Pore Networks in Membranes. (20 pts) Consider two membranes below, with equal void space, but differently...

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Pore Networks in Membranes. (20 pts) Consider two membranes below, with equal void space, but differently configured. The membrane on the left consists of a narrow and a wide pore in parallel, while the membrane on the right consists of pores which are narrow and wide in series. Assume the narrow and wide parts of the two membranes have the same widths. An electrical "model" of these two membranes, corresponding to steady state flow, would assign resistances Rn and Rw to the narrow and wide parts of the pores in the membrane on the right side. The two membranes then can be modeled by the following resistor networks: Rn Rn Rw Rw -n Rn W Using the well-known formulas for series and parallel combinations of resistors, show that the total resistance of the network on the right is greater than that on the left, and therefore the corresponding permeation resistance of the membrane on the right is greater. Pore Networks in Membranes. (20 pts) Consider two membranes below, with equal void space, but differently configured. The membrane on the left consists of a narrow and a wide pore in parallel, while the membrane on the right consists of pores which are narrow and wide in series. Assume the narrow and wide parts of the two membranes have the same widths. An electrical "model" of these two membranes, corresponding to steady state flow, would assign resistances Rn and Rw to the narrow and wide parts of the pores in the membrane on the right side. The two membranes then can be modeled by the following resistor networks: Rn Rn Rw Rw -n Rn W Using the well-known formulas for series and parallel combinations of resistors, show that the total resistance of the network on the right is greater than that on the left, and therefore the corresponding permeation resistance of the membrane on the right is greater.