Rheology:
Rheology Darshan R. Telange Assistant Professor, SPTM, Shirpur campusA general idea:
A general idea Rheology is science that concerned with flow of fluids and deformation of solid. study of flow properties of liquids is important in the manufacture of several dosage forms i.e. simple liquids, gels, creams, pastes. These system can change their flow behavior when exposed to different stress conditions .PowerPoint Presentation:
Manufacture of dosage forms : Materials undergo mixing, flowing through pipes, containers influence the selection of mixing equipment. Handling of drugs for administration : The syringibility of medicine, pouring of liquids from containers, extrusion of ointment from tubes all depend on the flow of behavior of dosage formsPowerPoint Presentation:
Flow property of simple liquid is expressed in terms of viscosity. Viscosity is an expression of resistance to flow of liquid, Higher the viscosity of liquid, greater is the resistance to flow. For eg. Groundnut oil, honey, syrups all resist the flow more in comparison to water or alcohol . On molecular level, the motion is transferred between molecules of syrups is slower than molecules for waterNewtonian systems (Simple liquids):
Newtonian systems ( Simple liquids ) Newton was the first to study flow properties of liquids , where he recognized that the higher the velocity of a liquid greater is the F/A ( Shearing stress) required to produce certain rate of shear. Now consider, a block of liquid consisting of parallel plates of molecules d dv d dr d F Top layers Bottom layers Fig.1 Block of liquidPowerPoint Presentation:
In this fig.1, the bottom layer is fixed and top layers of liquid is moved at constant velocity, so each lower layer will move with velocity directly proportional to its distance from stationary bottom layers. The difference of velocity dv, between two planes of liquid separated by infinitesimal distance dr, is velocity gradient or rate of shear i.e. dv/dr Means F/A required to bring about flow is called as “shearing stress” & it is given by symbol F. Hence, rate of shear α shearing stressPowerPoint Presentation:
i.e ------------ eq.1 In which η is coefficient of viscosity , usually referred as Viscosity, eq.1 is written as, -------------eq.2 When, graph is plotting F vs G, a straight line is passing through the origin is obtained for Newtonian system. G F Rheogram F /A = η dv/dr η = F/GPowerPoint Presentation:
The unit of viscosity is poise Poise is defined as shearing force (stress) required to produce a velocity of 1 cm/sec between two parallel planes of liquid each 1cm2 in area and separated by distance of 1cm. It is also expressed in centipoise ( cp = 0.01 poise ). CGS system for poise is dyne.cm/cm2 or g.cm-1.sec-1Kinematic viscosity:
Kinematic viscosity Kinematic viscosity is the absolute viscosity defined as viscosity ( η ) divided by density ( δ ) of the liquid at a specific temprature. The units are stokes (s) and centistokes (cs) Sometimes, the term ( φ ) Fluidity is used, it is defined as reciprocal of viscosity. Kinematic viscosity = η / δPowerPoint Presentation:
Absolute viscosities of some common Newtonian liquid. Liquids Viscosities (cp) Castor oil 1000 CHCl3 0.563 Ethanol 1.19 Glycerin 93 % 400 Olive oil 100 Water 1.0019Effect of temprature on viscosity:
Effect of temprature on viscosity As the temprature increases, the viscosity of liquid is decreases, boz the liquid acquired thermal energy which shows the breaking of cohesive forces. Where as the fluidity of liquid is increases. In case of gases, temprature increases with increase in viscosity due to increased molecular interaction and collision.PowerPoint Presentation:
The relationship between viscosity and temprature expressed by equation analogues to the Arrhenius equation. Where, A = Cost. Depend on molecular weight & volume of liquid Ev= Activation energy required to initiate flow between molecules η = A e Ev RTPowerPoint Presentation:
The energy of vaporization of liquid is energy required to remove the molecule from liquid, leaving a “hole” behind equal in size to that of molecule which has removed, then another molecule is moves into hole . The activation energy for flow has been found to be 1/3 that of energy of vaporization i.e. free space required for flow is 1/3 the volume of molecule. Because a molecule in flow can back, turn and maneuver in smaller space than actual size i.e. Car in a parking lotPowerPoint Presentation:
More energy is required to break bonds and permit flow in liquids composed of molecules that are associated through hydrogen bonds. These bonds are broken at high temprature by thermal movement and decreases Ev.Non-newtonian system:
Non- newtonian system The majority of fluids in P’ceutical field are not simple liquids and hence do not exhibit the Newtonian flow, so these system called as non-Newtonian system. Eg. Heterogeneous dispersions i.e. Emulsion, Suspension and ointments When non-Newtonian fluids are analyzed by viscometer, the were results plotted. A various curves were found representing the flows.PowerPoint Presentation:
Types of flows Plastic flow Pseudo plastic flow Dilatants flow Plastic flow :
Plastic flow The curve for the plastic flow is as fallows. Shearing stress, F Rate of shear, G Yield value Slope = mobilityPowerPoint Presentation:
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.PowerPoint Presentation:
