Dear Alessandro
Thanks for your kind words and your brilliant analysis of the problem.
There are two separate cases which need to be considered.
1a) The channel. Here we have a relatively small number of ions, say less
than 30, but there are many types needed, if we are to do something useful,
e.g., at least 3 mobile ions (say Na, Ca, and Cl) often 4 mobile ions (Na, Ca,
K, and Cl) and often 2 semimobile ions of opposite sign. "Semimobile"
means they suffer constraints to keep them within a region.
1b) The channel. We must deal carefully with boundary conditions between
the channel and the bath. The bath can be described in macroscopic averaged
terms but the connection with the channel must be done very carefully to avoid
boundary layers that are artifacts of the model we use. We have avoided this
in the past by having an intermediate zone just outside the channel, more
or less 2 nm long (the channel itself might be 0.7 nm long) in which the cross
sectional area is allowed to rapidly increase (with distance from the channel) and
the diffusion coefficient and dielectric coefficient have BULK values but otherwise the intermediate
zone is treated as the channel is.
2) The bulk.
Here our view is that a description in two singlet probability distributions P(charge), P(mass)
will be very very very much more realistic (i.e., the higher order terms will be much smaller)
than one in terms of P(Na) and P(Cl) for example. WE KNOW this from experiments which
show that purely electrical and purely diffusion descriptions work very very well in separate
domains. This is my motivation to derive such equations.
I hope this is helpful
As ever
Bob[Quoted text hidden]
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