During respiration, individual bacteria (and mitocondria) produce a relatively large potential difference (∼100 mV) between the inside and outside, using energy to pump $H^+$ out of the cell to the liquid environment (a proton motive force is created). Together with proton pumps, or sources, also sinks of protons are present, channels which reuse the voltage difference for other goals.
Imagine a cell like a bag, with only very few and sparse sources and sinks of protons. At the limit, take only 1 source and 1 sink, diametrically opposed, which continuously work. Is it reasonable to assume that the voltage difference created is homogeneous in space (it has same value everywhere along the surface)? How would this depend on the size of the cell?
My guess is that the homogeneity of the voltage should depend on the speed of diffusion of protons in water, which I imagine is extremely fast (but how fast?). So all variations around the mean value would be washed out on very short time scales (shorter than the shortest times of μs−ms which are biologically relevant). But I may miss something. Any insight will be appreciated.
