Ubbelohde viscometer

(1877-1964).

ASTM and other test methods are: ISO 3104, ISO 3105, ASTM D 445, ASTM D 446, IP 71, BS 188 [ [http://www.rheotek.com/scat.asp?id=69 ASTM Ubbelohde Viscometer ] ]

The Ubbelohde viscometer is closely related to the Ostwald viscometer. Both are u-shaped pieces of glassware with a reservoir on the right and a measuring bulb with a capillary on the left. A liquid is introduced and a pressure head forces this liquid from the bulb through the capillary to the reservoir. The time it takes for the liquid to pass through two calibrated marks is a measure for viscosity. The Ubbelohde device has a third arm extending from the end of the capillary and open to the atmosphere. In this way the pressure head only depends on a fixed height and no longer on the total volume of liquid.

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

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

where t is the time it takes for a volume V to elute. The ratio 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:

:$Delta\; P\; =\; ho\; g\; Delta\; H\; ,$

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:

:$eta\_r\; =\; frac\{eta\}\{eta\_0\}\; =\; frac\{t\; ho\}\{t\_0\; ho\_0\}$.

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

:$ho\; simeq\; ho\_0\; ,$

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:

:$eta\_\{sp\}\; =\; [eta]\; c\; +\; k\; [eta]\; ^2\; c^2\; +\; .......\; ,$

or

:$frac\{eta\_\{sp\{c\}\; =\; [eta]\; +\; k\; [eta]\; ^2\; c\; +\; .......\; ,$

where η_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