I have a problem checking the units for the variables in the zeta potential equation: 𝜁 = 113000 EM Vt/Dt.
Can anyone help m
Please define the terms in your equation. I'm guessing EM is electrophoretic mobility but I don't know what Vt and Dt are.
John Francis Miller Sure 𝜁: zeta potential, EM: electrophoretic mobility at actual temperature, vt: viscosity of the suspending liquid at temperature t, Dt: dielectric constant of the suspending at temperature t. I really don't know how 𝜁 unit becomes v.
The equation is:
zeta potential = electrophoretic mobility x viscosity / (dielectric constant x permittivity in free space)
The dimensions of each of the right-hand terms are:
electrophoretic mobility = velocity/electric field = [L T-1] / [M L T-3 A-1] = M-1 T2 A
dielectric constant = dimensionless
permittivity = M-1 L-3 A2 T4
viscosity = M L-1 T-1
So, zeta potential = [M-1 T2 A] x [M L-1 T-1] x [M L3 A-2 T-4]
= M L2 T-3 A-1
and
dimensions of electric potential = M L2 T-3 A-1
i.e., zeta potential has dimensions of electrical potential.
See https://en.wikipedia.org/wiki/SI_electromagnetism_units for how I got the dimensions for voltage and permittivity.
John Francis Miller Thank you for your comprehensive and understandable answer. But the problem is that in the equation that I have written, there is no permittivity in free space term, however, how can I reach these dimensions (M L2 T-3 A-1)?
I suspect the 113000 factors in the permittivity.
Permittivity of free space 8.854 x 10-12 F.m-1. The reciprocal of that is 112.9 x 109. That's 1,000,000 times your factor which is probably to allow you to use cP for viscosity (instead of SI units) and mV for zeta potential.
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