Chapter 1 Measurement of Viscosity

Outlines Introduction - What is Viscosity? - Why should I measure Viscosity? Newtonian & Non Newtonian behavior - Newtonian behavior - Non Newtonian behavior - Pseudo plastic - Dilatants - Plastic - Thixotropy - Rheopexy

1. Introduction Viscosity is a quantitative measure of a fluid’s resistance to flow. It is defined as the internal friction of fluid. Lack of slipperiness is called as viscosity Rheology: The study of the change in form and the flow of matter, embracing elasticity, viscosity, and plasticity. We generally measures two types of viscosity : Absolute/ Dynamic Viscosity (ƞ) Kinematic Viscosity (Ʋn)

Viscosity Viscosity is the measure of the internal friction of a fluid. This friction becomes apparent when a layer of fluid is made to move in relation to another layer. The greater the friction, the greater the amount of force required to cause this movement, which is called shear. Shearing occurs whenever the fluid is physically moved or distributed, as in pouring, spreading, spraying, mixing, etc. Highly viscous fluids, therefore, require more force to move than less viscous materials.

Isaac Newton defined viscosity by considering the model represented in the figure below. Two parallel planes of fluid of equal area A are separated by a distance dx and are moving in the same direction at different velocities V1 and V2.

Newton assumed that the force required to maintain this difference in speed was proportional to the difference in speed through the liquid, or the velocity gradient. To express this, Newton wrote: where Ƞ is a constant for a given material and is called its viscosity.

The velocity gradient, dv/dx , is a measure of the change in speed at which the intermediate layers move with respect to each other. It describes the shearing the liquid experiences and is thus called shear rate. The term F/A indicates the force per unit area required to produce the shearing action. It is referred to as shear stress. So, mathematically Viscosity can be defines as

Why should I measure Viscosity? From viscosity measurement, we can obtain much useful behavioral and predictive information for various products. A frequent reason for the measurement of rheological properties can be found in the area of quality control, where raw materials must be consistent from batch to batch. For this purpose, flow behavior is an indirect measure of product consistency and quality.

Types of Viscosity

Newtonian fluids

This type of flow behavior Newton assumed for all fluids is called Newtonian. It is, however, only one of several types of flow behavior you may encounter. Graph A shows that the relationship between shear stress and shear rate is a straight line. Graph B shows that the fluid's viscosity remains constant as the shear rate is varied. Typical Newtonian fluids include water and thin motor oils.

Non Newtonian fluids A non-Newtonian fluid is broadly defined as one for which the relationship   is not a constant. It means that there is non-linear relationship between shear rate & shear stress. In other words, when the shear rate is varied, the shear stress doesn't vary in the same proportion (or even necessarily in the same direction). E.g. Soap Solutions & cosmetics, Food such as butter, jam, cheese, soup, yogurt, natural substances such as lava, gums, etc. 

Pseudo plastic

This type of flow behavior is sometimes called "shear-thinning. This type of fluid will display a decreasing viscosity with an increasing shear rate. Probably the most common of the non-Newtonian fluids, pseudo-plastics include paints, emulsions, and dispersions of many types. This type of flow behavior is sometimes called "shear-thinning.

Dilatants

Increasing viscosity with an increase in shear rate characterizes the dilatant fluid. Although rarer than pseudo plasticity, dilatancy is frequently observed in fluids containing high levels of deflocculated solids, such as clay slurries, candy compounds and sand/water mixtures. Dilatancy is also referred to as shear-thickening flow behavior.

Plastic (Bingham Plastic)

This type of fluid will behave as a solid under static conditions. A certain amount of force must be applied to the fluid before any flow is induced; this force is called the yield stress (f'). Tomato catsup is a good example of this type fluid; its yield value will often make it refuse to pour from the bottle until the bottle is shaken or struck, allowing the catsup to gush freely. Once the yield value is exceeded and flow begins, plastic fluids may display Newtonian, pseudoplastic, or dilatant flow characteristics. 

Some fluids will display a change in viscosity with time under conditions of constant shear rate. There are two categories to consider: 1) Thixotropy 2) Rheopexy

Thixotropy

Rheopexy

Viscosity coefficients Viscosity coefficients can be defined in two ways: 1) Dynamic or Absolute viscosity 2) Kinematic Viscosity Viscosity is a tensorial quantity that can be decomposed in different ways into two independent components. The most usual decomposition yields the following viscosity coefficients: 1) Shear Viscosity 2) Extensional Viscosity

Dynamic Viscosity/ Absolute Viscosity Proportionality constant between shear stress and velocity gradient is often called as “Dynamic Viscosity / Absolute Viscosity”. Reciprocal of Dynamic Viscosity is “Fluidity”. Ratio of Shear stress to the velocity gradient of the fluid is known as Absolute Viscosity.

