Facilitated transport consider here the transport of a solute S across a homogeneous membrane from one external solution to another as a complex CS with a carrier C unable to leave the membrane phase. The solute $ may be considered to be insoluble in the membrane and convection to be negligible (see Fig. 24C.8). Assume further that: 

1. Equilibrium exists at both membrane surfaces according to C_CS = K_DC_CC_S where the concentration of S is that in the external solution and those of C and CS are in the membrane. 7 

2. Both C and CS follow the simple rate expression N₁ = D_im∆c_i. Develop a general expression for the transport rate of S in terms of the total amount of carrier plus carrier complex present in the membrane, the solution concentrations of S the quantity K_D, and the diffusivities. What is the maximum rate of transport of S (that is, as its concentration at the left of the diagram becomes very high and that at the right is zero)?

Membrane CS Distance Concentration