Fluid Flow in Membrane Microreactors

Microreactors have a small characteristic length (or hydraulic diameter), which makes the Reynold s number (Re) very small, hence the flow in the microchannels of MMRs is predominantly laminar. Secondary molecular effects can be significant as the characteristic length decreases to a point where properties like density, temperature, and velocity are not continuous functions of position, and the fluid-surface interaction becomes more important than the fluid-fluid interactions. At this moment, the continuum assumptions for the normal reactors are no 

The departure of the flow in microchannels from the continuum assumption can be measured by the Knudsen munher, that is, the ratio of the mean free path A to the hydraulic diameter of the microchannel [44]  

It is generally agreed that the continuum assumption holds only with R 10 and the flow can be described by the application of the Navier-Stokes equations with their customarily used no-slip boundary conditions (that is, the velocity on the wall is zero), whereas the behavior of the fluid for K 10 has to be described with molecular-level modeling. For most microchannel systems, is less than 0.1 and the fluid flow is in the slip regime (10 R 0.1) [45]. In this case, the fluid flow can still be described using the continuum conservative equations, but slip boundary conditions must be incorporated since velocity slip and temperature jump may occur at the microchannel surfaces [46]. 

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