We would like to explore the behavior of a particle size distribution (PSD) during the process of steady state sedimentation in a stagnant fluid (v=0). For convenience let us have the z axis pointing downwards, in the same direction as gravity. Let us neglect Brownian Diffusion, and also Coagulation and Growth. The General Dynamic Equation (which is the Balance Equation for the PSD) then reduces to: 0=zcz(vp,z)n(vp,z)+Browniandiffusion+=0Rcoagulation+Rgrowth We wish to obtain an expression for cz(vp,z), and then calculate the (steady state) spatial evolution of the PSDn(vp,z), given an initial distribution, n(vp,0). In the Lagrangian Frame of Reference show that for a single particle of size vp cz(t)=pg[1exp(t/p)] where p=18pCcvp2/3 Obtain an expression for cz(vp,z) in the Eulerian Frame of Reference by obtaining an expression of particle position as a function of travel time, z(t). I got z(t)=pg[t+pexp(t/p)] We want t(z) and plug that into the expression for cz(t) above. Alas, that is quite difficult except for two limiting conditions: 1) tp in which case z(t)=pgt and the velocity of all particles is constant at their terminal velocity. 2) tp in which case we are far from reaching the terminal velocity. I explored this case by expanding the exponent up to the t2 term. For Case 1 I got that n(vp,z) was not a function of z and was equal to n(vp,z)=n(vp,0) For Case 2 things got pretty complicated but yielded a non-linear first order ODE for n(vp,z) which I still haven't solved. Take this problem as far as you can. Can you interpret your results physically? Do they make physical sense