Dr Baker PCT 301 Rheology PDF

# Rheology ## Outline - Definition - Rheology - Newtonian and non-Newtonian systems - Thixotrophy - Application in Pharmacy ## Definitions Rheology is the science that studies the deformation of matter under the influence of a stress. Viscosity is an expression of the resistance of a fluid to fl...

# Rheology ## Outline - Definition - Rheology - Newtonian and non-Newtonian systems - Thixotrophy - Application in Pharmacy ## Definitions Rheology is the science that studies the deformation of matter under the influence of a stress. Viscosity is an expression of the resistance of a fluid to flow - the higher the viscosity, the greater the resistance. When stress is applied, it causes strain in the system which leads to deformations that can be either: - **elastic and spontaneously reversible.** - **permanently irreversibleviscoelastic.** ## Units of Viscosity - Centipoise (η) - coefficient of viscosity - complex unit - 1 centipoise = 1 mPa-s (1 millipascal*s) - 1 Pa = (kg.m/s²)/m² = kg/m.s² = N/m² ## Newtonian Systems Ideal viscous fluids known as Newtonian fluids show a direct relationship between shearing stress and shear rate. **Newton's Law**: Rate of shear should be directly proportional to the shearing stress. Consider a hypothetical cube of fluid made up of infinitely thin layers which are capable of sliding over one another like a pack of cards. When a tangential force, F’ is applied to the uppermost layer, it is assumed that each subsequent layer will move at progressively decreasing velocity and that the bottom layer is stationary. - A velocity gradient exists and this will be equal to the velocity of the upper layer (m/s) $dv$ divided by the height of the cube (m) $dx$. - Rate of flow or velocity gradient, Rate of shear = $dv/dx$ (s') - The applied stress of force per unit area (F/A) required to bring about flow is called the shear stress (S) and has units of N/m2. - Increased viscosity = increased shear force or shear stress required to produce a certain rate of shear. - A certain shear stress will produce a certain rate of shear. - Rate of shear should be directly proportional to the shearing stress. ## Non-Newtonian Systems Most pharmaceutical fluids do not follow Newton's equation because the viscosity of the fluid varies with the rate of shear. Hence, it is necessary to determine the relationship between the stress and rate of shear over a wide range of shear rates. Therefore, a single determination of viscosity at any one rate of shear cannot yield the entire rheological profile. The three types of non-Newtonian flow are: - Plastic or Bingham flow - Pseudoplastic flow - Dilatant flow ### 1. Plastic or Bingham Flow The rheogram does not pass through the origin but intersects with the shear stress axis at a point F_B, called yield value. This means that a plastic material does not flow until the yield value has been exceeded. At stresses below the yield value, the system acts like an elastic material while at stresses above the yield value, the relationship between shear stress and rate of shear becomes linear. In practice, deformation and flow usually occur at a lower shear stress value and this accounts for the curved portion of the curve. The viscosity decreases initially and then remains constant. The slope of the rheogram is called **Mobility** and its reciprocal is called **plastic viscosity.** Plastic flow is associated with the presence of flocculated particles in concentrated suspension. A yield value exists because of the contacts between adjacent particles (brought about by van der waals forces), which must be broken down before flow occurs. The yield value is an indication of the force of flocculation. The more flocculated the suspension, the higher the yield value. Once the yield value has been exceeded, there is a direct relationship between shear rate and shear stress. In effect, a plastic system resembles a Newtonian system at shear rates above the yield value. This is expressed by the **Bingham Equation**: $U = {1-f_B\over D}$ - U = Plastic viscosity, - f_B = Bingham yield value, - D = Shear rate, - τ = shear stress ### 2. Pseudoplastic Flow Many pharmaceutical products exhibit pseudoplastic flow. They include natural and synthetic gums e.g. liquid dispersions of tragacanth, sodium alginate, methylcellulose, sodium carboxymethylcellulose. As a general rule: - Pseudoplastic flow is exhibited by polymers in solution. The curve commences at the origin and there is no yield value. No part of the curve is linear, so viscosity cannot be expressed by any single value. The apparent viscosity may be obtained at any rate of shear from the slope of the tangent to the curve at the specified point. The viscosity decreases with an increasing rate of shear (shear-thinning systems). Pseudoplastic flow cannot be satisfactorily expressed by fundamental equations. **At the Particulate level**: The curved rheogram for pseudoplastic materials results from a shearing action on the long-chain molecules which become entangled and associated with immobilized solvent. As the shearing stress is increased, the randomly arranged particles tend to become disentangled and align their long axes in the direction of flow. This orientation reduces the internal resistance of the material and offers less resistance to flow. Some of the entrapped water will also be released. Both of these account for the lower viscosity. Once stress is removed, the structures reform spontaneously. ### 3. Dilatant Flow Dilatant flow - usually suspensions containing a high concentration (>50%) of small, deflocculated particles. Exhibit an increase in resistance to flow with increasing rates of shear. Systems increase in volume when sheared - termed dilatant. It is the reverse of pseudoplastic systems. - Pseudoplastic systems – shear-thinning systems. - Dilatant materials - shear-thickening systems. **At the particulate level**: At rest (zero shear), particles are closely packed with interparticulate voids at a minimum. Consequently at low shear rate such as those created by pouring, the vehicle can lubricate adequately the relative movement of the particles (the vehicle is sufficient to fill this volume). This allows the particles to move relative to one another at low rates of shear. Hence, a dilatant suspension can be poured from a bottle without shaking as it is relatively fluid without shear stress applied. If the shear stress is increased by shaking, the bulk expands or dilates as the particles move quickly past each other and take an open form of packing. - Close packed particles: minimum void volume: sufficient vehicle: relatively low consistency. - Open