CHAPTER 1: CO 2 CAPTURE
4. Experimental Equipment and Techniques
4.2 Introduction to Viscosity
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τ=η∗D!
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To obtain dynamic viscosity, one must reformulate newton law.
Only Newtonian liquids can be described by this simple relation. A fluid is Newtonian if the viscosity is independent of the external force -i.e. shear rate at a given temperature. In other words, when the shear stress is linearly dependent on the share rate, then the fluid is Newtonian fluid and is obeying Newton’s law. The other type of fluid is called Non-Newtonian fluid, which does not obey Newton’s law, and the viscosity of this type changes with the shear rate, and in this case for exact definition, one has to specify the apparent viscosity [216].
! Temperature dependence of viscosity
The viscosity depends on the thermodynamic state of the fluid and is usually specified by the pairs of variables (T, P) or (T, ρ) for a pure fluid, to which must be added a composition dependence in the case of mixtures. A fluid’s viscosity strongly affected by its temperature. Due to the inversely proportional relation between viscosity and temperature, and increases in temperature cause a fluid’s viscosity to decrease and vice versa. Viscosity is typically independent of pressure at low or medium pressure, however, under extreme pressure liquids often experience an increase in viscosity [216].
! Types of viscosity 4.2.2.1! Dynamic viscosity
As mentioned earlier, the dynamic viscosity η (eta), called absolute viscosity or just viscosity, is calculated by reformulation of the Newton’s Law through dividing the shear stress by shear rate [216].
η= τ L
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The SI unit of viscosity is the pascal-second [Pa.s] or [mPa.s] millipascal-second. Other commonly used units are [P] Poise or [cP] centipoise. The relation between units:
P = 100 cP,1 cP = 1 mPa.s.
4.2.2.2! Kinematic viscosity
The other type of viscosity is called kinematic viscosity (represented by the Greek letter ν "nu") which is a measure of the substance’s flow under the influence of gravitational force. The ratio of the dynamic viscosity of a fluid to its density is referred to Kinematic viscosity [216].
M =η ρ
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The SI unit of kinetic viscosity is [m2/s] square meters per second or [mm2/s] square millimeters per second.
4.2.2.3! Apparent viscosity
Ideally viscous or Newtonian fluids have constant viscosity for all shear rate values at a given temperature. On the other hand, for shear-dependent fluids, the viscosity changes as the shear rate are varied. Hence, to have a meaningful viscosity measurement, the shear rate must be stated or defined. This is the “apparent viscosity” or “apparent shear viscosity”. Each apparent value is one point of the viscosity function (eta over shear rate). Apparent viscosity has the SI derived unit of Pa·s [216] .
! Viscosity measurement techniques
Since a precise viscosity measurement is fundamental to correctly analyze many engineering situations that involve fluid flow, various methods have been developed to obtain the viscosity over the years. Generally, the simplicity, accuracy, and suitability of the method for certain types of fluid are important factors in choosing the proper viscosity measurement technique. Various theories that have been developed for prediction or estimation of viscosity must be verified using experimental data. This section outlines various types of viscometers with the further discussion regarding their operation modes. Viscometers can be generally classified into five categories based on their designs and experimental techniques used, including capillary, rotational, oscillatory- body, falling-body, and vibrating wire viscometers. This list is by no means thorough, there are
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Capillary viscometer is one of the earliest widely used viscometers to precisely determine the kinematic viscosity of Newtonian fluids [217]. These types of viscometers are very simple in operation, need a small volume of liquid and inexpensive. The prior knowledge of the volume and density of the sample is required for the determination of the viscosity. These viscometers measure the time taken for a defined quantity of fluid to travel between two graduation marks through a capillary tube of known length, width, and very small diameter. The liquid flows through the capillary tube either under gravitational force ( Gravimetric Capillary Viscometer) or under an external force. In the viscometer where an external force is applied, the liquid is forced to travel a specific distance at a determined rate through the capillary and the pressure drop across the capillary is measured. Kinetic viscosity can be calculated from the measured flow time (tf) multiply by the so-called capillary constant (KC) [217].
