EOF inside Cylindrical Pores

The net flux Jo of the fluid through the pore is given by the integral of %(r) over the area of cross-section as 

The negative sign in Equation 8.90 gives the correct direction of the flow. For positively charged cylindrical pore 0), the flow is in the opposite direction 

It must be noted that for high values of ku, that is, for the pore radius being larger than the Debye length, which can be realized at higher salt concentrations, the pore radius influences the EOF velocity only as the cross-sectional area of the pore. On the other hand, if there were a pressure drop Ap/L across the pore, then the total flux would be 

In the steady state, when the drift contribution dominates, the ionic current obeys the Ohm s law. In the absence of either drift or barriers, the behavior of ions is according to the Pick s law. The GHK equations offer a convenient way to describe the crossover behavior between the diffusion-, drift-, and barrier-dominated regimes. We have also shown the utility of the numerically solved results from the PNP equations for the ionic currents through the GA channel and the aHL protein pore. The PNP calculations show that the steepest gradient in the electrical potential is only very near and across the pore. We have 

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