Rheology and Methods of Analysis

Prof. S. S. Patil

Rheology is defined as the science of flow and deformation of materials. The term came from Greek rheo meaning to flow and logos means science.¹

It is the study of the change in form and the flow of matter, embracing elasticity, viscosity and plasticity. Rheological properties are studied with rheometry. In rheometry is used to determine the correlations between deformation, shear stress and time.

Viscometry:

Study of flow of materials and determines the correlations between shear rate, shear stress and time.

Viscosity:

Viscosity is an expression of the resistance of fluid to flow; the higher the viscosity, the greater the resistance². Viscosity is a material property, which is independent of geometry³. It is defined as the internal friction of a fluid, caused by molecular attraction, which makes it resist a tendency to flow. This friction becomes apparent when a layer of fluid is made to move in relation to another layer. The greater the friction, the greater the amount of force required to cause this movement, which is called shear. Viscosity is a quantity that describes a samples resistance to flow in contradiction to quantities as plasticity, elasticity and viscoelasticity. Sample is forced to flow by the force F (Figure 1). When force is removed the sample stops to flow. This is described by the quantity called dashpot. The dashpot is a symbol for Newtonian flow according to Newton’s viscosity law.

Figure 1: Force applied to fluid

Elasticity:

For materials that does not flow but shows solid properties a spring is used to describe them. A spring, described by Hooke´s law of elasticity. Elastic samples are studied by pulling the spring with a force F (Figure 2). The larger F the larger is the spring deformation. When force F is removed the sample returns to original shape and position

Figure 2: Spring with force

Plasticity:

Plastic materials show flow properties in the same way as viscous samples. Flow occurs first after that a minimum critical shear stress is exceeded, i.e. the yield stress. As soon as the force is lower than the yield point the flow will cease.

Viscoelasticity:

A viscoelastic sample shows both viscous and elastic properties. Viscoelasticity depends on the time scales of experiment (t) compared with the time scale of the sample, i.e. relaxation time (t).

De= t / t

Figure 3: Diagrammatic representation of viscosity, elasticity, plasticity and Viscoelasticity.

Viscosity - The viscous sample flows on the surface until surface tension stops further flow (surface tension > gravitational force)

Elasticity - The elastic sample will bounce at contact with table

Plasticity - The plastic sample will deform at impact with surface. Deformation will depend on the yield stress (yield stress compared with gravitational force)

Viscoelasticity - the viscoelastic sample will initially bounce upon contact with surface (short time scales). After longer times the sample will come to rest on surface and will start to flow (long time scales)

Figure 4: Viscosity model showing the parallel plates

Shear stress    

The shear stress is a measure of the amount of force applied to the sample per unit area, defined as: σ = F / A

The area is defined as the area used to shear the sample at equidistant sample elements (Figure 5)

Figure 5: Area used to shear the sample at equidistant sample elements

Shear rate      

γ = dy / dt = v/y

A rheometer is based on the application of a rotational speed to the measuring system. In the gap in the measuring system the shear rate is defined.  Shear rate is a sample parameter whereas the rotational speed is an instrument parameter (Figure 6).

Figure 6: Measuring system showing rotational speed and shear rate.

Viscosity  

  η= σ / γ

Strain

(shear deformation)

Shear deformation, g, is a measure of the samples deformation (strain)

Yield stress

(yield value or yield point)

The yield stress, σ_y, is a measure of the lowest shear stress which is needed to break the structure and start the flow

The fundamental unit of viscosity measurement is the “poise”. A material requiring a shear stress of one dyne per square centimetre to produce a shear rate of one reciprocal second has a viscosity of one poise, or 100 centipoise. Viscosity is also expressed in “Pascal-seconds” (Pa·S) or “milli-Pascal-seconds” (mPa·S). These are units of the International System and are sometimes used in preference to the Metric designations. One Pascal-second is equal to ten poise. One milli Pascal-second is equal to one centipoises.

Classification of fluids

Isaac Newton classified the fluids in two types; Newtonian and Non-Newtonian.

Newtonian fluid:

The fluids which obey Newton’s law of fluid flow are called Newtonian fluid⁴. Newtonian liquids start to flow when a stress is applied, and deformation stops instantly when the stress is removed⁵. In Newtonian liquids the viscosity is constant with respect to the time of shearing and it does not change in the re-testing situation⁶. Viscosity is only dependent on temperature⁷. A Newtonian and non- Newtonian fluid is represented graphically in fig.No.7. Newtonian materials are often simple fluids like dilute solutions and solvents.

