Unable to form BC involving both dU/dt and dU/dx in PDE solver

Hello everyone,

I have been using the PDE solver within matlab for one of the modelling problems I have, but having trouble formatting the boundary conditions.

My problem involve a simple diffusion system, where the diffusant flows from a reservoir (concentration C_d(t), volume V_d0) through a material (thickness x_m, diffusion coefficient D_m) into a receiving reservoir (concentration C_r(t), volume V_r0). And the cross section concentration of the diffusant through the material would be described by C(x,t)

I have defined x = 0 as the interface between the donor reservoir and the material. So C(0,t) = C_d(t).

As the BC involve transfer of matter, the flux, as I understand, would not be zero. Whilst the flux is also related to the mass loss in the donor reservoir, I have formed the following boundary condition:

d/dt (C(0,t)) = k d/dx (C(0,t))

However, the PDE solver in matlab does not seem to allow the incorporation of dU/dt.

Is there something that I am missing? Or should I have formed my problem in a different way?

Any help would be appreciated.