VICOSITY DEPARTMENT OF PHARAMCETUICS CHALAPATHI INSTIUTTE OF PHARMACEUTICAL
- Slides: 34
VICOSITY DEPARTMENT OF PHARAMCETUICS CHALAPATHI INSTIUTTE OF PHARMACEUTICAL SCIENCES
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.
�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 forms
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 water
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 ddv Top layers d. F ddr Fig. 1 Block of liquid Bottom layers
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 stress
i. e ------eq. 1 F /A = η dv/dr In which η is coefficient of viscosity, usually referred as Viscosity, η = F/G 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 Rheogram F
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 1 cm 2 in area and separated by distance of 1 cm. It is also expressed in centipoise (cp = 0. 01 poise). CGS system for poise is dyne. cm/cm 2 or g. cm-1. sec-1
Kinematic viscosity is the absolute viscosity defined as viscosity (η) divided by density (δ) of the liquid at a specific temprature. Kinematic viscosity = η/δ The units are stokes (s) and centistokes (cs) Sometimes, the term (φ) Fluidity is used, it is defined as reciprocal of viscosity.
Absolute viscosities of some common Newtonian liquid. Liquids Castor oil CHCl 3 Ethanol Glycerin 93 % Olive oil Water Viscosities (cp) 1000 0. 563 1. 19 400 1. 0019
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.
The relationship between viscosity and temprature expressed by equation analogues to the Arrhenius equation. η=Ae Ev RT Where, A = Cost. Depend on molecular weight & volume of liquid Ev= Activation energy required to initiate flow between molecules
q 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. q 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. q Because a molecule in flow can back, turn and maneuver in smaller space than actual size i. e. Car in a parking lot
q More energy is required to break bonds and permit flow in liquids composed of molecules that are associated through hydrogen bonds. q These bonds are broken at high temprature by thermal movement and decreases Ev.
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.
Determination of rheologic (flow) properties Selection of viscometer Single point viscometer Ostwald viscometer Falling sphere viscometer Principle Stress α rate of shear Equipment works at Single rate of shear Application Newtonian flow Multi point Cup and bob Cone and plate Principle Viscosity det. at several rates of shear to get consistency curves Application non -Newtonian flow
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.
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. 1
Where, ρ1 = density of unknown liquid ρ2 = 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. η = П r 2 t Δ P / 8 l V eq: 2 Where, r = radius of capillary, t = time of flow, Δ P = pressure head dy/cm 2 , l = length of capillary cm, V = volume of liquid flowing, cm 3
For a given Ostwald viscometers, the r, V and l are combine into constant (K), then eq. 2 can be written as, η = KtΔP eq. 3 In which, The pressure head ΔP ( 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,
If these constants are incorporate into the eq. 3 then, viscosity of liquids may be expressed as: η 1 = K’ t 1 ρ1 eq. 4 η 2 = K’ t 2 ρ2 eq. 5 On division of eq. 4 and 5 gives the eq. 1, which is given in the principle, eq. 6
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 dispersions
Applications: ü It is used in the formulation and evaluation of P’ceutical dispersions system such as colloids, suspensions, emulsions etc. ü It is official in IP for the evaluation of liquid paraffin, light liquid paraffin and dextran 40 injection.
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
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. η = t ( Sb – Sf ) B 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.
Multi point viscometers (Rotational) Cup & bob viscometers Principle: Torque Bob 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. Cup 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. η = Kv w / v W= wt. on hanger (stress), v= shear rate, Kv= constant for instrument
Various instruments are available, differ mainly whether torque results from rotation of cup or bob. ü 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. Mc. Michael viscometer
ü 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.
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/cm 2 by using appropriate constants. Mathematical treatment: For, rotational viscometers, the shear – stress relationship can be expressed as, Ω = 1 T / η 4 П h ( 1/ Rb 2 – 1/ Rc 2) Where, Ω = Angular velocity ( radian / sec), Rb = Radius of bob T= Torque dy cm Rc = Radius of cup h = Depth of bob immersed in liquid eq. 1
Combining all constants, in eq. 1 η = Kv T/Ω eq. 2 Kv = 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, η = Kv w/v eq. 3 Kv is obtained by analyzing material of known viscosity in poise.
The equation for plastic viscosity (U), when used the stormer viscometer, U = K v W – Wf / V eq. 4 Wf = yield value intercept The yield value for plastic system is obtained by using the expression; f = K f × Wf eq. 5 Where, Kf = Kv × 2 П / 60 × 1 / 2. 303 log (Rc/Rb) Rc = Radius of cup & Rb = Radius of bob
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)
Viscosity for Newtonian system can be estimated by, η = C T/V eq. 1 Where, C = Instrument constant, T = Torque reading & V = Speed of the cone (rpm) Plastic viscosity determined by, U = C f T – Tf / v eq. 2 Yield value (f) = Cf × Tf Tf = Torque at shearing stress axis (extrapolate from linear portion of curve). Cf = Instrument constant