Figure 7: Typical rheograms illustrating Newtonian, pseudoplastic, dilatant and plastic flows

 Non- Newtonian fluid:

The fluids which do not obey Newton’s law of fluid flow are called Non-Newtonian fluids. The relationship between shear stress and shear rate is not constant. As non-symmetrical objects pass by each other, as happens during flow, their size, shape, and cohesiveness will determine how much force is required to move them. At another rate of shear, the alignment of the objects may be different and more or less force may be required to maintain motion.

There are several types of non-Newtonian flow behaviour, characterized by the way a fluid’s viscosity changes in response to variations in shear rate. The most common types of non-Newtonian fluids are -

Pseudoplastic: This type of fluid will display a decreasing viscosity with an increasing shear rate. This type of flow behaviour is also called as “shear-thinning”. e.g. Paints, Emulsions, Dilute polymer solutions, Slurries, Shampoo, Blood and Orange juice.

Dilatent: This type of fluid will display an increasing viscosity with an increase in shear rate characterizes the dilatant fluid. Dilatancy is also referred as “shear-thickening” flow behaviour. Dilatant flow may be a result of dispersions containing a high concentration (≥ 50%) of small, deflocculated particles⁸, concentrated slurries, 52% potato starch in Water, candy compounds.

Plastic: This type of fluid behaves as a solid under static conditions. A certain amount of force must be applied to the fluid before any flow is induced. This force is called the “yield valie.”⁹ Below the yield value, the material behaves essentially as an elastic solid¹⁰. Once the yield value is exceeded and flow begins, plastic fluids may display newtonian, pseudoplastic or dilatant flow characteristics. e. g. clay suspension.

Thixotropy and Rheopexy: Some fluids will display a change in viscosity with time under conditions of constant shear rate. There are two types of fluids

Thixotropic: A thixotropic fluid undergoes a decrease in viscosity with time, while it is subjected to constant shearing.

Rheopectic: this is essentially the opposite of thixotropic behaviour, in that the fluid’s viscosity increases with time as it is sheared at a constant rate. e.g. electrostatic stabilised dispersions

Figure 8: Rheograms depicting time-dependent non-Newtonian behaviors

 Advanced Methods of Rheological Analysis: ^11-15

Some times it is needed to define viscosity data in rheological terms. This requires a complete mathematical description of the viscometer’s operating parameters and analysis of the rheological behaviour of the fluid being studied.

Operating parameters of various accessories.

1. spindle

Cylindrical: the following equations apply to cylindrical spindles only.

Shear rate (per second):

        

2ω R_c² R_b²

S = ------------------------

            X² (R_c² - R_b²)

Shear stress (dynes/cm²):

              M

F =   ----------------

          2 πR_b²L

Viscosity (poise):

 F ́

 η = -------

                         S

Where   ω = angular velocity of spindle (rad/sec)*

R_c = radius of container (cm)

R_b = radius of spindle (cm)

X = radius at which shear rate is being calculated

M = torque input by instrument

L = effective length of spindle

                          2π

  * =   --------- N          N = RPM

                         60

           

Coaxial:

Shear rate (per second):

   

2 R_c²

S  = ------------------------ ω

            (R_c² - R_b²)

 

Shear stress (dynes/cm²):

  

           M

F =   ----------------

          2 πR_b²L

 

Viscosity (poise):

 

            F ́

 η = -------

                          S 

 

Where S  = shear rate at surface of spindle

2. Cone and Plate

Shear rate (per second):

            ω

S” = ------------------------

            Sin θ

Shear stress (dynes/cm²):

              M

            F” =   ----------------

          2/3 πr³

Viscosity (poise):

             F”

 η = -------

                        S”

Where θ = cone angle

            r = cone radius

Time-Independent Non-Newtonian fluids

Ratio Methods:

A common method for characterizing and quantifying non-Newtonian flow is to figure the ratio of the fluid’s viscosity as measured at two different speeds. These measurements are usually made at speeds that differ by a factor of 10 , but any factor may be established.

In constructing the ratio, the viscosity value at the lower speed should be placed in the numerator, the one at the higher speed in the denominator. Therefore, for pseudoplastic fluids, the ratios will exceed 1.0 as the degree of pseudoplastic behavior increases. Conversely, for dilatant fluids, the ratio will be less than 1.0 as the degree of dilatancy increases.

