I am trying to model the sedimentation of spherical colloidal suspensions. For that, I need to solve the differential equation (check image file). I am attaching the mathcad file and the original paper. What I want is to plot volume fraction (phi) as a function of height (x) at a certain time (t) (Something similar to figure 3 in the paper). I would greatly appreciate the help.
It should be convenient to install Mathcad 15 since it offers the possibility to solve partial differential equations, with the "Pdesolve" operator inserted in a solution block (there is an example), and of which Prime is deprived.
Unfortunately, the coefficient of x in the exponent is positive, and large (about 23 million /m), which means that the function goes steep to infinity...
I don't suppose this accurately models your phenomenon...where did I, or you, go wrong?
There is a slight confusion with your solution. The equation 4 that I had written is a modified version of equation 3 and is a boundary condition. Therefore I don't think phi (x,t) is independent of t. The derivative of the expression may be 0 at the boundaries but not everywhere else. Volume fraction will change along the solution length as sedimentation takes place with time. I am attaching the mathcad file with my comments. Take a look.
I guess you're right, I mistook the "x ∈ {0, xmax}" (= just 0 and xmax) for an "x ∈ [0, xmax]" (=the entire range from 0 to xmax).
Sorry about that.
Other than that, Werner already explained that PDEsolve is not available in Prime, if you want to use PDEsolve you'll have to use (real) Mathcad.
{ Note that as a licensed user of Prime you're allowed to install and use Mathcad 15 on the same machine. You can use the very same license file that you used for licensing Prime to license the Mathcad 15 application. }
