Rheology in Pharmacy Prepared By Muzamil Rashid M. Pharma Ist sem. ISF College Of Pharmacy , Moga Punjab

INTRODUCTION:

INTRODUCTION rheo – to flow logos – science Rheology is the study of the flow and deformation of matter under stress.

importance:

importance Formulation of medicinal and cosmetic creams, pastes and lotions. Formulation of emulsions, suspensions, suppositories, and tablet coating. Fluidity of solutions for injection. In mixing and flow of materials, their packaging into the containers, their removal prior to use, the pouring from the bottle. Extrusion of a paste from a tube . Passage of the liquid to a syringe needle.

Contd……………:

Contd …………… Can affect the patient’s acceptability of the product, physical stability, biologic availability, absorption rate of drugs in the gastrointestinal tract. Influence the choice of processing equipments in the pharmaceutical system.

NEWTONS LAW:

NEWTONS LAW According to NEWTONS LAW higher the viscosity of a liquid, the greater is the force per unit area (shearing stress F) required to produce a certain rate of shear( G). rate of shear α shearing stress F= ῃ G Where F= F’/ A G= dv / dr ῃ= viscosity

Types of flow:

Types of flow

Newtonian flow::

Newtonian flow: A Newtonian fluid (named for Isaac Newton ) is a fluid whose stress versus rate of shear curve is linear and passes through the origin . The constant of proportionality is known as the viscosity . Examples : Water, chloroform, Castor oil, ethyl Alcohol etc.

viscosity:

viscosity It is defined as resistance to the flow. ῃ is the coefficient of viscosity. And is calculated as ῃ =F/ G Where F= Shearing stress G= Rate of shear Unit of viscosity is Poise or dyne.sec/cm 2 .

Non newtonian flow:

Non newtonian flow A non newtonian flow is defined as one for which the relation between F and S is not linear. In other words when the shear rate is varied, the shear stress is not varied in the same proportion. The viscosity of such a system thus varies as the shearing stress varies. It can be seen in liquids and in solid heterogeneous dispersions such as emulsions, suspensions, colloids and ointments .

Non newtonian systems:

Non newtonian systems Three classes: PLASTIC FLOW PSEUDOPLASTIC FLOW DILATENT FLOW

PLASTIC FLOW::

PLASTIC FLOW : In which curve does not pass through the origin, the substance behaves initially elastic body and it fails to flow when less amount of stress is applied. As increase the stress, leads to non-linear Increase in shear rate but after that curve is linear. The linear portion extrapolated intersects the x axis at the point called as yield value So, plastic flow shows Newtonian flow above the yield value.

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The curve represents plastic flow, such materials are called as Bingham bodies. Bingham bodies does not flow until the shearing stress is corresponding to yield Value exceeded. So, yield value is important property of certain dispersions. The reciprocal of mobility is Plastic viscosity EXAMPLES: ZnO in mineral oil, certain pastes , paints and ointments.

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Plastic flow explained by flocculated particles in concentrated suspensions, ointments, pastes and gels. Flocculated Individual Particles particles Yield value Increase stress Flow F/A

Plastic flow :

Plastic flow The curve for the plastic flow is as fallows. Shearing stress, F Rate of shear, G Yield value Slope = mobility

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The equation describing plastic flow is, Where, f = Yield value F = Shearing stress G = Rate of shear U = F – f / G

Pseudo plastic flow:

Pseudo plastic flow Many P’ceutical products liquid dispersion of natural and synthetic gums shows pseudo plastic flow. eg. 1. Tragacanth in water 2. Sod. Alginate in water 3. Methyl cellulose in water 4. Sodium CMC in water .

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With increase in the shearing stress the disarranged molecules orient themselves in the direction of flow, thus reducing friction and allows a greater rate of shear at each shearing stress. Some of the solvent associated will be released resulting in decreased viscosity. This type of flow behavior is also called as shear thinning system.

