Problem 2

There is a multitude of applications where PDMS (polydimethylsiloxane) membranes are used to extract or deliver an analyte from/to an aqueous medium (e.g. Kwon et al. 2007 Journal link  Download paper); Kwon and Escher 2008 Journal link  Download paper); Mayer et al. 1999 Journal link  Download paper)). The transfer kinetics are governed by molecular diffusion through the aqueous boundary layer and the PDMS membrane itself. While the diffusion coefficients for any compound will be much larger in water than in PDMS this does not necessarily mean that diffusion in PDMS is the rate limiting step because the capacity of PDMS for non-polar compounds is orders of magnitude higher than that of water (i.e. the movement in PDMS is slower but there are much more molecules moving at any time).

Calculate for which partition coefficient K_PDMS/water (m³/m³) the diffusive transfer resistance through both layers is equal. Use PDMS thicknesses of 30, 100, and 500 µm, aqueous boundary layer thicknesses of 15 µm (achievable by strong stirring) and 100 µm, a D_PDMS of about 10^-7 cm²/sec (Kwon et al. 2007) and a D_water of about 10^-4 cm²/sec.