Viscosity

Viscosity is a property of liquids that is closely related to the resistance to flow.

It is defined in terms of the force required to move one plane surface continuously past another under specified steady-state conditions when the space between is filled by the liquid in question.

It is defined as the shear stress divided by the rate of shear strain.

BP

Dynamic viscosityKinematic viscosity

The dynamic viscosity or viscosity coefficient h is the tangential force per unit surface, known as shearing stress t and expressed in pascals, necessary to move, parallel to the sliding plane, a layer of liquid of 1 square metre at a rate (v) of 1 meter per second relative to a parallel layer at a distance (x) of 1 meter. The ratio dv/dx is a speed gradient giving the rate of shear D expressed in reciprocal seconds (s-1), so that h = t/D. The unit of dynamic viscosity is the pascal second (Pa·s). The most commonly used submultiple is the millipascal second (mPa·s).

Dynamic viscosity

Kinematic viscosity

The kinematic viscosity v, expressed in square metres per second, is obtained by dividing the dynamic viscosity h by the density r expressed in kilograms per cubic metre, of the liquid measured at the same temperature,

i.e. v = h/r.

The kinematic viscosity is usually expressed in square millimetres per second.

USP

The basic unit is the poise (according to USP)However, viscosities commonly encountered represent fractions of the poise, so that the centipoise (1 poise = 100 centipoises) proves to be the more convenient unit.

Measurement of Viscosity

The usual method for measurement of viscosity involves the determination of the time required for a given volume of liquid to flow through a capillary.

Many capillary-tube viscosimeters have been devised, but Ostwald and Ubbelohde viscosimeters are among the most frequently used.

A particularly convenient and rapid type of instrument is a rotational viscosimeter, which utilizes a bob or spindle immersed in the test specimen and measures the resistance to movement of the rotating part.

Different spindles are available for given viscosity ranges, and several rotational speeds generally are available.

• Other rotational instruments may have a stationary bob and a rotating cup.

• The Brookfield, Rotouisco, and Stormer viscosimeters are examples of rotating-bob instruments, and the MacMichael is an example of the rotating-cup instrument.

• Numerous other rotational instruments of advanced design with special devices for reading or recording, and with wide ranges of rotational speed, have been devised.

• Where only a particular type of instrument is suitable, the individual monograph so indicates.

• For measurement of viscosity or apparent viscosity, the temperature of the substance being measured must be accurately controlled, since small temperature changes may lead to marked changes in viscosity.

• For usual pharmaceutical purposes, the temperature should be held to within ±0.1 .  

Common methods for determination of viscosityMethod I (U tube viscometer)Apparatus

The apparatus consists of a glass U-tube viscometer made of clear borosilicate glass and constructed in accordance with the dimensions given in official books.

The monograph states the size of viscometer to be used.

Method • Fill the viscometer with the liquid being

examined through tube L to slightly above the mark G, using a long pipette to minimise wetting the tube above the mark.

• Place the tube vertically in a water bath and when it has attained the specified temperature, adjust the volume of the liquid so that the bottom of the meniscus settles at the mark G.

• Adjust the liquid to a point about 5 mm above the mark E.

• After releasing pressure or suction, measure the time taken for the bottom of the meniscus to fall from the top edge of mark E to the top edge of mark F.

Method II (Capillary viscometer method) (Ph. Eur. method 2.2.9) • The determination of viscosity using a suitable capillary

viscometer is carried out at a temperature of 20 ± 0.1 °C, unless otherwise prescribed.

• The time required for the level of the liquid to drop from one mark to the other is measured with a stop-watch to the nearest one-fifth of a second.

• The result is valid only if two consecutive readings do not differ by more than 1 per cent.

• The average of not fewer than three readings gives the flow time of the liquid to be examined.

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Calculate the dynamic viscosity h in millipascal seconds using the formula:

K = constant of the viscometer ρ = density of the liquid to be examined expressed in milligrams per cubic millimeter

t = flow time, in seconds, of the liquid to be examined. The constant k is determined using a suitable viscometer calibration liquid.

Method III (Rotating viscometer method) (Ph. Eur. method 2.2.10) • The principle of the method is to measure the force

acting on a rotor (torque) when it rotates at a constant angular velocity (rotational speed) in a liquid.

• Rotating viscometers are used for measuring the viscosity of Newtonian (shear-independent viscosity) or non-Newtonian liquids (shear dependent viscosity or apparent viscosity).

