Ubbelohde viscometer

The determination of viscosity is based on Poiseuille's law:

${\displaystyle {\frac {dV}{dt}}=v\pi R^{2}={\frac {\pi R^{4}}{8\eta }}\left({\frac {-\Delta P}{\Delta x}}\right)={\frac {\pi R^{4}}{8\eta }}{\frac {|\Delta P|}{L}},}$

where t is the time it takes for a volume V to elute. The ratio ${\displaystyle {\frac {dv}{dt}}}$ depends on R as the capillary radius, on the average applied pressure P, on its length L and on the dynamic viscosity η.

The average pressure head is given by:

${\displaystyle \Delta P=\rho g\Delta H\,}$

with ρ the density of the liquid, g the Standard gravity and H the average head of the liquid. In this way the viscosity of a fluid can be determined.

Usually the viscosity of a liquid is compared to a liquid with an analyte for example a polymer dissolved in it. The relative viscosity is given by:

${\displaystyle \eta _{r}={\frac {\eta }{\eta _{0}}}={\frac {t\rho }{t_{0}\rho _{0}}},}$

where t₀ and ρ₀ are the elution time and density of the pure liquid. When the solution is very diluted

${\displaystyle \rho \simeq \rho _{0}\,}$

the so-called specific viscosity becomes:

${\displaystyle \eta _{sp}=\eta _{r}-1={\frac {t-t_{0}}{t_{0}}}.\,}$

This specific viscosity is related to the concentration of the analyte through the Intrinsic viscosity [η] by the power series:

${\displaystyle \eta _{sp}=[\eta ]c+k[\eta ]^{2}c^{2}+\cdots \,}$

or

${\displaystyle {\frac {\eta _{sp}}{c}}=[\eta ]+k[\eta ]^{2}c+\cdots ,\,}$

where ${\displaystyle {\frac {\eta _{sp}}{c}}}$ is called the viscosity number.

The intrinsic viscosity can be determined experimentally by measuring the viscosity number as function of concentration as the Y-axis intercept.