VISCOSITY AND CONSISTENCY MEASUREMENT

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1 VISCOSITY AND CONSISTENCY MEASUREMENT Viscosity is a measure of the fluidity of the liquid or the gas. Many fluids undergo continuous deformation with the application of shearing stress. Application of shear force, therefore, produces a flow. If the force flow relation is linear, the fluid is Newtonian. For non Newtonian fluids, the force flow relation is not only nonlinear but changes from material to material. When continuous deformation occurs, the fluid tries to oppose this with a frictional resistance. This resistance can be measured in terms of consistency. Consistency of Newtonian fluid is called viscosity. A. VISCOSITY MEASUREMENT Viscosity is often formulated as the ratio of shear stress to shear rate. Some important terms associated with viscosity are, i. DYNAMIC / ABSOLUTE VISCOSITY (µ) : It is defined as the ratio of shear stress (S) to the velocity gradient (dv dz) produced by it. Unit of µ is poise. 1 poise = 0.1 N-s/m 2 ii. FLUIDITY : It is the reciprocal of viscosity. Its unit is rhe. iii. KINEMATIC VISCOSITY (ν) : It is the ratio of absolute viscosity (µ) to density of the fluid (ρ). Its unit is stokes. Vishnu College of Engineering Kidangoor 26

2 iv. SPECIFIC VISCOSITY (µ S ) : It is the ratio of absolute viscosity of the fluid (µ) to the absolute viscosity of a standard fluid (µ st ) at the same temperature. v. RELATIVE VISCOSITY (µ R ) : It is the ratio of absolute viscosity of the fluid at a given temperature (µ t ) to the absolute viscosity (µ st ) of a standard fluid at 20 C. vi. VISCOSITY INDEX (I v ) : It is an empirical number that indicates the effect of changes of temperature on viscosity of a fluid. Large I v means lower sensitivity to temperature. below. Some of the important viscosity meters or simply viscometers are given 1. Capillary Viscometer 2. Saybolt s Viscometer 3. Rotameter Type Viscometer 4. Searle s Rotating Cylinder Viscometer 5. Cone And Plate Viscometer 1. CAPILLARY VISCOMETER Of the different methods of viscosity measurement for liquids the classical method due to Poiseuille is still the standard and the viscometer based on this technique is known as the capillary viscometer. When the liquid flows through a tube of small diameter 2R as shown in figure 2.2, then for an annular flow channel of radial thickness dr at a distance r from the central line, the viscosity equation is given by, Vishnu College of Engineering Kidangoor 27

3 Where, v Velocity P Pressure difference across the tube of length l Integrating in the limits r = r R and corresponding v = v 0. Volume flow rate, Vishnu College of Engineering Kidangoor 28

4 Hence absolute viscosity is given by, The capillary method has been successfully used in refineries for measuring viscosities of petroleum products. The schematic arrangement is shown in figure 2.3. This is a continuous method. The liquid is forced at a constant velocity through the capillary (friction tube). The pressure drops across the ends of the tube is measured by a pneumatic force balance type Differential Pressure Transmitter (DPT). The indicator can be directly calibrated in viscosity. This method can measure viscosity from 10-3 poise to 3000 poise. It is usable at high static pressures and is suitable for remote indication and control. 2. SAYBOLT S VISCOMETER Saybolt s viscometer works upon the same principle of operation of capillary viscometer, but this method measures kinematic viscosity. The schematic set up of the method is shown in figure It consists of a graduated tube with a capillary at the bottom. The tube placed in a constant temperature bath is filled with the liquid and a measured quantity of liquid is drained trough the capillary. For varying viscosity, the time required should vary. The time t required to drain 60 cc of the liquid indicates viscosity and is denoted by Saybolt number. An empirical equation relating kinematic viscosity and time is as given below. Here A and B are constants. A is having a value of 24 and B, 1900 for Saybolt s viscometer. Vishnu College of Engineering Kidangoor 29

