Gel Layer Formation

When the solute is a macromolecular compound such as a protein or a polymer, there is the possibility that the solute concentration at the membrane interface exceeds the gel concentration, wg, at which concentration the solution is no longer a fluid. A gel layer thus forms at the membrane interface which creates an additional resistance to the permeation flux which consequently decreases. The flux continues to decrease until the solute concentration at the membrane interface equals the gel concentration, at which point steady state is reached. The flux at that point can be obtained from eqn [5]:

Figure 4 Solvent flux as a function of applied pressure as calculated from eqn [17]. The flux observed with solvent-solute mixtures is always less than the pure solvent flux. The deviation increases with increasing applied pressure, increasing solute concentration, and decreasing mass-transfer coefficient in the boundary layer.

but equal to 2 or higher for macromolecular solutes. Combining eqn [15] with eqn [5] and assuming wp = 0 gives:

and because wp is typically close to zero: ,/iimit = P • kbl • ln(wg/wb)

/solvent = (Ap - a ■ wl ■ exp(n • JLvent/pkbOVRn [17]

From eqn [17] it is clear that an increase in the flux Jswolvent leads to an exponential increase in the osmotic pressure and that the flux will increase less than linearly with the applied pressure. This means that any increase in driving force AP will be negated at least in part by the increase in osmotic pressure. The general effect of pressure on flux predicted by eqn [17] is illustrated in Figure 4 and is in agreement with the vast majority of experimental data. As can be seen from Figure 4, the flux observed with solvent-solute mixtures is always less than the pure solvent flux, and the deviation increases with increasing applied pressure, increasing solute concentration and decreasing mass transfer coefficient in the boundary layer. Figure 4 also shows that at higher applied pressures the flux becomes essentially independent of the applied pressure. This is often observed in ultrafiltration applications and is referred to as the limiting flux. Eqn [17] predicts that under 'limiting flux' conditions the flux is independent of

The steady-state flux _/Wmit is called the 'limiting flux' because any increase in applied pressure will just result in a thicker gel layer and not in a higher flux. From eqn [19] it can be seen that the limiting flux as predicted by the gel layer model is independent of the applied pressure as well as the membrane resistance. Additionally, eqn [19] predicts a straight-line plot of Jwmit versus ln(wb) with a slope equal to — p • kbl. All these predictions have been confirmed in a vast number of ultrafiltration experiments. Interestingly, the osmotic pressure model also predicts a limiting flux with the same attributes.

Solar Panel Basics

Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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