Consider the one dimensional case of sodium particles trapped between two filter

Question

Consider the one dimensional case of sodium particles trapped between two filters with an equilibrium concentration c(x). If a flow is turned on so that liquid flows through the filters carrying the particles with a flow-velocity (or drift velocity) or V_d in the x-direction. What is the flux of the particles in the region between the filters due only to flow? Considering all elements of flux, what is the equation for the concentration at X_2 in steady state? If the length of the section is L and the total concentration is B. What is the concentration at the far left end (x=0) in terms of L and B?

Explanation / Answer

a) Flux of particles = c(x) * F/A

b)    equation of concentration

= c(x1)*(1 + F/A*K) - c(x2)*(1 + F/A*K)

c)    Concentration at far left end

= c(L)*(1 + F/A*K) - c(0)*(1 + F/A*K)

=   c(L)*(1 + B) - c(0)*(1 + B)

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