Reference no: EM132409301

Mathematical Modeling Of Differential Equation Question -

Liposomes are small spherical bilayer membranes than can be used to deliver drugs at a controlled rate. As they interact with the immune system they must be surrounded with an encapsulant material. The figure below represents this device. It is a spherical system where the liposome has diameter d1 and is spherically encapsulated with a diameter d2. We assume that we have a drug inside the liposome that diffuses outwards in the radial direction.

(a) Write down a suitable word equation for the rate of change of mass in a spherical shell r to r + Δr and over a time interval t to t + Δt. Explain the steps used to come to your answer.

(b) Deduce a differential equation for the concentration at equilibrium. Explain the steps used to come to your answer.

(c) Now suppose that the diffusion coefficient depends on concentration instead of being constant. Does the differential equation in (b) remain the same? Justify your answer and write down the new equilibrium equation if it is the case.

Note - Must follow the standard of book Explain step and justify answer.

Textbook - MATHEMATICAL MODELLING WITH CASE STUDIES - Using Maple and MATLAB, Third Edition by B. Barnes and G. R. Fulford.