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Graph for pseudo plastic flow is like this In which curve is passing from origin (Zero shear stress), so no yield value is Obtained. As shear stress increases, shear rate increases but not linear. Shearing stress, F Rate of shear, G

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Pseudo plastic flow can be explained by Long chain molecules of polymer. In storage condition, arrange randomly in dispersion. Water Stress Polymer long chain with water molecules Polymer & water molecules align on direction of force

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On applying F/A , shearing stress molecules ( water & polymer) arrange long axis in the direction of force applied. This stress reduces internal resistance & solvent molecules released form polymer molecules. Then reduce the concentration and size of molecules with decrease in viscosity.

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The exponential equation shows this flow N = no. of given exponent η = Viscosity coefficient In case of pseudo plastic flow, N > 1 . i.e. More N >1 , the greater pseudo plastic flow of material. If N = 1 , the flow is Newtonian . F N = η G

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Taking Log on both sides, i.e. On rearrangement, we get This equation gives straight line, N log F = log η + log G log G = N log F - log η

Dilatant flow:

Dilatant flow Certain suspensions with high % of dispersed solids shows an increase in resistance to flow with increasing rates of shear , such system increase in volume when sheared , such system called as dilatant flow. Also, called as “ Shear thickening system” i.e. when stress is removed, dilatant system return to its original position

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Graph for dilatant flow is like this In which curve is passing from origin (Zero shear stress), so no yield value is Obtained. Non-linear increase in rate of shear. Increase resistance to flow on increase rate of shear Shearing stress, F Rate of shear, G

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In which, particles are closely packed with less voids spaces, also amount of vehicle is sufficient to fill the void volume. This leads particles to move relative to one another at low rate of shear. At rest close packed Less void volume Sufficient vehicle Low consistency Open packed High void volume Insufficient vehicle High consistency Increase rate of shear

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So therefore , dilatant suspension can be poured from bottle boz in these condition it is fluid. When stress is increased, the particles shows the open packing and bulk of system (void volume is increase) is increased. But the amount of vehicle is insufficient to fill this void space. Thus particles are not wetted or lubricated and develop resistance to flow. Finally system show the paste like consistency.

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Because of this type of behavior, the dilatant suspension can be process by high speed mixers, blenders or mills. The exponential equation shows this flow N = no. of given exponent η = Viscosity coefficient In which N < 1, and decrease as the dilatancy Increase If N = 1, the system is Newtonian flow F N = η G

Measurement of viscosity:

Measurement of viscosity

Determination of rheologic (flow) properties:

Determination of rheologic (flow) properties Selection of viscometer Single point viscometer Multi point viscometer Ostwald viscometer Cup and bob viscometer Falling sphere viscometer Cone and plate viscometer Principle Principle Stress α rate of shear Viscosity det. at several Equipment works at rates of shear to get Single rate of shear consistency curves Application Application Newtonian flow non -Newtonian flow Newtonian flow

Single point viscometers:

Single point viscometers Ostwald viscometer (Capillary) The Ostwald viscometer is used to determine the viscosity of Newtonian fluid. The viscosity of Newtonian fluid is determined by measuring time required for the fluid to pass between two marks .

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Principle: When a liquid flows by gravity, the time required for the liquid to pass between two marks ( A & B) through the vertical capillary tube. the time of flow of the liquid under test is compared with time required for a liquid of known viscosity (Water). Therefore, the viscosity of unknown liquid ( η 1 ) can be determined by using following equation: eq.1

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Where, ρ 1 = density of unknown liquid ρ 2 = density of known liquid t 1 = time of flow for unknown liquid t 2 = time of flow for known liquid η 2 = viscosity of known liquid Eq. 1 is based on the Poiseuille’s law express the following relationship for the flow of liquid through the capillary viscometer. Where, r = radius of capillary, t = time of flow, Δ P = pressure head dyne/cm 2 , l = length of capillary cm, V = volume of liquid flowing, cm 3 η = П r 2 t Δ P / 8 l V Eq:2

