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 viscosity Kinematic viscosity
Dynamic viscosityThe dynamic viscosity or viscosity coefficient h is thetangential force per unit surface, known as shearing stresst and expressed in pascals, necessary to move, parallel tothe sliding plane, a layer of liquid of 1 square metre at arate (v) of 1 meter per second relative to a parallel layer ata distance (x) of 1 meter.The ratio dv/dx is a speed gradient giving the rate of shearD 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 millipascalsecond (mPa·s).
Kinematic viscosityThe kinematic viscosity v, expressed in square metres persecond, is obtained by dividing the dynamic viscosity h by thedensity r expressed in kilograms per cubic metre, of the liquidmeasured at the same temperature, i.e. v = h/r.The kinematic viscosity is usually expressed in square millimetresper second.USPThe basic unit is the poise (according to USP)However, viscosities commonly encountered represent fractions ofthe poise, so that the centipoise (1 poise = 100 centipoises)proves to be the more convenient unit.
Measurement of ViscosityThe usual method for measurement of viscosity involves thedetermination of the time required for a given volume ofliquid to flow through a capillary.Many capillary-tube viscosimeters have been devised, butOstwald and Ubbelohde viscosimeters are among the mostfrequently used.A particularly convenient and rapid type of instrument is arotational viscosimeter, which utilizes a bob or spindleimmersed in the test specimen and measures the resistanceto 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.•
Calculate the dynamic viscosity h in millipascal seconds using the formula:K = constant of the viscometerρ = density of the liquid to be examined expressed inmilligrams per cubic millimetert = flow time, in seconds, of the liquid to be examined.The constant k is determined using a suitableviscometer 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 geometryis not defined.The measurements result in relative viscosity values, whichcannot be compared with absolute values or other relativevalues if not determined by the same relative viscometermethod.Different measuring systems are available for givenviscosity ranges as well as several rotational speeds.
ApparatusThe following types of instruments aremost common.Concentric cylinder viscometers(absolute viscometers)In the concentric cylinder viscometer(coaxial double cylinder viscometer orsimply coaxial cylinder viscometer), theviscosity is determined by placing theliquid in the gap between the inner cylinderand the outer cylinder.Viscosity measurement can be performedby rotating the inner cylinder (Searle typeviscometer) or the outer cylinder (Couettetype 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 byrotating a spindle (for example, cylinder- or disc-shaped, asshown in Figures) immersed in the liquid.Relative values of viscosity (or apparent viscosity) can bedirectly calculated using conversion factors from the scalereading at a given rotational speed.
In a general way, the constant k of the apparatus may bedetermined at various speeds of rotation using a certifiedviscometer calibration liquid. The viscosity ƞ thencorresponds 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 liquidsusing 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 beexamined from one ring mark to the other is determined.If no stricter limit is defined for the equipment used the result isvalid only if 2 consecutive measures do not differ by more than1.5 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.•
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 secondsusing the formula:k = constant, expressed in millimeter squared per secondsquared,ρ1 = density of the ball used, expressed in grams per cubiccentimeter,ρ2 = density of the liquid to be examined, expressed in gramsper cubic centimeter.t = falling time of the ball, in seconds.