v=KC⋅tf
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For most of the capillary viscometers, KC is obtained by calibrating the capillary using one or more reference fluid of known viscosity and density. A typical capillary viscometer basically consists of a liquid reservoir, a capillary of known dimensions, a pressure controller, the flow rate meter, and a thermostat to keep the required temperature. The essential component used in capillary viscometers is a “U-shaped” glass which gives them the commonly associated name, the U-tube capillaries. Based on the type of glass used in viscometers, glass capillaries are classified into reverse-flow and direct-flow models. For reverse-flow types, the reservoir is positioned above the distance marks while in direct-flow capillaries the sample reservoir is placed below [217].
The established types of glass capillaries are shown in Figure 4-2:
Figure 4-2 Types of glass capillaries [217]
1.! Ostwald capillary 2.! Ubbelohde capillary 3.! Cannon-Fenske capillary 4.! Houillon capillary
With the development of the automatic gravimetric capillary viscometer, utilizing the stop watch for measuring manually the flow time was replaced with automatic registration of the fluid.
The most advanced models automatically fill, measure, clean, and dry. Moreover, some advantages of automatic gravimetric capillary viscometer include eliminating human reading errors, utilizing less measuring volume than the original types, and covering an extended viscosity range. Such automatic viscometers mainly coupled with a thermoelectric system, for temperature control [217].
4.2.3.2! Rotational viscometers
The operational principle of Rotational viscometers relies on the idea that the amount of power (torque) required to turn a spindle in the fluid at a known speed is directly proportional to the viscosity of that fluid. These viscometers use a motor drive, which is considerably stronger than the earth’s gravitational force. They can, therefore, be used to measure the viscosity of more highly viscous substances. Since these instruments do not use the force of gravity to function, their measurements are based on the fluid's internal shear stress. Rotational viscometers measure dynamic viscosity that is sometimes also referred to as shear viscosity. The shear stress remains
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constant throughout the fluid sample; therefore, these viscometers are most suitable for studying non-Newtonian fluids. Different types of rotational viscometers are commercially available based on their geometries [217].
These viscometers can be classified into three general categories including Coaxial-Cylinder Viscometer, Cone and Plate Viscometer, Coni-Cylinder Viscometer [218], as shown in Figure 4-3.
Figure 4-3 Types of rotational viscometers [219]
A typical rotational viscometer basically consists of a sample cup, a head unit with a motor, and a bob or spindle driven by the motor. The viscosity is determined by measuring the resistance of a bob rotating in the sample-filled cup. There are two main principles in use based on which part is driven by motor [217]:
-The Couette principle: The motor rotates the sample-filled cup around the stationary measuring spindle.
-The Searle principle: The instrument’s motor turns the measuring spindle inside a fixed sample- filled vessel.
In most commercial Rotational viscometers, the theory of the operation is based on the Searle principle. Two different sets up are used to measure viscosity using Rotational viscometers [217].
- Spring Motor
The Spring instruments utilize a stepper motor to drive the main shaft. A spring and pivot assembly rotate on the shaft. The spindle hangs from this assembly. The spring is deflected by the viscosity
of the sample under test when the spindle rotates. The type of spring totally depends on the viscosity of the substances. For the high viscosity samples, the spring needs to be more robust while for substances in the low viscosity range a more sensitive spring is required [217].
- Servo Motor
The servo device uses a precision servo motor to drive the main shaft and a digital encoder to record the rotational speed. The Spindle is attached directly to the shaft. High-speed microprocessors measure the speed from a digital encoder and calculate the current required to drive the rotor at the test speed. The required current is proportional to the viscosity of the sample under test. servo motor viscometers cover a wider measuring range compared to spring instruments and are more robust. Moreover, the digital encoder and motor allow for wider speed and torque range and therefore a wider range of viscosity than is possible with a spring viscometer. However, the measurement accuracy at low speeds and low viscosity is lower than for spring viscometers [217].