This procedure is commonly known as the “thixotropic index.” The name is misleading since this ratio quantifies time-independent non-Newtonian behavior, not thixotropy, which is a time-dependent phenomenon.

A similar method eliminates calculation of viscosity and simply utilizes dial/display readings to derive what is known as a “viscosity ratio.”

Viscosity ratio:

-         log ( M_x / M10_x)

Where    M_x = Viscometer reading at speed x

         M10_x   = Viscometer reading at speed 10_x

Graphic methods:

The most basic graphic method of analyzing non-Newtonian flow is constructing a plot of viscosity versus spindle speed. Generally, viscosity is plotted along the Y-axis and speed (rpm) along the X-axis. The slope and shape of the resulting curve will indicate the type and degree of flow behavior.

Another method is to plot viscometer reading (on the X-axis) as a function of speed (on the Y-axis). If the graph is drawn on log-log paper, the result is frequently a straight line (indicating the type and degree of non-Newtonian flow) and its intercept with the X-axis can be used as empirical constants.

When shear rate and shear stress are known, as with cylindrical spindles or coaxial cylinder geometry, these values may be substituted for speed and viscometer reading in the above methods. Thus, predictions of viscosity at other shear rates may be made by interpolating between or extrapolating beyond the values available with particular spindle geometry.

When using these methods with disc spindle geometries, it is best to plot speed on the Y-axis and to make all measurements with the same spindle. An assumption that can be made with regard to shear rate is that, for a given spindle, the shear rate is proportional to the speed.

Template method:

A more sophisticated technique for the analysis of non-Newtonian fluids involves the use of a “template.” Its use is limited to fluids that follow the “power law,” meaning ones that display one type of non-Newtonian flow, rather than shifting from one type to another as shear rate is varied. e.g. a material that changed from pseudoplastic to dilatant flow when a certain shear rate is exceeded would not follow the power law over the full range of shear rates measured.

The template method is usable only with data generated with cylindrical spindles or coaxial cylinders. The data is fitted to a template to determine a constant called the “STI.” The STI is a convenient way to characterize non-Newtonian flow, much like the viscosity Index. Certain parameters of the viscometer in use and the STI are fitted to a second template, which is then used to predict the fluid’s viscosity at any selected shear rate.

Yield value determination:

Some fluids behave much like a solid at zero shear rate. They will not flow until a certain amount of force is applied, at which time they will revert to fluid behavior. This force is called the “yield value” and measuring it is often worthwhile. Yield values can help determine whether a pump has sufficient power to start in a flooded system, and often correlate with other properties of suspensions and emulsions. The pourability of a material is directly related to its yield value.

A simple method for determining a relative yield value is

                          V_a - V_b

Yield value =    -------------

                                     100

Where   V_a  = viscosity @ slowest available viscometer speed

             V_b = viscosity @ next-to-slowest viscometer speed

With this method, Newtonian fluids will show a yield value of 0, while plastic fluids will show an increasing yield value as the predicted viscosity at zero shear increases.

More accurate method of determining yield value involves plotting viscometer readings on the X-axis versus speed (RPM) on the Y-axis on standard graph paper. The line thus obtained is extrapolated to zero RPM. The corresponding value for the viscometer reading represents the yield value. If a cylindrical spindle is used t make the readings, the yield value may be calculated from this equation

Yield value = X₁ fa

Where X₁ = viscometer reading @ 0 RPM

                        fa = constant related to spindle.

Extrapolating the line to zero RPM is easy if the line is fairly straight. This is called Bingham flow. If the line is curved, as in pseudoplastic or dilatant flow, an estimate of X₁ must be made by continuing the curve until it intersects the X-axis. This estimated value of X₁ is them subtracted from all the other readings that comprise the graph. These new values are plotted on log-log paper, viscometer reading versus speed. This graph will usually be a straight line for power law fluids if the value for X₁ was estimated accurately. A curved line on this graph indicates that another estimate of X₁ should be made.

Once a straight line is obtained the angle this line forms with the Y-axis is measured. The power law index of this fluid can then is calculated from this equation:

Power law index

N = tan θ

Where θ = angle formed by plot line with Y-axis of graph

If θ is less than 45 degrees, the fluid is pseudoplastic; greater than 45 degrees, dilatant. The power law index can be used to calculate the defective shear rate at a given speed by using this equation

Shear rate (sec^-1)

              N

 S    = ------------------------

                           (0.2095) N

Where   N = power law index

                        N = viscometer speed

Another method for determining yield value and plastic viscosity when a plot of viscometer reading versus speed produces a curved line is to plot the square foot of the shear stress versus the square root of the shear rate. This often straightens the line and facilitates extrapolation to zero shear rates. This method is most suitable for pseudoplastic fluids with a yield value conforming to a model of flow behavior known as the Casson equation.