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 slope of Rheogram is called as Mobility which analogeus to fluidity in Newtonian system. The reciprocal of mobility is Plastic viscosity (U).PowerPoint Presentation:
The equation describing plastic flow is, Where, f = Yield value F = Shearing stress G = Rate of shear U = F – f / GPowerPoint Presentation:
Plastic flow explained by flocculated particles in concentrated suspensions, ointments, pastes and gels. Flocculated Individual Particles particles Yield value Increase stress Flow F/APowerPoint Presentation:
In which, When F/A apply on the flocculated particles (particle – particle contacts) the contacts are broken and yield value is reached. Yield value is indication of break down of contacts so particle behave individually. After getting yield value, the increase in stress (F – f) increase in rate of shear.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 .PowerPoint Presentation:
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, GPowerPoint Presentation:
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 forcePowerPoint Presentation:
The curved graph obtained from shearing action on long chain molecules of polymer. 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.PowerPoint Presentation:
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 GPowerPoint Presentation:
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 ηDilatant 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 positionPowerPoint Presentation:
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, GPowerPoint Presentation:
Pseudo plastic flow can be explained by Suspension with high conc. of solid ( > 50 %) deflocculated Particles Suspension with starch in water Inorganic pigments in water e.g. Kaolin 12 % in water Zno 30 % in waterPowerPoint Presentation:
In which, particles are closely packed with less voids spaces, also amount of vehicle is sufficient to fill the void volume. This leads to particles are 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 shearPowerPoint Presentation:
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.PowerPoint Presentation:
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 GThixotrophy (Gel-Sol-Gel):
Thixotrophy (Gel-Sol-Gel) It is defined as, isothermal and comparatively slow recovery on standing of material of a consistency lost through shearing. It is shear thinning system , when agitated and kept aside it is expected to return its original state of fluidity, but takes longer time to recover compared to the time taken for agitation. Thixotropic behavior can be shown by plastic and pseudo plastic system. Thixotrophy concept (particle – particle interactions) (Gel – Sol – Gel transformation):
Thixotrophy concept (particle – particle interactions) (Gel – Sol – Gel transformation) Multi point contacts (High consistency or high viscosity) Contacts break down (low consistency or low viscosity) Particle contacts form due to brownian motion At rest ( On storage) Gel state On shear (equilibrium) Sol state Gel state Set aside (removal of stress) Rapid process slow processPowerPoint Presentation:
The Rheogram of thixotropic material depends on: Rate at which shear increased or decreased. Length of time during which sample is subjected to any one rate of shear. The thixotrophy phenomena can be observed by constructing consistency curves. :
The thixotrophy phenomena can be observed by constructing consistency curves. From the graph up curve ab is obtained, up to maximum point b . If the rate of shear is reduced , then down curve bc is obtained. In Non-Newtonian system , the down curve is displaced to left of the up curve. In this graph, the material has low consistency at any rate of shear on down curve compared to that shown on up curve . lly, thixotropic curves constructed for pseudo plastic system . In Newtonian system, down curve superimposed to up curve. Shear stress, F Rate of shear, G a b c Plastic system Pseudo plastic systemAnti-thixotrophy (-ve thixotrophy):
Anti-thixotrophy (-ve thixotrophy) Anti-thixotrophy represents an increase in consistency (high viscosity) rather decrease in consistency in the down curve . The increase in thickness or resistance to flow with increase time of shear observed for ( magnesia magma). Anti – thixotrophy is flocculated system containing low solid content ( 1 – 10 %). Dilatancy system is deflocculated system containing solid content ( > 50 %).PowerPoint Presentation:
Individual particles (in large no. Of small flocs) (Low viscosity) Particle collision & contacts are more (Large flocs in small no.) ( High viscosity) Flocs contacts break individual particles (Low viscosity) At rest ( On storage) On shear (equilibrium) Sol state Set aside (removal of stress)The Anti - thixotrophy phenomena can be shown by Magnesia magma:
The Anti - thixotrophy phenomena can be shown by Magnesia magma From the Rheogram it is observed that, When Magnesia magma was alternatively sheared at sing and sing rate of shear , magma got thick continuously. Finally, reach the equilibrium state in which, further cycling of sing and sing rate of shear no longer sing consistency of material. Equilibrium state where gel was found. When allow to stand , material return to sol like property. A B C D Shear stress, F Rate of shear, G UP curve Down curveRheopexy:
Rheopexy Rheopexy is phenomena in which a sol forms a gel more readily when shaken or sheared than when allow to form the gel while the material is kept at rest. e.g. Magnesia magma , Clay suspension In rheopectic system , the gel is the equilibrium state. In anti – thixotropic system , the sol is the equilibrium state.Measurement of thixotrophy:
