds volumetrically a mixture of both sedimentary material and water,... 

Note that the S-shaped grade efficiency curves do not necessarily start from the origin—in applications with a considerable underflow to throughput ratio (by volume) R, the grade efficiency curves tend to the value G x) = / f as X —> 0. This is a result of the splitting of the flow, or dead flux that carries even the finest solids into the underflow in proportion to the volumetric split of the feed. Section 3.4 discusses possible modifications to the efficiency definitions which account for the volumetric split and illustrate only the net separation effect. Such reduced efficiencies are widely used for hydrocyclones and nozzle-type disc centrifuges where large diluted underflows occur. 

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