• Rotating viscometers can be divided in 2 groups, namely absolute and relative viscometers.

• In absolute viscometers the flow in the measuring geometry is well defined. The measurements result in absolute viscosity values, which can be compared with any other absolute values.

In relative viscometers the flow in the measuring geometry is not defined. The measurements result in relative viscosity values, which cannot be compared with absolute values or other relative values if not determined by the same relative viscometer method. Different measuring systems are available for given viscosity ranges as well as several rotational speeds.

Apparatus The following types of instruments are most common. Concentric cylinder viscometers (absolute viscometers) In the concentric cylinder viscometer (coaxial double cylinder viscometer or simply coaxial cylinder viscometer), the viscosity is determined by placing the liquid in the gap between the inner cylinder and the outer cylinder. Viscosity measurement can be performed by rotating the inner cylinder (Searle type viscometer) or the outer cylinder (Couette type viscometer), as shown in Figures.

Cone-plate viscometers (absolute viscometers) • In the cone-plate viscometer, the liquid is introduced into

the gap between a flat disc and a cone forming a define angle.

• Viscosity measurement can be performed by rotating the cone or the flat disc, as shown in Figures below. For laminar flow, the viscosity (or apparent viscosity) h expressed in Pascal-seconds is given by the following formula:

Spindle viscometers (relative viscometers) In the spindle viscometer, the viscosity is determined by rotating a spindle (for example, cylinder- or disc-shaped, as shown in Figures) immersed in the liquid. Relative values of viscosity (or apparent viscosity) can be directly calculated using conversion factors from the scale reading at a given rotational speed.

In a general way, the constant k of the apparatus may be determined at various speeds of rotation using a certified viscometer calibration liquid. The viscosity ƞ then corresponds to the formula:

Method • Measure the viscosity (or apparent viscosity) according to

the instructions for the operation of the rotating viscometer. • The temperature for measuring the viscosity is indicated in

the monograph. • For non-Newtonian systems, the monograph indicates the

type of viscometer to be used and if absolute viscometers are used the angular velocity or the shear rate at which the measurement is made.

• If it is impossible to obtain the indicated shear rate exactly, use a shear rate slightly higher and a shear rate slightly lower and interpolate.

• With relative viscometers the shear rate is not the same throughout the sample and therefore it cannot be defined.

• Under these conditions, the viscosity of non-Newtonian liquids determined from the previous formula has a relative character, which depends on the type of spindle and the angular velocity as well as the dimensions of the sample container (Ø = minimum 80 mm) and the depth of immersion of the spindle.

• The values obtained are comparable only if the method is carried out under experimental conditions that are rigorously the same.

Method IV (Falling ball viscometer method) (Ph. Eur. method 2.2.49) The determination of dynamic viscosity of Newtonian liquids using a suitable falling ball viscometer is performed at 20 ± 0.1 °C, unless otherwise prescribed in the monograph. The time required for a test ball to fall in the liquid to be examined from one ring mark to the other is determined. If no stricter limit is defined for the equipment used the result is valid only if 2 consecutive measures do not differ by more than 1.5 per cent.

Apparatus  • The falling ball viscometer consists of: a glass tube

enclosed in a mantle, which allows precise control of temperature;

• six balls made of glass, nickel-iron or steel with different densities and diameters.

• The tube is fixed in such a way that the axis is inclined by 10 ± 1° with regard to the vertical.

• The tube has 2 ring marks which define the distance the ball has to roll.

• Commercially available apparatus is supplied with tables giving the constants, the density of the balls and the suitability of the different balls for the expected range of viscosity.

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Method  • Fill the clean, dry tube of the viscometer, previously

brought to 20 ± 0.1 °C, with the liquid to be examined, avoiding bubbles.

• Add the ball suitable for the range of viscosity of the liquid so as to obtain a falling time not less than 30 s.

• Close the tube and maintain the solution at 20 ± 0.1 °C for at least 15 min. Let the ball run through the liquid between the 2 ring marks once without measurement.

• Let it run again and measure with a stop-watch, to the nearest one-fifth of a second, the time required for the ball to roll from the upper to the lower ring mark. Repeat the test run at least 3 times.

Calculate the dynamic viscosity ƞ in millipascal seconds using the formula:

k = constant, expressed in millimeter squared per second squared, ρ1 = density of the ball used, expressed in grams per cubic

centimeter, ρ2 = density of the liquid to be examined, expressed in grams

per cubic centimeter.

t = falling time of the ball, in seconds.