Bulk-flow process, entropy flows

The forms of the two balances depend on the particular circumstances of the process. As an illustration, we will consider a bulk flow process in steady state (Figure 2) in a chamber with a fixed volume. The energy and entropy rate balances are ... 

We must differentiate between bulk flow and molecular flow. If in the capillary would be a movable plunger or barrier, then the subsystem with the lower pressure would expand at the cost of the other system. However, this process will occur even when there is no barrier. The subsystem moves into the area of the other subsystem. If there is a membrane, not permeable to the flow of entropy, but permeable to matter, then the subsystem will exert to the other system a pressure, but no flow will occur. The situation is similar to that of osmosis. However, when matter moves, it carries entropy. So, under ordinary conditions, it is difficult or impossible to fabricate such a membrane. 

Equal temperatures guarantee that there is no entropy flow, and equal chemical potentials guarantee that there is no mass flow across the membrane. We did not make any statement on the pressure. If we would fix the volumes of the two subsystems, then even in the absence of gravity a pressure difference would develop. We must fix the position of the membrane. If we would not fix the position of the membrane, a pressure difference would tend to move the membrane and the volume of the solution would try to increase in the cost of the volume of the pure solute. This process would take place, even when the chemical potentials on both sides of the membrane are equal. Thus, a pressure difference causes a bulk expansion and... 

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