An Ubbelohde type viscometer or suspended-level viscometer is a

measuring instrument Instrumentation is a collective term for measuring instruments, used for indicating, measuring, and recording physical quantities. It is also a field of study about the art and science about making measurement instruments, involving the related ...

which uses a capillary based method of measuring

viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...

. It is recommended for higher viscosity cellulosic polymer solutions. The advantage of this instrument is that the values obtained are independent of the total volume. The device was developed by the German chemist

Leo Ubbelohde Leo Ubbelohde (4 January 1877, Hanover – 28 February 1964, Düsseldorf) was a German chemist. During his career he served as a professor in Karlsruhe and Berlin. He is known for his research on mineral oils, fuels, catalysis and viscosity. He ...

(1877-1964).

ASTM ASTM International, formerly known as American Society for Testing and Materials, is a standards organization that develops and publishes voluntary consensus technical international standards for a wide range of materials, products, systems and s ...

and other test methods are: ISO 3104, ISO 3105, ASTM D445, ASTM D446, ASTM D4020, IP 71, BS 188.ASTM Ubbelohde Viscometer
/ref> The Ubbelohde viscometer is closely related to the Ostwald viscometer. Both are u-shaped pieces of glassware with a reservoir on one side and a measuring bulb with a

capillary A capillary is a small blood vessel, from 5 to 10 micrometres in diameter, and is part of the microcirculation system. Capillaries are microvessels and the smallest blood vessels in the body. They are composed of only the tunica intima (the inn ...

on the other. A liquid is introduced into the reservoir then sucked through the capillary and measuring bulb. The liquid is allowed to travel back through the measuring bulb and 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.

Determination of viscosity

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

\frac = v \pi R^ = \frac \left( \frac\right) = \frac \frac,

where t is the

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

it takes for a

volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...

V to elute. The ratio

\frac

depends on R as the capillary

radius In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is th ...

, on the average applied

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...

P, on its length L and on the dynamic

η. The average pressure head is given by: :

\Delta P = \rho g \Delta H \,

with ρ the

density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

of the liquid, g the

Standard gravity The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant ...

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 Relative viscosity (\eta_) (a synonym of "viscosity ratio") is the ratio of the viscosity of a solution (\eta) to the viscosity of the solvent A solvent (from the Latin language, Latin ''wikt:solvo#Latin, solvō'', "loosen, untie, solve") is a ...

is given by: :

\eta_r = \frac = \frac,

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_ = \eta_r - 1 =  \frac. \,

This specific viscosity is related to the

concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number concentration'', ...

of the analyte through the

Intrinsic viscosity Intrinsic viscosity \left \eta \right/math> is a measure of a solute's contribution to the viscosity \eta of a solution. If \eta_0 is the viscosity in the absence of the solute, \eta is (dynamic or kinematic) viscosity of the solution and \phi is ...

�by the

power series In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots where ''a_n'' represents the coefficient of the ''n''th term and ''c'' is a co ...

: :

\eta_ =

eta Eta ( ; uppercase , lowercase ; ''ē̂ta'' or ''ita'' ) is the seventh letter of the Greek alphabet, representing the close front unrounded vowel, . Originally denoting the voiceless glottal fricative, , in most dialects of Ancient Greek, it ...

c + k

2 c^2 + \cdots\, or :

\frac =

+ k

2 c + \cdots,\, where

\frac

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

{{Reflist Laboratory glassware Polymer chemistry Viscosity meters