Time dependent non-Newtonian fluids

In most cases, analysis of thixotropic and rheopectic fluids involves plotting changes in viscosity as a function of time. The simplest method is to select a spindle and speed and leave the viscometer running for an extended period, noting the dial or display reading at regular intervals. It is important to control the temperature of the sample fluid carefully so that variations in temperature won’t affect the results. A change in the fluid’s viscosity over time indicates time-dependent behavior: a decrease signifies thixotropy and increase reopexy.

A second method is to graph the viscometer reading versus speed, using a single spindle. Starting at a low speed, note the reading at each successively higher speed until the reading goes off scale. A graph of these readings is the “up curve.” Without stopping the viscometer, reduce the speed incrementally to the starting point, again noting the reading at each speed. This is the “down curve.” It is best to allow a consistent time interval between each speed change. If the fluid is time-independent, the “up curve” and the “down curve” will coincide. If they do not, the fluid is time-dependent. The position of the up curve in relation to the down curve indicates the type of flow behavior: i.e. the up curve indicates a higher viscosity than the down curve, the fluid is thixotropic; lower, rheopectic.

An indication of the recovery time of the fluid can be obtained by turning off the viscometer at the end of the down curve, waiting for a given period of time, restarting the viscometer and immediately taking a reading.

A more sophisticated approach is to calculate the “thixotropic breakdown coefficient.” This is a single number which quantifies the degree of thixotropy displayed by the sample fluid. First, plot viscometer reading versus log time, taking readings at regular intervals. This usually produces a straight line. Then, apply the following equation

Thixotropy breakdown coefficient

                     St₁ – St₂

Tb =   ---------------------------          x     F

               ln t₂  / t₁

Where St₁ = viscometer reading at t₁ minutes

            St₂ = viscometer reading at t₂ minutes

            F = Factor for spindle / speed combination

 

Plot of thixotropic behavior may sometimes be used to predict the gel point of a fluid. One way to do this is to plot log viscometer reading versus time, using a single spindle and speed. If the resulting line has a steep slope, gelling is likely to occur. If the line curves and flattens out, gelation is unlikely.

Another technique is to plot time versus the reciprocal of the viscometer reading. In this method, the gel point can be read from the curve intercept at a viscometer reading of 100. Fluids which do not gel will be asymptotic to the vertical axis.

Temperature dependence of viscosity:

The viscosity of most fluids decreases with an increase in temperature. By measuring viscosity at two temperatures, it is possible to predict a flow curve representing the temperature dependence of the viscosity of a fluid according to the following relationships using the application of simultaneous equations.

η = A e^(B/T)

where B = (T₁ . T₂ / T₁ - T₂) . ln (η₂ / η₁)

A = η_{1 .} e^{(-B/ T}₁⁾

T₁ = temperature at which viscosity η₁ was measured

T₂ = temperature at which viscosity η₂ was measured

Viscoelastic test methods

Viscoelastic test methods should be used to get comprehensive information about the structural properties of pharmaceutical products. With viscoelastic rheological measurements the elastic properties of solids and the viscous properties of liquids, and the ratios between these two, can be determined.

Two different types of methods are available to determine the linear viscoelastic behavior of a material: dynamic and static methods⁶. The dynamic methods involve the application of harmonically varying stress or strain. The static methods involve the imposition of a step change in the stress or strain and the observation of the subsequent development of the strain or stress as a function of time. Analyses of the viscoelastic materials are designed not to destroy the structures, so that the measurements can provide information about the intermolecular and interparticle forces of the materials².

Dynamic methods

In oscillation tests the viscoelastic samples are subjected to sinusoidal oscillation stresses or oscillation strains⁴. In an oscillation test, a sinusoidally varying stress/strain of a fixed or varying period is applied to the sample, and the resulting sinusoidal strain/stress is measured. For a linearly viscoelastic material, the amplitude of stress is proportional to the amplitude of strain, and the stress alternates sinusoidally at the same frequency, but it is out of phase with the strain¹⁶ (Fig. No. 9). The in-phase response, at phase angle 0°, shows that the sample is ideal elastic material, and the out-of-phase response, at phase angle 90°, shows that the sample is ideal viscous material¹⁷. With viscoelastic materials the phase angle, δ, between the applied stress/strain and the resulting strain/stress is between 0° and 90° . The phase angle is a good indicator of the overall viscoelastic nature of the material¹⁸.