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For a given Ostwald viscometers, the r, V and l are combine into constant (K) , then eq. 2 can be written as, In which, The pressure head Δ P ( shear stress) depends on the density of liquid being measured, acceleration due to gravity (g) and difference in heights of liquid in viscometers. Acceleration of gravity is constant , & if the levels in capillary are kept constant for all liquids, η = Kt Δ P Eq.3

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If these constants are incorporate into the eq. 3 then, viscosity of liquids may be expressed as: On division of eq. 4 and 5 gives the eq .1 , which is given in the principle, eq. 6 η 1 = K’ t 1 ρ 1 eq. 4 η 2 = K’ t 2 ρ 2 eq. 5

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Equation.6, may be used to determine the relative and absolute viscosity of liquid. This viscometer, gives only mean value of viscosity because one value of pressure head is possible. Ostwald viscometer is used for highly viscous fluid i.e. Methyl cellulose Dispersions

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Applications : It is used in the formulation and evaluation of P’ceutical dispersions system such as colloids, suspensions, emulsions etc. It is official in IP for the evaluation of liquid paraffin , light liquid paraffin and dextran 40 injection.

Falling sphere viscometers:

Falling sphere viscometers It is called as Hoeppler falling sphere viscometers . Principle : A glass or ball rolls down in vertical glass tube containing the test liquid at a known constant temprature. The rate at which the ball of particular density and diameter falls is an inverse function of viscosity of sample. Construction: Glass tube position vertically. Constant temprature jacket with Water circulation around glass tube

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Working: A glass or steel ball is dropped into the liquid & allowed to reach equilibrium with temprature of outer jacket. The tube with jacket is then inverted so that, ball at top of the inner glass tube. the time taken by the ball to fall between two marks is measured, repeated process for several times to get concurrent results. For better results select ball which takes NLT 30 sec. to fall between two marks. Where, t = time in sec.for ball to fall between two marks Sb & Sf = Specific gravities of ball and fluid under examination. B = Constant for particular ball. η = t ( Sb – Sf ) B

Multi point viscometers (Rotational):

Multi point viscometers (Rotational) Cup and Bob Various instruments are available, differ mainly whether torque results from rotation of cup or bob. Couette type viscometers : Cup is rotated , the viscous drag on the bob due to sample causes to turn. The torque is proportional to viscosity of sample. Ex. McMichael viscometer

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Searle type viscometers : Bob is rotated , the torque resulting from the viscous drag of the system under examination is measured by spring or sensor in the drive to the bob. Ex. Stormer viscometer Working: The test sample is place in space between cup and bob & allow to reach temprature equilibrium. A weight is place in hanger and record the time to make 100 rotations by bob, convert this data to rpm. This value represents the shear rate, same procedure repeated by increasing weight.

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So then plotted the rheogram rpm Vs weights the rpm values converted to actual rate of shear and weight converted into units of shear stress, dy/cm2 by using appropriate constants . Mathematical treatment : For, rotational viscometers , the relationship can be expressed as, η = Kv w/v where v , rpm generated by weight w , in gm Kv is obtained by analyzing material of known viscosity in poise.

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Cone and plate viscometer (Rotational viscometer) Principle: The sample is placed on at the center of the plate, which is raised into the position under the cone. The cone is driven by variable speed motor and sample is sheared in the narrow gap between stationary plate and rotating cone. Rate of shear in rpm is increased & decrease by selector dial and viscous traction or torque (shearing stress) produced on the cone.

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Viscosity for Newtonian system can be estimated by, Where, C = Instrument constant, T = Torque reading & V = Speed of the cone (rpm) Plastic viscosity determined by, Yield value ( f ) = C f × T f T f = Torque at shearing stress axis (extrapolate from linear portion of curve). C f = Instrument constant η = C T/V eq.1 U = C f T – T f / v eq.2

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