Magnitude of Typical Streaming Potentials Above, we asserted that streaming potential can be used to measure the zeta potential. Of interest is the magnitude of these streaming potentials. Consider a capillary subjected to a pressure difference of 5 atm (this is easy to generate with a handheld syr

Question

Magnitude of Typical Streaming Potentials

Above, we asserted that streaming potential can be used to measure the zeta potential. Of interest is the magnitude of these streaming potentials. Consider a capillary subjected to a pressure difference of 5 atm (this is easy to generate with a handheld syringe), inducing flow of an aqueous solution with a conductivity of 180 [latex]\mu \mathrm{S} / \mathrm{cm}[/latex]. If the surface zeta potential is [latex]-20 \mathrm{mV}[/latex], what will the measured streaming potential be? Will these voltages be easy to measure?

Accepted Answer

The Helmholtz-Smoluchowski equation gives:

[latex]\begin{aligned}\Delta \phi &=\frac{\varepsilon \zeta}{\sigma \mu} \Delta p ,\ \varepsilon &=80 imes 8.85 imes 10^{-12}=7.1 imes 10^{-10} \mathrm{C} / \mathrm{V} \mathrm{m}, \ \sigma &=180 imes 10^{-6} \mathrm{~S} / \mathrm{cm}=180 imes 10^{-4} \mathrm{~S} / \mathrm{m}, \ \mu &=1 \mathrm{mPa} \mathrm{s}=10^{-3} \mathrm{~Pa} \mathrm{~s}, \ \Delta p &=-5 \mathrm{~atm}=-5 imes 0.101 \mathrm{MPa} \doteq-0.5 imes 10^{6} \mathrm{~Pa}, \ \zeta &=-20 \mathrm{mV}=-0.02 \mathrm{~V}, \ \Delta \phi &=\frac{\left(7.1 imes 10^{-10} ight)(-0.02)}{\left(180 imes 10^{-4} ight)\left(10^{-3} ight)}\left(-0.5 imes 10^{6} ight)=0.39 \mathrm{~V}, \end{aligned} [/latex]

in which the outlet (low pressure) will have the more positive voltage. Voltages on the order of 1 volt are quite easy to measure!

Question 12.6: Magnitude of Typical Streaming Potentials Above, we asserted...

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