5 3. ROTAMETER TYPE VISCOMETER In this type, rotameter bobs may be designed to be viscosity sensitive. Therefore with a rotameter in the line of flow, viscosity can be measured if flow rate is constant. Figure 2.4 shows a scheme of the method. A rotameter with two bobs, one sensitive and another immune to viscosity is mounted in a bypass line through which the flow is regulated by a suitable regulator. By adjusting the regulator, the flow rate index is set at the index mark. The other bob will indicate viscosity. If the range is required to be changed, the flow rate can be changed and the scale readings can then be related to the viscosity by empirical calibration. The calibration curves for three different flow rates are shown in figure 2.5. This method is commonly used up to a viscosity of 300 centipoises(cp), but the range is extendible. It measures viscosity and also checks consistency at high static pressure. 4. SEARLE S ROTATING CYLINDER VISCOMETER This method includes the measurement of torque produced by a cylinder rotated at constant speed in the viscous fluid. The torque may be converted into an electrical signal by connecting a motor driven shaft with cylinder through a spiral spring. Due to changes in viscosity, the motor shaft and the cylinder maintain an angular relationship which is proportional to the torque on the spring. For high viscosity fluids, the rotating cylinder method of Searle is used where the torque is measured by a mechanical method. This method is also known as Couette concentric cylinder viscometer. The sketch of such a method is shown in figure 2.6. The inner cylinder is fixed while the outer cylinder rotates at constant velocity ωr 2 since the gap between the two cylinders is constant, the velocity gradient is also assumed uniform so that velocity gradient on the vertical Vishnu College of Engineering Kidangoor 30

6 and horizontal sides are and respectively, for both b << r 1 and a << r 1. The shear-stress torque relation on the two sides are given by Horizontal Vertical The total torque is By measuring T, angular velocity ω and apparatus dimensions r1, r2, l, a and b, the dynamic viscosity is easily evaluated. This type can measure viscosity from poise and having an accuracy of ±1%. rotates. Brookfield viscometer is a variation of this type where the inner cylinder 5. CONE AND PLATE VISCOMETER This method can be considered as a variation of the rotating cylinder method. This is popularly known as the cone-and-plate viscometer used in both Newtonian fluids and non-newtonian ones for measurement of consistency. The schematic is shown in figure 2.7.There is a flat plate (FSP) and a conic plate (RCP) and in between, the fluid exists as shown. The angle θ shown is very small usually less than 4. The conic plate is rotated at a fixed angular velocity ω and in consequence the flat plate would also rotate which may be made stationary by applying a torque T given the relation For Newtonian fluids, where, R is cone radius. For non- Newtonian fluids the relation is similar but µ is replaced by µ c, the consistency which is no longer constant. of ±1%. This type can measure viscosity from poise and having an accuracy Vishnu College of Engineering Kidangoor 31

7 B. CONSISTENCY MEASUREMENT Consistency measurement is also important in industry particularly in the manufacturing processes. Some commonly used methods are 1. Rotating Vane Consistency Meter 2. Oscillating Type Consistency Meter 1. ROTATING VANE CONSISTENCY METER In paper or food processing industries, online consistency control is done by suspending an agitator wheel in the flow box and driving it by an electric motor. The method is similar to the one described earlier. When the consistency of the material changes there is a change in torque of the driving motor which can be measured by either pneumatic or electrical methods. By measuring the power required to drive the agitator motor, consistency can also be measured. The wattmeter is empirically calibrated. The schematic circuit is shown in figure OSCILLATING TYPE CONSISTENCY METER This system is schematically shown in figure 2.9. It consists of two concentric cylinders. The inner cylinder is given an axial sinusoidal motion through a mechanical drive rod as shown. The fluid in the annular space gets a shearing force and the motion to the inner cylinder will be transmitted to the outer cylinder because of the metal bellows. The magnitude of this transmission will depend on the consistency of the fluid flowing through the instrument. The magnitude of transducer outputs are compared for the consistency. This also requires empirical calibration. Vishnu College of Engineering Kidangoor 32

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