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## Lesson 9. VISCOSITY, NEWTONIAN, AND NON-NEWTONIAN BEHAVIOR OF FLUIDS

**Module 5. Viscosity**

**Lesson 9VISCOSITY, NEWTONIAN, AND NON-NEWTONIAN BEHAVIOR OF FLUIDS **

**9.1 Introduction**

Viscosity is an important physical property of fluids. Viscosity is influenced by temperature and pressure exerted in the system. Moreover, the nature, concentration and type of milk components have a direct bearing on the viscosity. Therefore it is necessary to have some knowledge about this property of fluids and it is also necessary for designing various equipment of the milk processing.

**9.2 Definition of Viscosity and its Units**

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In simple terms taking example of fluids, viscosity is termed as "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while milk is "thick", having a higher viscosity. In others words it could simply be defined as the resistance of liquid to flow or pour, meaning the less viscous the fluid is, the greater its ease of movement or fluidity.

Viscosity of liquids can be defined as the resistance of a liquid to the motion of its layers relative to one another. Viscosity is also defined as ratio of shearing stress (S) to the shear rate which pertains to simple shear flow (i.e. laminar flow with parallel streamlines). In such fluids the shear rate is then equal to the velocity gradient G which is perpendicular to the direction of flow.

**9.2.1 Units of viscosity **

The usual symbol for dynamic viscosity is the Greek letter *μ*. The symbol *η* is also used by chemists. The SI physical unit of dynamic viscosity is the pascal-second (Pa·s) which is equivalent to N·s/m^{2}, or kg/(m·s). The c.g.s physical unit for dynamic viscosity is the *poise. * It is more commonly expressed as *centi poise *(cP)

**9.3 Types and Forms of Viscosity **

Newton's law of viscosity is not a fundamental law of nature but an approximation that holds in some materials and fails in others. Thus there exist a number of forms of viscosity:

**9.3.1 Newtonian fluids**

** **Fluids for which the viscosity coefficient depends only on temperature and pressure and is independent of the rate of shear are called " Newtonian". Newtonian fluid is the fluid in which the viscosity remains constant for all rates of shear if constant conditions of temperature and pressure are maintained. 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. Other examples may be aqueous solutions, emulsions. Gases, pure liquids, and solutions of materials of low molecular weight exhibit behavior of this type. E.g. Skim milk and whole milk do not differ appreciably from Newtonian behavior. For a Newtonian fluid, the viscosity depends only on temperature and pressure not on the forces acting upon it if the fluid is a pure substance or else it will also be influenced by the chemical composition if it is not a pure substance.

**9.3.2 Non newtonian fluids**

**A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Generally speaking, a non-Newtonian fluid is defined as one in which the relationship between shear stress and shear rate ***(S/R)* is not constant. Most commonly the viscosity of non-Newtonian fluids is dependent on shear rate or shear rate history. The viscosity of non-Newtonian fluids changes as the shear rate is varied. Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradient than simple linearity. There are several types of non-Newtonian flow behavior, characterized by the way a fluid's viscosity changes in response to variations in shear rate.

1. Shear thickening: viscosity of the substance increases with the shear rate is increased.

2. Shear thinning: viscosity of the substance decreases with the shear rate is increased.

3. Thixotropic: It is the property of certain gels or fluids that are viscous under normal conditions, but become thin, less viscous and flow over time when shaken, agitated, or otherwise stressed. Shear thinning liquids are very commonly, but misleadingly, described as thixotropic.

4. Rheopectic: It is the rare property of some non-Newtonian fluids to show a time-dependent change in viscosity; the longer the fluid undergoes shearing force (shaken, agitated, or otherwise stressed) the higher its viscosity

5. A Bingham plastic is a material that behaves as a solid at low stresses but flows as a viscous fluid at high stresses.

6. A magnetorheological fluid is a type of "smart fluid" which, when subjected to a magnetic field, greatly increases its apparent viscosity, to the point of becoming a viscoelastic solid.

Many materials also exhibit hysteresis, where by the coefficient of viscosity at a particular shear rate depends upon whether the shear rate is being decreased or increased. The cream, concentrated milks, butter and cheese exhibit varying degree of non-Newtonian behavior

** **

**Fig. 9.1 Relationship between shear stress (S) and shear rate (R)**

Fig 9.1 shows the relationship between shear stress *S* and shear rate *R* and the fluid's viscosity at a varying shear rate *R*. At a given temperature the viscosity of a Newtonian fluid remains constant regardless of which viscometer model, spindle or speed is used to measure it.

**9.3.3 Apparent viscosity**

**It is the viscosity of a fluid measured at a given shear rate at a fixed temperature. In order for a viscosity measurement to be meaningful, the shear rate must be stated or defined. This type of viscosity is ordinarily met in*** *concentrated fluid milk products particularly in ice cream mix. It refers to a thickened condition of the product which can be dispelled by agitation. It results from the formation of gel structure in the medium.

**9.3.4 Plasticity**

**The property exhibited by a complex, non-newtonian fluid in which the shear force is not proportional to the shear rate. This property is ordinarily differentiated from viscosity on the basis of the force necessary to cause flow. Liquids of substantial fluidity start to flow and continue to do so by driving force of their own weight. However, certain relatively non fluid substances will only start to flow after application of initial external pressure. These substances are said to exhibit plastic flow. **

**9.4 Stoke's Law **

When small spherical bodies move through a viscous medium, the bodies drag the layers of the medium that are in contact with them. This dragging results in relative motion between different layers, which are away from the body. Therefore, a viscous drag comes into play, opposing the motion of the body. It is found that this backward force or viscous drag increases with increase in velocity of the body.

According to Stoke, the viscous drag 'f ' , depends on the coefficient of viscosity 'η' of the medium, the velocity (v) of the body and radius (r) of the spherical body

f = k η v r

Where k is found to be 6π** **