Units of Absolute Viscosity

Kinematic Viscosity  

Shear Viscosity The most important one, often referred to as simply viscosity, describing the reaction to applied shear stress; simply put, it is the ratio between the pressure exerted on the surface of a fluid, in the lateral or horizontal direction, to the change in velocity of the fluid as you move down in the fluid (this is what is referred to as a velocity gradient).

Volume Viscosity or Bulk Viscosity Bulk viscosity becomes important only for such effects where fluid compressibility is essential. Examples would include shock waves and sound propagation. It appears in the Stokes' law (sound attenuation) that describes propagation of sound in Newtonian liquid.

Extensional Viscosity A linear combination of shear and bulk viscosity, describes the reaction to elongation, widely used for characterizing polymers. For example, at room temperature, water has a dynamic shear viscosity of about 1.0 * 10−3 Pa·s and motor oil of about 250 * 10−3 Pa·s.

Instruments for Measuring Viscosity

Measurement of Shear viscosity Depends upon dynamics of shear force acting upon fluid either Newtonian / non- Newtonian. Instruments which measures the viscosity are called as Viscometers. Viscometers only measures under one flow condition. Most popular viscometers to measure shear viscosity are Capillary flow viscometer Circular couette flow viscometer Cone & plate flow viscometer Parallel plate flow viscometer

Principle of Viscosity Measurement

Capillary Flow Viscometer Capillary flow viscometers are based on pressure drop

With this as a starting point we can derive the Hagen-Poiseuille Equation:

Couette Viscometer

Cone & Plate Viscometer

Parallel Plate Viscometer

Shop Floor Viscometers Mainly used in Industrial applications to measure viscosity of mostly Newtonian types of fluid. These viscometers consisting simple & convenient method for viscosity measurement. Most popular shop-floor viscometers : Rotational Viscometer Flow through restriction type Viscometer Flow around type Viscometer

Rotational Viscometer (Brook field Viscometer) Determine viscosity by measuring the resistance on a shaft rotating in the fluid . They are designed to make a direct measurement of the absolute Viscosity. The theory of operation of a rotational viscometer is based on the Couette flow model for fully developed, steady and laminar flow between two surfaces, one of which is moving. Pointer displacement is directly proportional to fluid viscosity.

Flow through restriction type

Flow around obstruction type

Viscometer standard table

Most popular flow around type Viscometer

Measurement of Extensional Viscosity

Operating Principle

Effect of Temperature The viscosity of liquids decreases with increase the temperature. The viscosity of gases increases with the increase the temperature. The lubricant oil viscosity at a specific temperature can be either calculated from the viscosity - temperature equation or obtained from the viscosity-temperature chart.

Viscosity Temperature equations

Viscosity Index An entirely empirical parameter which would accurately describe the viscosity- temperature characteristics of the oils. The viscosity index is calculated by the following formula: VI = (L - U)/ (L - H) * 10 where , VI is viscosity index U is the kinematic viscosity of oil of interest L and H are the kinematic viscosity of the reference oils

Effect of Pressure Lubricants viscosity increases with pressure. For most lubricants this effect is considerably largest than the other effects when the pressure is significantly above atmospheric. The Barus equation :

Online Viscosity Measurement

Applications Selection of lubricants for various purpose. - we can choose an optimum range of viscosity for engine oil. - for high load and also for speed operation high viscous lubricants is required. In pumping operation - for high viscous fluid high power will require. - for low viscous fluid low power will require. In making of blend fuel - less viscous fuels easy to mix. In the operation of coating and printing.

Important Questions Explain Coutte Viscometer in detail. Define Viscosity. What are the different methods of Viscosity measurement? Explain any one method with basic Principle, working & suitable application. Explain the measurement of viscosity under extremes of temperature and pressure. Explain in detail construction and working of cone and plate viscometer and parallel plate viscometer. Define the viscosity with necessary equation and discuss Newtonian and non-Newtonian behavior of various fluids Explain the measurement of shear viscosity using capillary viscometer with necessary equation Give explanation about following terms: Viscosity, Bingham Plastic, Pseudoplastic, Shear Thinning, Shear Thickening, Thixotropy & Rheopexy