Figure 9. Oscillation curves of a viscoelastic fluid, a Newtonian liquid and an ideal solid. The stress is obtained as a function of strain. The behavior is presented with a four-element viscoelastic model. π is the angular deflection in radians; π corresponds to 180°, 2π to a full circle of 360°.

When the amplitude ratio and the phase angle are measured, the parameters representing viscoelastic behavior can be calculated. A complex shear modulus, G*, represents the total resistance of a material against the applied stress. The complex modulus G* is separated into the in-phase and out-of-phase components

G* = G´ + iG´´

where the storage modulus G´ is the in-phase (real) component and the loss modulus G´´ is the out-of-phase (imaginary) component. The storage modulus G´ gives information about the elastic properties of the material

G´ = (σ /ã ) cos δ

where σ is the stress, ã is the strain and δ the phase angle. The greater the G´, the more elastic are the characteristics of the material. The loss modulus G´´ gives information about the viscosity of the material

G´´ = (σ /ã ) sin δ

The greater the G´´, the more viscous are the characteristics of the material. The storage

modulus represents the spring-like deformation in mechanical models, while the loss modulus represents the dashpot-like deformation. A loss tangent, tan δ, is obtained by following equation

tan δ = G´´ / G´.

The loss tangent is the ratio between viscous and elastic properties, showing which one is the dominant one. With a tan δ value of 1, the elastic and viscous properties of the material are equal. The smaller the loss tangent is, the more elastic is the material¹⁹. Tan δ is often the most sensitive indicator of various molecular motions within the material²⁰.

Static methods

Static methods are either creep tests at constant stress or relaxation tests at constant strain. The creep test is used far more often than the relaxation test. In the creep test a constant stress is applied and the strain of a sample is determined as a function of time²¹. In the relaxation test the sample is subjected to a predetermined strain, and the stress required to maintain this strain is measured as a function of time.

During the creep test the strain is measured as a function of applied stress and presented in terms of compliance, J. The compliance is calculated from the measured strain,ã , and the applied stress, σ,

J (t) = ã (t) / σ

The smaller the J, the more elastic are the characteristics of the material. The creep curve of pharmaceutical semisolids can usually be split up into three separate regions: the instantaneous elastic region representing elastic stretching of primary structural bonds, the curved viscoelastic region representing the orientation of crystals or droplets due to the breaking and reforming of secondary bonds, and the viscous flow²² (Fig. No.10). In Fig. 10, the region A-B corresponds to the perfectly elastic movement as a result of the Maxwell spring. The region BC corresponds to the gradual increase in the strain curve, viscoelastic behavior that is related to the Voigt elements. The region C-D corresponds to the response of an ideal Newtonian fluid related to the Maxwell dashpot. The instantaneous elastic region recovers totally and the viscoelastic region partly²³.  The viscous region does not recover. In the recovery curve, in Fig. 10, the region D-E corresponds to the instantaneous elastic recovery and it is equivalent to the region A-B. The region E-F represents the elastic recovery and it is equivalent to B-C. The unrecoverable part of the curve corresponds to the viscous flow. The unrecoverable viscous flow represents the irreversibly broken internal bonds in the material.

Figure 10. Creep recovery curve of wool fat as a function of time. The structure is presented with a six-element viscoelastic model. Region A-B corresponds to instantaneous elastic response, region B-C to viscoelastic response and region C-D to viscous response. Regions D-E and E-F correspond to instantaneous elastic and elastic recoveries, respectively.

If the sample is tested under conditions within the linear viscoelastic region, the elements that cause an elastic response will give an equal contribution to both the creep and recovery phases.

Miscellaneous methods

There are many other techniques available for analyzing the rheological behaviour of fluids under a variety of conditions e.g.

• Approximation of shear rate and shear stress values using disc type spindles
• Techniques for determination of extremely low-sear viscosity and levelling behaviour of coating materials using spring relaxation procedures.
• Computer analysis of certain rheological characteristics.

