Consider a drug-eluting balloon catheter deployed into a blood vessel. The balloon is inflated to perfectly adhere to the vessel walls. Drug is released from the outer surface of the balloon and diffuses radially through the endothelial tissue only in the r-direction. Let the outside radius of the balloon be r = R_0, where the drug has a constant concentration c_0. The drug diffuses into the tissue as far as r = R, where the concentration of the drug becomes zero. Assume cylindrical geometry, steady state conditions and no chemical reaction involving the drug. The drug diffusion coefficient in tissue is D.
(a) Find an expression for the profile c(r) inside the tissue (i. e. from R_0 to R).
(b) Determine the diffusive flux at the outer surface of the balloon.

a)  Cr = Co - Fx / D

b)   ΔC / Δx = ( CR - Cr )  / ( xR - xRo )

Explanation:

A) Derive an expression for the profile c(r) inside the tissue

F = DΔC / X  = D ( Co - Cr ) / X   ------ 1

where : F = flux , D = drug diffusion coefficient

            X = radial distance between Ro and R

Hence : Cr = Co - Fx / D

B) Express the diffusive flux at outer surface of the balloon

Diffusive flux at outer surface =  ΔC / Δx = CR - Cr / xR - xRo

One of the benefits of working with chlorinated polyvinyl chloride (CPVC) pipe is that it can be cut with a variety of different tools that don’t require any electricity or heat. However, different cutting methods are preferred over others, depending on the application.

When cutting CPVC pipe, it is important to make a square, flat cut. An uneven cut limits the bonding area and weakens the fitting.

To help you make the best possible cut, we’ve put together the following dos and don’ts when cutting CPVC pipe in different situations.