K kD kDD kD1 D

kMKD

where 1 — is the rejected fraction of substance i, 1 — is the corresponding fraction that is trapped in the acceptor solution, and kD, kM and kA are the mass transfer coefficients of the permeating fractions of substance i for the donor, the membrane and the acceptor phases, respectively. k'A and kD are the mass transfer coefficients for the so-called inactive form of substance i, which cannot permeate the membrane. In many cases the mass transfer across the phase boundary is to be considered additionally, e.g. for homogeneous membranes, supported liquid membranes (SLM) and gas-filled microporous membranes. Then the expression shown in eqn [19] should be added to the right term of eqn [18]:

kpDM and kpAM are the phase transfer coefficients from the donor solution into the membrane phase and from there into the acceptor phase, respectively.

From the general equation some cases of analytical interest can be deduced.

Example 1: Dialysis Through Hydrophilic and Microporous Membranes. Because = = 1, Kdm = Kam = 1 and no phase transfer takes place, eqn [18] can be simplified to eqn [20]:

Solar Panel Basics

Solar Panel Basics

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