An Ubbelohde type viscometer or suspended-level viscometer is a

measuring instrument A measuring instrument is a device to measure a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Establ ...

which uses a capillary based method of measuring

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

. 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 an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, an ...

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 A viscometer (also called viscosimeter) is an instrument used to measure the viscosity of a fluid. For liquids with viscosities which vary with flow conditioning, flow conditions, an instrument called a rheometer is used. Thus, a rheometer can be c ...

. 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 (μm) in diameter. Capillaries are composed of only the tunica intima, consisting of a thin wall of simple squamous endothelial cells. They are the smallest blood vessels in the body: ...

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 continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...

it takes for a

volume Volume is a measure of occupied 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). The de ...

V to elute. The ratio

\frac

depends on R as the capillary

radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...

, 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 e ...

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 substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

of the liquid, g the

Standard gravity The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. ...

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 (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a s ...

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'', an ...

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. It should not be confused with inherent viscosity, which is the ratio of the natural logarithm of the relative viscosity to th ...

�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 ''an'' represents the coefficient of the ''n''th term and ''c'' is a const ...

: :

\eta_ =

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

c + k

2 c^2 + \cdots\, or :

\frac =

+ k\eta + \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