Reference:

1. E. K. Fischer, 1948 J. Colloid Sci. 3, 73,
2. Martin, A., 1993. Physical Pharmacy. 4th Ed., Lea & Febiger, Philadelphia.
3. Tschoegl, N. W., 1989. The Phenomenological Theory of Linear Viscoelastic Behavior, An Introduction. Springer-Verlag, Berlin.
4. Schramm, G., 1994. A Practical Approach to Rheology and Rheometry. Gebrueder HAAKE GmbH, Karlsruhe.
5. Morrison, F.A., 2001. Understanding Rheology. Oxford University Press, Inc., New York.
6. Barnes, H.A., Hutton, J.F., Walters, K., 1989. An Introduction to Rheology. Elsevier, Amsterdam.
7. Briceno, M.I., 2000. Rheology of Suspensions and Emulsions. In: Nielloud, F., Marti-Mestres, G. (Ed.), Drugs and Pharmaceutical Sciences; Pharmaceutical Emulsions and Suspensions, Vol. 105, Marcel Dekker, Inc., New York, pp. 557-607.
8. Marriott, C., 1988. Rheology and Flow of Fluids. In: Aulton, M.E. (Ed.), Pharmaceutics: The Science of Dosage Form Design. Churchill Livingstone, New York. pp. 17-37.
9. Wood, J.H., 1986. Pharmaceutical Rheology. In: Lachman, L., Lieberman, H.A., Kanig, J.L. (Ed.), The Theory and Practice of Industrial Pharmacy. Lea & Febiger, Philadelphia, pp. 123-145.
10. Barry, B.W., 1983. Rheology of Dermatological Vehicles. In: Dermatological Formulations, Percutaneous Absorption. Marcel Dekker, Inc., New York, pp. 351-407.
11. Skelland A.H.P., 1967, Non-Newtonian flow and heat transfer, John Wiley & Sons, New York, NY.
12. Patton Temple C., 1979, Paint flow and pigment dispersion, second edition, Interscience Publishers, New York, NY.
13. Fredrickson Arnold G., 1964, Principles and applications of Rheology, Prentice-Hall Inc., Englewood Cliffs, NJ.
14. Colmen, Markovitz and Noll; 1966, Viscometeric flows of non-Newtonian fluids, Springer-Verlag New York Inc., New York, NY.
15. Van Wazer, Lyons, Kim, Colwell; 1963, Viscosity and flow measurement, Interscience Publishers, New York, NY.
16. Barry, B.W., 1974. Rheology of Pharmaceutical and Cosmetic Semisolids. In: Bean, H.S., Beckett, A.H., Carless, J.E. (Ed.), Advances in Pharmaceutical Sciences. Vol 4, Academic Press Inc., London, pp. 1-72.
17. Davis, S.S., 1974. Is pharmaceutical rheology dead? Pharm. Acta Helv. 49, 161-168.
18. Tamburic, S., Craig, D.Q.M., Vuleta, G., Milic, J., 1996. An investigation into the use of thermorheology and texture analysis in the evaluation of w/o creams stabilized with a silicone emulsifier. Pharm. Dev. Tech. 1, 299-306.
19. Davis, S.S., 1971. Viscoelastic properties of pharmaceutical semisolids III: Nondestructive oscillatory testing. J. Pharm. Sci. 60, 1351-1355.
20. Radebaugh, G.W., Simonelli, A.P., 1983. Phenomenological viscoelasticity of a heterogenous pharmaceutical semisolid. J. Pharm. Sci., 72, 415-422.
21. Davis, S.S., 1969. Viscoelastic properties of pharmaceutical semisolids, I: Ointment bases. J. Pharm. Sci. 58, 412-417.
22. Barry, B.W., Warburton, B., 1968. Some rheological aspects of cosmetics. J. Soc. Cosmet. Chemists 19, 725-744.
23. Barry, B.W., Eccleston, G.M., 1973, Influence of gel networks in controlling consistency of o/w emulsions stabilised by mixed emulsifiers. J. Texture Stud. 4, 53-81.

About Authors

1. Prof. S. S. Patil*

Assistant Professor, Appasaheb Birnale College of Pharmacy, South Shivajinagar, Sangli, M. S., India. Phone No. Off. 0233-2320062, Cell- 9422582605, Fax – 0233-2325677 shitalkumarpatil@yhoo.co.in

*Author for correspondence

2. Dr. C. S. Magdum, Vice-Principal, Appasaheb Birnale College of Pharmacy, South Shivajinagar, Sangli, M. S., India.Phone No. Off. 0233-2320062, Cell- 9423042749, Fax – 0233-2325677