The determination of viscosity is based on
Poiseuille's law: : \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 \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: :\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: :\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 :\rho \simeq \rho_0 \, the so-called
specific viscosity becomes: :\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: :\eta_{sp} = [\eta] c + k [\eta]^2 c^2 + \cdots\, or :\frac{\eta_{sp}}{c} = [\eta] + k[\eta]^2 c + \cdots,\, where \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. == References ==