4.2.3.3! Falling-body viscometers
Falling body methods that are used to measure viscosity include the falling ball, falling sinker, and rolling ball type methods[220]. A falling -ball viscometer is based on the gravimetrical force as a drive. This type of viscometer is used to measure the falling time of a ball of a defined diameter and density traveling a specified distance through a sample-filled glass tube with a defined inner diameter. The viscosity can be directly measured based on this time, and calibration tests using the viscosity of standard fluids. The more viscous the fluid is, the more time takes the fluid pass a distance between two specified lines on the cylindrical tube. The inclination angle of the capillary allows for adjusting the driving force. Dynamic viscosity with the standard dimension of [mPa.s]
is measured using falling ball viscometers. The Hoppler viscometer, named after Fritz Hoppler, is the worldwide firs falling-ball viscometer to determine dynamic viscosity which states an inclination angle of exactly 80° [221]. When the ball moves through the fluid, a portion of the gravitational force drives the ball downwards. The buoyancy and friction act as the upward forces and slow down the ball movement. According to Newton’s law of motion for a falling ball, that
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states there are gravitational force, buoyancy force, and friction force, and these three forces reach a net force of zero, the viscosity is calculated using the following equation [217], [220]:
η= K. (ρE− ρ?).tÓ
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Where η is the dynamic viscosity[mpa.s], K is the proportionality constant, „O and„P!are the density of ball and sample[g/cm3], respectively. For Q= R.œfi
è(.S d is the radius of the ball, l is the distance,58 is falling time through distance l [s] [220]. Equation (4-11) shows the relation between the viscosity of a fluid and the terminal velocity of a falling ball through it.
4.2.3.4! Oscillating-Body viscometers
The oscillating-body viscometer consists of an axially symmetrical body suspended from an elastic strand that is immersed in a fluid medium. The oscillating system is gently rotated in a fluid to start the harmonic oscillation motion. The fluid applies a viscous drag on the oscillator causing the change in angular frequency of the oscillation and the damping decrement of the resulting harmonic compared with those in a vacuum. The magnitude of the change depends on the fluid’s viscosity and density as well as the physical characteristics properties of the suspension system. In other words, the viscosity of a fluid can be measured by observation of the decay of damped harmonic oscillations of the oscillating system. Oscillating Cylinder viscometers, Oscillating spheres viscometers, and Oscillating disks viscometers are the most commonly used examples of these viscometers [222].
4.2.3.5! Vibrating viscometer
In the vibrating viscometers, the oscillations include periodic distortions of the solid body itself, which is in contact with the test fluid. Vibrational viscometers measure the damping of an oscillating electromechanical resonator immersed in the fluid whose viscosity to be determined.
The resonator may be a cantilever beam, oscillating sphere, or tuning fork which generally oscillates in torsion or transversely in the test fluid. The higher the viscosity, the larger the damping imposed on the resonator [223]. The resonator's damping can be determined by one of the following methods [223]:
- Measuring the power input required to keep the oscillator vibrating at a constant amplitude. The higher the viscosity, the more power is needed to maintain the amplitude of oscillation. The vibrating probe accelerates the fluid and power input is proportional to the product of viscosity and density.
- Measuring the decay time of the oscillation when the vibration of the resonator is switched off.
The higher the viscosity, the faster the signal decays.
- Measuring the frequency of the resonator as a function of the phase angle between excitation and response waveforms. The higher the viscosity, the larger the frequency change for a given phase change.
The main advantage of vibrating viscometers is the small volume of sample required for their use that leads to ease of operation over extreme conditions of temperatures and pressures. Furthermore, these instruments are of simple mechanical construction than those of oscillatory bodies. Easy cleanout and prospect of construction with easily available materials is another important feature of vibrational viscometers [223].