Viscosity is a measure of a liquid's resistance to flow. It is defined as the shear stress divided by the rate of shear strain. There are several methods to measure viscosity, including using capillary tubes, rotating viscometers, and falling ball viscometers. The measurement involves determining the time required for liquid to flow through a capillary or for a ball to fall between marks in a viscometer tube, from which the dynamic viscosity in mPa·s can be calculated. Viscosity measurements require controlling the temperature accurately, usually within 0.1°C.

1. 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

2. Dynamic 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).

3. 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.

4. 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.

5. • 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 .

6. Common methods for determination of viscosity
Method 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.

7. 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.

8. 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.
•

9. 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.

10. 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.

11. 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.

12. 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.

13. 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:

14. 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.

15. 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:

16. 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.

17. • 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.

18. 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.

19. 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.
•

20. 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.

21. 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.