Pharmaceutics I اينالديصيدلينيات 1 Unit 6 Rheology of suspensions 1
Rheology, the science of the flow or deformation of matter (liquid or soft solid) under the effect of an applied force. It addresses the viscosity characteristics of powders, fluids, and semisolids. Viscosity is the resistance of a fluid to flow; the higher the viscosity the greater the resistance. Materials are divided into two general categories, Newtonian and non- Newtonian, depending on their flow characteristics. The choice depends on whether or not their flow properties are in accord with
The unit of viscosity is the poise, the shearing force required to produce a velocity of 1 cm per second between two parallel planes of liquid, each 1 cm 2 in area and separated by a distance of 1 cm. The most convenient unit to use is the centipoise, or cp (equivalent to 0.01 poise).
Newton s law of flow Newton law of flow relates parallel layers of liquid, with the bottom layer fixed, when a force is placed on the top layer, the top plane moves at constant velocity, each lower layer moves with a velocity directly proportional to its distance from the stationary bottom layer. The velocity gradient, or rate of shear (dv/dr), is the difference of velocity dv between two planes of liquid separated by the distance dr. The force (F /A) applied to the top layer that is required to result in flow (rate of shear, G) is called the shearing stress (F).
NEWTONIAN S LOW OF FLOW Let us consider a block of liquid consisting of parallel plates of molecules as shown in the figure. The bottom layer is considered to be fixed in place. If the top plane of liquid is moved at constant velocity, each lower layer will move with a velocity directly proportional to its distance from the stationary bottom layer Representation of shearing force acting on a block of material
A shear stress, is applied to the top of the square while the bottom is held in place. This stress results in a strain, or deformation, changing the square into a parallelogram. (velocity gradient) The Shearing Stress F'/A = F Is the force per unit area required to cause flow Rate of Shear dv/dr = G Is the velocity difference dv between two planes of liquid separated by an infinite distance dr. (velocity gradient) Indicates how fast ( the velocity)a liquid flows when a stress is applied on it :Newton recognized that The higher the viscosity of a liquid, the greater the force per unit area (shearing stress) required to produce a.certain rate of shear
Thus, the rate of shear is directly proportional to the shearing stress. F'/A α dv/dr where η is the viscosity coefficient or viscosity F = F /A G = dv/dr. Fluidity is reciprocal of viscosity The unit of viscosity is poise or dyne.sec.cm -2.
EXAMPLE What is the shear rate when an oil is rubbed into the skin with a relative rate of motion between the fingers and the skin of about 10 cm per seconds and the fi lm thickness is about 0.02 cm? Rate of Shear dv/dr = G G= 10 cm per seconds / 0.02 cm = 500 Sec -1
Newtonian flow Newtonian flow is characterized by constant viscosity, regardless of the shear rates applied In common terms, this means the fluid continues to flow, regardless of the forces acting on it. For example, water is Newtonian, because it continues to exemplify fluid properties no matter how fast it is stirred or mixed. For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure (and also the chemical composition of the fluid if the fluid is not a pure substance), not on the forces acting upon it. upon plotting G vs F A Newtonian fluid will plot as a straight line with the slope of the line being η.
Newtonian flow Newtonian systems like water, simple organic liquids, true solutions and dilute suspensions and emulsions
Non-Newtonian flow Non-Newtonian substances are those that fail to follow Newton s equation of flow. Non-Newtonian flow is characterized by a change in viscosity characteristics with increasing shear rates. Example materials include colloidal solutions, emulsions, liquid suspensions, and ointments.
There are three general types of non- Newtonian materials: 1. plastic, 2. pseudoplastic, 3. dilatant.
Plastic flow Substances that exhibit plastic flow are called Bingham bodies. Plastic flow does not begin until a shearing stress corresponding to a certain yield value is exceeded. The flow curve intersects the shearing stress axis and does not pass through the origin. After yield value With increasing shearing stress, the rate of shear increases; consequently, these materials are also called shear-thinning systems. In other words; it does not to begin to flow until shearing stress corresponding to yield value is exceeded. The materials are elastic below the yield value.
Plastic flow i.e. (Tomatoes Sauce, Honey, Flocculated particles in a concentrated suspensions usually show plastic flow ) After exceeding yield value any increase of shear stress (F)is directly proportional to an increase in rate of shear (G).
Pseudoplastic flow Pseudoplastic substances begin flow when a shearing stress is applied; therefore, they exhibit no yield value. The consistency curve begins at origin or at least approach it at low rate of shear. With increasing shearing stress, the rate of shear increases; consequently, these materials are also called shear-thinning systems. It is postulated that this occurs as the molecules, primarily polymers, align themselves along the long axis and slip or slide past each other.
Pseudoplastic flow A large number of pharmaceutical products, including natural and synthetic gums, e.g. liquid dispersions of tragacanth, sodium alginate, methyl cellulose, and Na-carboxymethylcellulose show pseudoplastic flow
Dilatant flow Dilatant materials are those that increase in volume when sheared, and the viscosity increases with increasing shear rate. High resistance to flow with high shear. These are also called shear-thickening systems. (They are the inverse to the plastic and pseudo plastic) Dilatant systems are usually characterized by having a high percentage of solids in the formulation. When shear is removed the system returns to original state of fluidity. Example deflocculated suspension
Dilatant behavior may be explained as follows: Accordingly, the resistance to flow increases because the particles are no longer completely wetted or At rest, the particles are closely packed with the minimum interparticle volume, or voids. The amount of vehicle in the suspension is sufficient, however, to fill this volume and permits the particles to move As the shear stress is increased, the bulk of the system expands or dilates. The amount of vehicle (constant), becomes insufficient to fill the increased voids between particles.
Dilatant flow This figure is the inverse of pseudo plastic diagram High shear rate leads to high viscosity Substances possessing dilatant flow properties are suspensions containing a high concentration (about 50 percent or greater) of small, deflocculated particles.
Other types of flow Thixotropic flow is used to advantage in some pharmaceutical formulations. It is a reversible gel sol transformation. Upon setting, a network gel forms and provides a rigid matrix that will stabilize suspensions and gels. When stressed (by shaking), the matrix relaxes and forms a sol
Thixotropy, may be defined as: an isothermal and relatively slow-recovery, on standing of a material, of a consistency lost through shearing. As so defined, thixotropy may only be applied to shear-thinning systems. Measurement of Thixotropy The most apparent characteristic of a thixotropic system is the hysteresis loop using a planimeter. A thixotropic agent such as microcrystalline cellulose is incorporated into the suspensions or emulsions to give a high viscosity. Shear strain hysteresis loop Shear stress
Rheology of suspensions An ideal pharmaceutical suspension would exhibit a high apparent viscosity at low rates of shear so that, on storage, the suspended particles would either settle very slowly or, preferably, remain permanently suspended. At higher rates of shear, such as those caused by moderate shaking of the product, the apparent viscosity should fall sufficiently for
The product, if for external use, should then spread easily without excessive dragging, but should not be so fluid that it runs off the skin surface. If intended for injection, the product should pass easily through a hypodermic needle with only moderate pressure applied to the syringe plunger
A flocculated system partly fulfils these criteria. In such a system pseudoplastic or plastic behaviour is exhibited as the structure progressively breaks down under shear. The product then shows the time-dependent reversibility of this loss of structure, which is termed thixotropy.
Although a flocculated system may exhibit some thixotropy and plasticity, unless a high concentration of disperse phase is present it may not be sufficient to prevent rapid settling, In these cases suspending agents may be used to increase the apparent viscosity of the system. A deflocculated system, however, would exhibit newtonian behaviour