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In 1948, term Rheology was suggested by Bingham and Crawford, and it describes branch of science which deals with deformation and flow of mater. Rhe/ology (Greek) To flow Science Viscosity (: it is an expression of resistance of fluid to flow, that means with high resistance to flow the viscosity is high and vice versa. Rheology affects in the following pharmaceutical issues 1. Mixing and preparation of dosage forms 2. Packaging in containers 3. Removal prior to use including pouring from bottle, extrusion from tube, and passage through the needle 4. Physical stability 5. Patients acceptability 6. Biological availability (↔ absorption rate from GIT) Rheology of material is described by 3 parameters A. Stress B. Strain C. Time A. Shearing stress Block of liquid consist of parallel of molecules like cards Representation of the shearing stress = F/A= force per unit area required to cause flow Shearing stress unit System SI unit Cgs system Unit Pascal, pa Dynes/ cm2 Note that 1 pa = 10 dynes/ cm2 1 Exercise: 1 gm weight is hung from rubber band with cross sectional are of 0.049 cm 2. Find the stress on the rubber band? S = F/ A= weight X g (acceleration due to the gravity) / A = [1 gm X 980.7 cm / sec 2] / 0.049 cm 2 = 1 x 10 4 dynes/ cm 2 = 1000 pa = 1 kpa Dynes = gm. cm/ sec 2 B. Strain Strain: deformation of a body in response to a stress Type of strain A. Elongation and compression strain = Δ L Change in length / original length B. Shear strain= rate of shear= velocity of gradient (liquid) Rate of shear dv V4 V3 dr V2 V0 V1 o Bottom layer is stationary layer o Each layer moves with velocity directly proportional to the distance from stationary layer o Velocity gradient = dv/ dr = difference of velocity between two planes of liquid distance Unit of rate of shear is Sec –1 2 C. Time Time effects on the rheology of some materials (time dependent) Basically is the length of time that material subjected to stress It will be discussed fully in one the flowing lectures Elasticity and viscosity Elasticity: it is the ability of material to restore to its original shape upon releasing of stress Young’s Modulus defines the elasticity (E) as follows: S, shearing stress F/A Pa or dynes/ cm2 E = = = = Pa or dynes/ cm2 Elongation or compression Δ L No unit Newton theory Newton establish the following relationship: 1. With higher viscosity, the greater was the force required to cause liquid to flow. Higher shearing stress 2. Shearing stress rate of shear S or F G Newton introduced as constant and the equation became F G F=G Viscosity = shearing stress / rate of shear F/G 3 F/G = [Dyne/ cm 2 ] / sec -1 = [(gm.cm/Sec 2)/ cm 2 ] / Sec -1 gm/Sec. cm Unite of viscosity SI unit Pascal-sec “ pa-sec” Cgs unit Poise “ p” Note that 1 pa-sec = 10 poise = 10 dyne. Sec/ cm Centipoises “ cp”= 0.01 poise Fluidity Fluidity = = 1/ the opposite of viscosity) Example of viscosity of some liquid, at temperature 20 0C Liquid p) Water 0.01 Ethanol 0.012 Benzene 0.0065 Glycerin 15 Caster oil 10.3 4 Viscosity expression 1. Kinematic viscosity: this expression is used in the U.S. Pharmacopoeia. Kinematic viscosity is defined as absolute viscosity-divided by the density of liquid at a definite temperature: Kinematic viscosity = / Unit of the kinematic viscosity = [gm. Sec/ cm 2 ]/ [gm/cm3] = cm 2 /sec (SI unit) = m 2/ sec (Cgs system) Usually it is expressed as Stoke “s” = 10 –4 m 2 / sec or as centistokes “cs”= 10 –6 m 2/ sec. 2. Relative viscosity: r: it is defined as the ratio of the viscosity of the solution to that of the solvent. Relative viscosity = r o It should be noted that relative viscosity has no unit. 3. Specific viscosity: this term is defined as the relative increase in viscosity of the solution over that of solvent alone. Note that sp has no unit. Specific viscosity= sp = - o = o]-1 = r –1 Specific viscosity can be used to determine the volume of a molecule in solution based on the following equation sp = [2.5 C. N.V]/ M C = concentration N= avogadro numbers V= volume of the molecule M = molecular mass 5 4. Reduced viscosity: (number viscosity) it is can be obtained through dividing the specific viscosity by concentration. Reduced viscosity= sp / C 5. Intrinsic viscosity: (limited viscosity number): when reduced viscosity is determined at various concentration and results are plotted as shown in the following figure, the resulting line can be extrapolated to c = 0 to obtain the intercept ( the intercept is known as the intrinsic viscosity and is given the symbol [ its unit = ml/ gm Reduced viscosity sp/ C intrinsic viscosity Concentration gm/ dl The Intrinsic viscosity is an important quantity in polymer science for it is used to obtain the average molecular weight of high polymer science. Determination of the approximate molecular mass of polymer can be obtained using “ Mark- Houwink equation”: [M [intrinsic viscosity M= molecular weight K and = constant can be obtained at given temperature for specific polymer-solvent system 6 Temperature dependence and the theory of viscosity The viscosity of gases increases with temperature. The viscosity of liquids decreases with temperature, while the fluidity of liquids increases with temperature. The relation between viscosity and temperature is found by Arrhenius and can be expressed by the following equation “Arrhenius equation” A e Ev/RT viscosity A= arrhenius factor, constant depend on molecular weight and molar volume of liquid Ev= activation energy that required to initiate flow between molecules R= gas constant “1.987” R Ev/ pe = TR TR + A nl nl + A nl nl Slo ln vE vE Intercept = ln A 1/T The explanation of effect of raising the temperature on lowering the viscosity of liquids is that braking down the bonds between liquids molecules happens with raising the temperature resulting in less resistant to flow (↓ An example of effect of temperature on the viscosity: Temperature 20 o C 50 o C 99 o C Viscosity of water 0.01 p 0.0055 p 0.0028 p 7 Newtonian and Non-Newtonian systems Fluids have been classified into two types of systems that described the viscosity behaviors of the fluids. This classification is based on the obedience of the Newtonian’s law. Newtonian fluids Newtonian fluids Doesn’t obey Newtonian’s law Obey Newtonian’s law dependent on the rate of shear F/G Examples are suspensions and Examples are water and milk ointments Linear relationship between shear Dependant on time stress and rate of shear Classified into 1- Plastic 2-Pseudo-plastic Rate of shear, G Shearing stress, F e= 3-Dilatant op pe= Sl Slo Rate of shear, G Shearing stress, F It is not dependant on arte of shear Rate of shear It is not dependant on time Time It is dependant on temperature 8 Non-Newtonian systems Most of the pharmaceutical products are considered Non-Newtonian systems. In the following sections those types will be discussed. A- Plastic Flow It is called Bingham bodies, the following graph describes the viscosity of plastic material: Rate of shear fB = yield value Shearing stress As you noted that the line doesn’t pass through (0,0) Under the yield value substance behaves as a solid “ elastic material”. Increase in F accompanied with no change in rate of shear. It doesn’t flow until exceed this value (fB). U= plastic viscosity = [F- fB]/ G Above the yield value, fB, plastic system resembles Newtonian system U= plastic viscosity = 1/slope = 1/ An example of plastic flow is flocculated particles in concentrated suspension. As you see in the flowing graph, we need the yield value (stress) to brake down the bond “ vander waals forces” between suspended particles F and G is still zero Like Newtonian Rate of shear, G 9 B-Pseudoplastic Flow It is called shear thinning fluids Examples of pharmaceutical products that exhibit psuedoplastic flow are natural and synthetic gum (tragacanth, sodium alginate, methylcellulose). Another examples are paint and shampoo. Psuedoplastic flow is exhibited by polymers in solution, in contrast to plastic systems, which are composed of flocculated particles in suspension. The following graph describes the flow behavior of pseudoplastic material. G F No yield value, it starts to flow with beginning of applying the stress The curve is not linear in any part Viscosity can’t be expressed by single value, therefore, you can calculate the apparent viscosity instead 1 G slope of the tangent to the specific curve at F specified point ↑ rate of shear = ↓ F 10 An explanation of psudoplastic flow behavior: (suspending agent like gelatin) A B H2O H2O H2O Shear H2O H2O H2O H2O H2O H2O A- At rest the molecules (long chain molecules) lie in random arrangement, intertwined and bound to the solvent molecules resulting in high resistant (↑ B- Under shear the molecules align and squeeze out the bound water molecules (associated water molecules). The viscosity of the system consequently decreases proportional to the increase in rate of shear. C-Dilatant Flow The flow properties is inverse to that of pseudoplastic It is called shear thickening, the fluids exhibit an increase in resistance to flow with increasing rates of shear. An Example of this type is suspension with high percentage of dispersed solids (50%), like “ Ketchup” that is a high concentrated starch suspension. The