packed (dilated) particles: increased void volume: insufficient vehicle: relatively high consistency. Such an arrangement results in a significant increase in the void volume (i.e. the system dilates), with the vehicle now being insufficient to fill the voids between the particles. The resistance to flow increases considerably since the particles are no longer completely wetted or lubricated by the vehicle. Caution must be taken in processing dilatant materials. Usually, the processing of dispersions containing solid particles is carried out using high speed mixers, blenders, or mills. Dilatant materials may solidify under these conditions of high shear, thereby overloading and damaging the rotor of the processing equipment. A good example of dilantancy is when starch is made into a paste with cold water, it can be stirred slowly but tends to solidify if the stirring rate is increased. Dilatancy is also encountered when deflocculated suspension settles out on storage. The sediment is dilatant i.e. caking and claying of suspension and it will resist any energetic attempt at stirring or shaking. This is best avoided by formulating as slightly flocculated suspension. ## Thixotropy For all Newtonian and some non-Newtonian systems if the rate of shear was reduced, the down-curve would be identical with and superimposed on the up-curve. For most non-Newtonian systems, the flowing elements, whether particles or macromolecules, may not adapt immediately to the new shearing conditions. When subjected to a particular shear rate, the shear stress and consequently the viscosity, will decrease with time. Therefore the down-curve can be displaced with regard to the up-curve. Thixotropic systems usually contain asymmetric particles and through numerous points of contact, these particles set up a loose 3-D network throughout the sample. At rest, this structure confers some degree of rigidity on the system, and it resembles a gel. As shear is applied and flow starts, this structure begins to break down as the points of contact are disrupted and the particles become aligned in the general direction of flow. The material undergoes a gel to sol transformation and exhibits shear thinning. Upon removal of the stress, the structure starts to reform. This is not instantaneous, but is a progressive restoration of consistency as the asymmetric particles come into contact with each other by undergoing random Brownian movement. - **Shear-thinning systems (plastic and pseudoplastic)** The down-curve is frequently displaced to the left of the up-curve. The rheogram exhibits a hysteresis loop. It indicates a breakdown of structure that does not reform immediately when the stress is removed. This phenomenon is known as thixotropy and may be defined as: "An isothermal and comparatively slow recovery, on standing of a material whose consistency is lost through shearing". According to this definition, thixotropy can only be applied to shear-thinning systems. There is however negative thixotropy or antithixotrophy in dilatancy systems where there is an increase rather than a decrease in consistency on the downward curve. ## Thixotropy in Formulation Thixotropy is a desirable property in liquid to maintain the particles in a suspended state. Pharmaceutical systems that ideally should have a high consistency in the container yet pour or spread easily e.g. 1. A well-formulated suspension will not settle out readily in the container. Suspension exists as a gel in the resting phase. Upon shaking the gel will convert to solution (It will become fluid on shaking and will remain so long enough for a dose to be dispensed), then revert back to gel upon storage (to maintain the particles in a suspended state.) 2. Also desirable with lotions, creams and ointments: Formulations should spread easily on the skin and retains its original form on removal of stress in order to adhere to the site of application. 3. Injections (Procaine penicillin for intramuscular depot therapy). Transform from gel to sol when passing through the needle, then reverts back to gel at the site of intramuscular injection where the drug is slowly released into the body. # Application of Rheology in Pharmacy The rheological properties of pharmaceutical formulations should be carefully considered in order to have a product of good elegance/appearance and adequate release profile. The importance of rheological control in different formulations are stated below: 1. **Suspensions** Most Paediatric formulations are presented as suspensions. Their rheological properties must be carefully adjusted so that: - The product is easily poured from the bottle. - Sedimentation is retarded or prevented; if it does occur redispersion should be easy. An ideal suspension should exhibit high apparent viscosity at low shear rate so that on storage, the suspended particles would either settle very slowly or preferably remain permanently suspended. At high shear rate such as those caused by moderate shaking, the apparent viscosity should fall sufficiently for the product to be easily poured from the container. - The product if intended for external use should spread easily without excessive dragging, but must not be too fluid that it runs off the skin. - Suspension meant for injection should pass easily through the needle with moderate pressure applied to the plunger. - The product should be elegant in appearance. A flocculated suspension gives elegant appearance. 2. **Solids** - Flow of powders from hoppers and into the die cavity in tabletting should be adequate. 3. **Semisolids** - The viscosity should be appropriate to allow extrusion from tubes. - The viscosity should be appropriate to allow extrusion for the release of the drug from the base. - Formulations should spread easily on the skin and retain its original form on removal of stress in order to adhere to the site of application. 4. **Cosmetics** - Toothpaste. After applying a rate of shear in squeezing the tube, the toothpaste must flow onto the bristles. It must then recover its viscosity sufficiently to maintain its ribbon shape on the brush. With shear, it must thin rapidly for ease in brushing. 5. **Fluids** - Mixing. - Particle size reduction of disperse systems with shear (e.g. creams). - Passage through orifices. - Fluid transfer. - Physical stability of disperse systems. 6. **Processing** - Production capacity and power requirements of equipment. - Manufacturing equipment fitted with strain gauges to permit monitoring of torque measurements. ## Measurement of Viscosity ### Newtonian - Capillary tube method. - Falling sphere. - Parallel plate. ### Non Newtonian - Rotational viscometer.