Measurement of thixotrophy The most apparent characteristics of thixotropic system is the Hysteresis loop formed by up curve & down curves of the rheograms. The area of Hysteresis loop has been used to measure the thixotropic breakdown and can be obtained by means of Planimeter . With plastic ( Bingham ) bodies ; two approaches are used to estimate degree of thixotrophy.PowerPoint Presentation:
Two approaches To det. Structural breakdown with time at constant rate of shear To det. Structural breakdown due to increasing shear rate.PowerPoint Presentation:
In which, The shear rate of thixotropic material is increased from a to b and then decrease at same rate back to e . This results in Hysteresis loop abe . If the sample taken to point b & shear rate held constant for certain period of time (t1 sec.) then stress & consistency decrease to an extent depend on rate, time of shear & str. of sample , results the Hysteresis loop abce . If sample held for same rate of shear for (t2 sec.) , then loop abcde observed. d t1 b c e a Shear stress, F Rate of shear, G t2 1/U1 1/U2To det. Structural breakdown with time at constant rate of shear:
To det. Structural breakdown with time at constant rate of shear Based on such Rheogram the Thixotropic coefficient B , The rate of breakdown with time at constant rate of shear , calculated as fallows. Where, U1 & U2 = Plastic viscosities of two down curves after shearing at a constant rate for t1 & t2 seconds . A method for characterizing thixotropic behavior is to measure fall in stress with time at several rates of shear Shear stress, F Rate of shear, G 1/U1 1/U2 t2 B = U 1 – U 2 / In t 2 /t 1 a b c d e t1To det. Structural breakdown due to increasing shear rate:
To det. Structural breakdown due to increasing shear rate In which two hysteresis loops are obtained having different maximum rate of shear, V1 & V2 . In this, thixotropic coefficient, M, represents loss in shearing stress per unit increase in shear rate , is obtained as fallows. Where, M = dyne sec/cm2 M value depend on rate of shear boz shear rates affect the down curves. Shear stress, F Rate of shear, G V 2 V 1 1/U2 1/U1 M = U 1 – U 2 / In ( V 2 / V 1 )Application of thixotrophy:
Application of thixotrophy Thixotrophy is desirable property in emulsion and suspension Higher the thixotrophy, higher the physical stability of suspension. The degree of thixotrophy is related to the specific surface of penicillin used.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 flowSingle point viscometers:
Single point viscometers Ostwald viscometers (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 .PowerPoint Presentation:
Principle: When a liquid is 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.1PowerPoint Presentation:
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 dy/cm2 , l = length of capillary cm, V = volume of liquid flowing, cm3 η = П r 2 t Δ P / 8 l V eq:2PowerPoint Presentation:
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.3PowerPoint Presentation:
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. 5PowerPoint Presentation:
Equation.6, may be used to determine the relative and absolute viscosity of liquid. This viscometer, gives only mean value of viscosity boz one value of pressure head is possible. Suspended level viscometers is used for highly viscous fluid i.e. Methyl cellulose dispersionsPowerPoint Presentation:
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 tubePowerPoint Presentation:
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 ) BMulti point viscometers (Rotational):
Multi point viscometers (Rotational) Cup & bob viscometers Principle: In which, the sample is sheared in space between the outer wall of a bob & inner wall of a cup into which the bob is fits. Now, either the bob or cup is made to rotate and torque resulting from viscous drag is measured by spring or sensor in the drive of the bob. The no. of rpm & torque showing rate of shear and stress resp. W = wt. on hanger (stress), v = shear rate, Kv = constant for instrument η = K v w / v Cup Bob TorquePowerPoint Presentation:
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 viscometerPowerPoint Presentation:
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.PowerPoint Presentation:
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 shear – stress relationship can be expressed as, Where, Ω = Angular velocity ( radian / sec), R b = Radius of bob T = Torque dy cm R c = Radius of cup h = Depth of bob immersed in liquid Ω = 1 T / η 4 П h ( 1/ R b 2 – 1/ R c 2 ) eq.1PowerPoint Presentation:
Combining all constants, in eq.1 K v = constant for instrument, in modified stormer viscometers, Ω is function of v , rpm generated by weight w , in gm proportional to T . so, eq. 2 written as, Kv is obtained by analyzing material of known viscosity in poise. η = Kv T/ Ω eq.2 η = Kv w/v eq.3PowerPoint Presentation:
The equation for plastic viscosity (U), when used the stormer viscometer, W f = yield value intercept The yield value for plastic system is obtained by using the expression; Where, K f = K v × 2 П / 60 × 1 / 2.303 log (R c /R b ) Rc = Radius of cup & Rb = Radius of bob U = K v W – W f / V eq.4 f = K f × W f eq.5PowerPoint Presentation:
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. Plot of rpm (shear rate) Vs scale reading (shear stress)PowerPoint Presentation:
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