Pharmaceutics I صيدالنيات 1

Unit 6

1 Rheology of suspensions • Rheology, the study of flow, addresses the viscosity characteristics of powders, fluids, and semisolids.

• Materials are divided into two general categories, Newtonian and non-Newtonian, depending on their flow characteristics. • 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 cm2 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 ☻Rate of Shear dv/dr = G Is the velocity difference dv between two planes of liquid separated by an infinite distance dr. Indicates how fast ( the velocity )a liquid flows when a stress is applied on it

☻The Shearing Stress F'/A = F Is the force per unit area required to cause flow.

☻ 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 F'/A = η dv/dr (1) where η is a constant known as viscosity η = F / G. (2)

The unit of viscosity is poise or dyne.sec.cm-2 . • where η is the viscosity coefficient or viscosity

• F = F′/A G = dv/dr. 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.

• 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.

• 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 ) Pseudoplastic flow

• Pseudoplastic substances begin flow when a shearing stress is applied; therefore, they exhibit no yield value.

• 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.

• These are also called shear-thickening systems.

• Dilatant systems are usually characterized by having a high percentage of solids in the formulation. Dilatant behavior may be explained as follows:

 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 , becomes insufficient to fill the increased voids .

Accordingly, the resistance to flow increases because the particles are no longer completely wetted or lubricated by the vehicle.

Thus, the suspension will set up as a firm paste Dilatant flow

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 with the characteristics of a liquid dosage form for ease of use. 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 Factors affecting rheological properties 1. Chemical factors A- Degree of polymerization -The longer polymer molecules will be accompanied by increase in viscosity - Sodium alginate (the flow viscosity at a given temperature rises rapidly with increasing DP for all polymers ).

B- Extent of Polymer Hydration hydration of hydrophilic polymers gives rise to an increased viscosity.

C- Impurities, Trace Ions and Electrolytes Chemical impurities are the major factors in changing the viscosity of natural polymers e.g. in Na alginate solution, the viscosity increase if traces of Ca are present, due to the formation of calcium alginate.

D- Effect of pH Changes in pH greatly affect the viscosity and stability of the hydrophilic natural and synthetic gums.The natural gums usually have a relatively stable viscosity over 5 or 4 pH . Above and below this pH range viscosity decreases sharply. 2- Physical Factors A- Temperature A temperature increase usually produces a rapid viscosity decrease, with the exception of certain synthetic polymers such as methyl cellulose, B- Aeration Aerated products usually result from high shear milling. Aerated samples appear to be more viscous or have more viscous creamed layer than non- aerated samples (c) Light Various hydrocolloids in aqueous solutions are reported to be sensitive to light. These colloids include carbopol, Na alginate, and Na CMC. To protect photosensitive hydrocolloids from decomposition and resultant viscosity change use light-resistant containers 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 to be poured easily from its container. • 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