flow properties are illustrated in the following graphs: 11 increases with raising the shear G F G An explanation of dilatancy: Increasing Rate of shear Particles deflocculated Expansion, open packed (dilated) Close packed particles particles Volume of the voids is small Increase inter-particle void volume and the vehicle is sufficient Insufficient vehicle to fill the increase to wet the particle in voids Relatively low viscosity Increase in due to the particles no longer wetted or lubricated by liquid Note that with high rate of shear, the viscosity increases and this considers disadvantageous in manufacturing. Dilatant materials may solidify under high shear conditions, therefore, it could damage the processing equipment (mill). 12 Time dependent behavior Newtonian systems are time independent. The viscosity of fluid will not vary with shear rate and it is independent on the of length time that the shear rate is applied. Also, replication of the same shear rate will get the same viscosity. Non-newtonian systems are time dependent meaning that the viscosity changing based on the length of the time that shear is applied and history of the fluid. The following figures illustrate the effect of time on viscosity: e urv w n-c Newtonian system: it is time independent do meaning through out the up-curve and G down curve the viscosity is the same rve The curves are -cu up superimposed F Pseudo-plastic Plastic Dilatant G F Non-Newtonian system is time dependent In pseudo-plastic and plastic fluids the viscosity is lower in down curve that up-curve In dilatant fluids the viscosity is higher in down curve than up- curve Incase of plastic and pseudo-plastic fluids, after applying a certain level of shear and removing this shear…particles don’t reform immediately (meaning stay in low viscosity status due to breakdown in the structure) It is called Thixotrpy 13 Thixotropy Rheopectic It means “ to change by touch” Viscosity increases with time Definition: it isothermal and comparatively slow In dilatant fluids recovery or standing of a material of a It happens rarely consistency lost through shearing Formally: applied for pseudoplastic Commonly: named for plastic and pseudoplastic fluids Thixotropy in formulation: Advantage: With shear 1. Pour or spread easily 2. Accurate of dosing 3. In storage, lo settle (↑ ↑ ↓ Desirable: in suspension, emulsions, lotions, creams and ointments Greater thixotropy: low rate of settling suspension Examples: 40-70% w/v procaine suspension in water Measurement of Thixotropy: Quantitative measurement can be done in the following way: 1. Determine structure breakdown with time at constant shear 2. Determine structure breakdown due to raising in shear rate 14 A-Determine structure breakdown with time at constant shear t2 t1 d c b 1/U2 G 1/U1 e a F Shear rate after reaching point a, has been held constant for t1 and t2 Viscosity = 1/slope rate of breakdown = (U1-U2)/ ln (t2/t1) B= with time and constant shear rate B-Determine structure breakdown due to raising in shear rate 1/U2 V2 V1 G 1/U1 F M= Thixotropic coefficient = (U1-U2)/ ln ( V2/V2) Measure the loss in shearing stress per unit in increase in shearing rate. Unit is dyne. Sec/ cm 2 V1 and V2 are the maximum rate of shear 15 Viscosity measurement Newtonian system Rate of shear (G) directly proportional to shearing stress (F) “one point” instrument can be operated at single rate of shear Non-Newtonian system “multipoint” instrument can be operated at a variety of rates of shear and shearing stress 1. Capillary viscometer: = ostwald viscometer Use for Newtonian systems Measure the time required for liquid to pass between two marks and compare this time to standard solution u/ s = (p 1 t1)/ (p2 t2) rel = u/ s t…time, p ..density, and …. viscosity 1…unknown and 2… standard solution Example: assume that time required for acetone to flow between the two marks on the capillary viscometer is 45 sec , and for water the time was 100 Sec at 25 oC. The density of acetone is 0.786 g/cm3 and that of water is 0.997 g/cm2 at 25 o C. the viscosity of water is 0.8904 centipoise at this temperature. Find the viscosity of acetone at 25 oC. u/ s = (p 1 t1)/ (p2 t2) u/ 0.8904 = (0.786 x 45)/ (0.997 x 100) u = 0.316 cp 16 2. Falling sphere viscometer: This type of viscometer uses for Newtonian systems Can measure wide range of viscosity “0.5-200,000 poise” Record the time interval that a specific ball falls between two marks Viscosity can be calculated from t (Sb- Sf) B viscosity t= time interval (Sec) Sb= Specific gravity of ball Sf= specific gravity of liquid B= constant is provided by manufacture for the balls 17