Viscosity

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

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.

Non Newtonian fluids

Units of Absolute Viscosity

Kinematic Viscosity

Instruments for Measuring Viscosity

Principle of Viscosity Measurement

Capillary Viscometer

Capillary Viscometer

Rotational Viscometer

• Though gravity is available everywhere for free, it is sometimes not strong enough as a driving force.

• For highly viscous fluids a measurement based on gravity would take far too long. • Therefore, rotational viscometers use a motor drive. Unlike capillary viscometers,

rotational viscometers provide dynamic or shear viscosity results.• A rotational viscometer consists of a sample-filled cup and a measuring bob that is

immersed into the sample. There are two main principles in use:

• The Couette Principle• The Searle Principle

Rotational Viscometer

The Couette PrincipleIf the bob stands still and the drive rotates the sample cup, this is the Couette principle (named after M. M. A. Couette, 1858 to 1943). Although this construction avoids problems with turbulent flow, it is rarely used in commercially available instruments. This is probably due to problems with the insulation and tightness of the rotating sample cup.

Rotational Viscometer

The Searle PrincipleIn most industrially available viscometers the motor drives the measuring bob and the sample cup stands still. The viscosity is proportional to the motor torque that is required for turning the measuring bob against the fluid’s viscous forces. This is called the Searle principle (named after G. F. C. Searle, 1864 to 1954).When employing the Searle principle, the bob's rotational speed in low-viscosity samples should not be too high. Otherwise turbulent flow could occur due to centrifugal forces or the effects of inertia.

The motor turns a measuring bob or spindle in a container filled with sample fluid. While the driving speed is preset, the torque required for turning the measuring bob against the fluid’s viscous forces is measured.

Rotational Viscometer

• Servo Devices• This viscometer type uses a servo motor to drive the main shaft. The spindle with

the measuring bob (rotor) is attached directly to the shaft. A high-resolution digital encoder measures the rotational speed. The motor current is proportional to the torque caused by the viscosity of the sample under test. The viscosity can be computed based on rotational speed and current.

• Compared to models with a pivot bearing and spring systems, viscometers with a servo motor cover a wider measuring range and are more robust. The electronic decoder and motor allow for greater torque and speed ranges than is possible with a mechanical spring.

• However, the accuracy for low speeds and low viscosity is lower than for spring systems, as the friction of the motor and bearing influences the measurement.

1 … Servo motor with high-resolution current measurement2 … High-resolution optical encoder3 … Encoder disc4 … Measuring bob (rotor)

Rotational Viscometer

Coaxial cylinder geometry

• The rolling-ball principle uses gravity as the driving force. A ball rolls through a closed capillary filled with sample fluid which is inclined at a defined angle. The time it takes the ball to travel a defined measuring distance is a measure for the fluid’s viscosity. The inclination angle of the capillary permits the user to vary the driving force. If the angle is too steep, the rolling speed causes turbulent flow. For calculating the viscosity from the measured time, the fluid’s density and the ball density need to be known.

• Instruments that perform at inclination angles between 10° and 80° are rolling-ball viscometers.

• If the inclination angle is 80° or greater, the instrument is referred to as a falling-ball viscometer.

• Another variety of this principle is the bubble viscometer, which registers the rising time of an air bubble in the sample over a defined distance.

Rolling- / Falling-Ball Viscometer

Rolling- / Falling-Ball Viscometer

• The Rolling-ball principle• FG … Effective component of gravity

FB … Effective component of buoyancyFV … Viscous force

• The following forces have a dominating influence on the rolling ball: While gravity pulls the ball downwards, the buoyancy inside the liquid and the liquid's viscosity oppose the gravitational force. The stronger the viscous force is, the slower the ball rolls.

Rolling- / Falling-Ball Viscometer

• To calculate the ball’s viscosity from the rolling time, the gravitational and buoyancy influence have to be considered. While the influence of gravity (FG) depends on the ball's density and volume, an object's buoyancy depends also on the liquid's density. This is why both the density of the liquid and the density of the ball need to be known to obtain a viscosity result

Online Viscosity Measurement

Online Viscosity Measurement

• There are two flow paths in the sensing unit - a purge flow path (solid line) and a bypass flow path (dotted line).

• A control signal from the measurement unit to the 3-way valve opens the purge path for a specified interval. While the purge path is open, process fluid flows into the measuring tube and the falling piston is pushed upward by the force of the flow.

• When a preset interval of time (purge time) elapses, the measurement unit sends a control signal to the 3-way valve which closes off the purge flow path and opens the bypass flow path. When the purge flow path is closed, the flow of process fluid in the measuring tube ceases and the falling piston begins to descend at a velocity proportional to the viscosity of the liquid.

Online Viscosity Measurement

• A permanent magnet is incorporated in the falling piston. • Two magnetic sensors are positioned at the side of the measuring tube. • The upper magnetic sensor is referred to as the starting point sensor and the lower

magnetic sensor is referred to as the ending point sensor. • The measurement unit computes the time it takes for the falling piston to transit

the starting and ending point sensors (‘fall time’). It then converts this ‘fall time’ into viscosity which is displayed in % or SI units and outputs current and voltage signals in addition to various warning and status signals. 5. When the preset fixed time (measurement time) elapses, the measurement unit sends a control signal to the 3- way valve which closes off the bypass flow path and opens the purge path - in other words, returning the cycle to step [1]

Online Viscosity Measurement

Online Viscosity Measurement

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

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 :

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.