ME 409 Viscosity and pH Measurement Lab 

1) Operation Principle of Viscometers
A rotating bob in a stationary measurement cell is driven by a motor in the metering head at a constant speed through the magnetic coupling. When viscosity changes the torque on the motor will change. This change in torque is proportional to the viscosity change. 

Measurement of Viscosity of Pressurized Liquid using Falling Ball Method 

The Spherical Object falling in High Viscous Liquid is used to know the Viscosity by the measurement on the Falling Speed. A Falling Ball Viscometer using Ruby ball, 1 to 3 mm in Diameter, is developed and engaged in the Viscosity Measurement of Pressurized Liquid up to 500 MPa.

Ref: J. Reed, "Principles of Ceramic Processing", TP807 R36, 1994, John Wiley, pp 279-289

Theory of viscosity measurement 
Viscosity is of paramount importance to lubrication engineers, rheologists, chemical engineers, and many more besides. This report describes the background, development, operation and testing of a portable automatic instrument for the measurement of bulk viscosity. 

Briefly, this mechanism stirred the fluid using a glass rod, indirectly driven via a conventional tension spring by a small motor. The extension of the spring was kept constant by means of an electrical contact. Brushes made connection to a simple electronic control circuit which increased the speed while the contact was broken, and decreased it while closed. Thus the rotation rate oscillated around a certain mean value, which was proportional to the viscosity. (See further details on the theory in section 2.) A timer switched the device on at regular intervals for a few seconds, and an output voltage was produced indicating motor speed. This could be plotted on a chart recorder, to obtain a direct graph of relative viscosity against time. 

Ref: http://www.hanssummers.com/electronics/viscometer/theory.htm

2.1 Types of viscometer 

The two main types of viscometer are the tube and rotational instruments [ref. 1], The former observe the rate of flow through tubes due to a known pressure difference. These types are unsuitable for this application, because a suitable viscometer must allow the nest of the experiment to proceed normally in the intervals between measurements, The lubrication fluid is contained in a small lest tube or beaker and therefore any tube-like measurements would be impractical and hard to automate.  

The vast majority of rotational viscometers fall into two categories: those where two concentric cylinders rotate relative to one another around a common axis; and those consisting of a cone of large vertical angle (approaching 180 degrees), and plate whose plane is through the apex of the cone. Many variations on this theme are possible, but in all types the test fluid is sheared between the rotating parts. The cone on plate type is again rejected for this application, as it would not be possible to perform oxidation experiments inside the viscosity measurement apparatus. 

A concentric cylinder viscometer can easily be formed by regarding a beaker in which the experiments are performed as the outer cylinder, and placing a rotating inner cylinder centrally within it. The suitability and simplicity of this arrangement makes it the ideal choice here. Hence the following theoretical derivations are only concerned with instruments of this type. 


2.2 Viscosity 

Prior to detailed mathematical consideration, it is necessary to define two variables used in the description of fluid flow: shear stress and shear strain. Stress is measured in units of Pascals (1 Pa = I Nm-2). Consider a point P in a body, surrounded by a plane of area A. The material above, below and to the sides of P exert a resultant force F on the element. As the area is varied the force changes, and the ratio F/A approaches a limit as A tends to zero, known as the traction across the area. This traction has a perpendicular component, the 'normal stress', and a parallel component the 'shear stress' s. Shear strain y is defined as the relative displacement of two layers in the fluid, divided by their separation. 

A Newtonian fluid is one in which the ratio of shear stress to the rate of shear strain is constant [ref. l].This parameter is the viscosity n. That is, 
n = s / y. 
The unit of viscosity is the poise. Kinematic viscosity v is often used and is defined as 
v= n / p, 
where p is the density of the fluid. The unit of kinematic viscosity is the Stokes; lubricants are usually specified, by convention, in terms of their kinematic viscosity in centistokes (cst). 

A non-Newtonian fluid is one in which the viscosity is not a constant parameter, it depends in some way on the shear rate. The Newtonian model is accurate over a large range for most low molecular weight fluids, including water and many aqueous solutions, liquid metals, organic compounds, and silicones. Other fluids such as suspensions obey various more complex models. A large number of such models have been proposed, for example the Bingham [ref. 2], power law fluid [ref. 3], and Casson [ref. 1] models. This report is only concerned with the measurement of viscosity for Newtonian fluids, although modifications to allow for Non-Newtonian behaviour would not be difficult (See discussion, Section 5). 


2.3 Concentric cylinder viscometer. 

The formulae derived apply to the measurement of Newtonian fluids, confined between concentric cylinders of infinite length, and neglecting any inertial effects [ref. 1]. The inner and outer cylinders are of radius R1 and R2 respectively, and rotate with a relative angular velocity O. Considering the fluid between the inner cylinder and a tadius r; each particle moves with a constant angular velocity, such that the net torque on the fluid is zero. The torque G per unit length on a cylindrical surface at radius r is  G = 2 pi R1^2 s1 
where s1 is the shear stress on the inner cylinder, The shear stress at any radius r is 
s = G / 2 pi r^2 
and in particular, at the outer cylinder is 
s2=G / 2 pi R2^2. 
fluid element.

An expression for the strain rate may be derived using figure 1, which shows sectors of two cylindrical surfaces separated by a small distance dr. In a time dt the radial line AB moves to AB', as opposed to A'C, had the fluid been a rigid body. Now, 
BB' = (r + dr) (w + dw) dt 
and 
BC= (r + dr) w dt 
so the shear strain is 
y = B'C / CA' = (r + dr) dw dt / dr, 
which in the limit as dr tends to zero, gives 
dy / dt = r dw / dr 
Substituting these results into the Newtonian fluid equation leads to 
r dw / dr = G / 2 pi v r^2 
Applying the boundary conditions to w = 0 at r = R1, w = O at r = R2, and integrating gives 
O = G ( 1 / R1^2 - 1 / R2^2 ) / 4 pi n 
For a Newtonian fluid a graph of angular velocity against torque per unit length will be linear through the origin, and have gradient 
(1 / R1^2 - 1 / R2^2) / 4 pi n 
This formula will be used to obtain the viscosity. If the instrument is calibrated with a liquid of known viscosity, or used to measure relative viscosity, then all subsequent measurements can be referenced to this and it is not necessary to know R1 or R2 explicitly, provided they remain constant. 

Temperature dependence 

Viscosity is highly dependent on temperature. The relation is often found to approximate 
v = A exp ( Ev / k T) 
over a large temperature range, where v is the kinematic viscosity, k Boltzmann's constant, and T the temperature. The constants A and Ev (known as the activation energy for viscous flow) exhibit a large variation between different fluids. This relation was tested, see section 4.2. 

The fluid must he kept at a known and constant temperature throughout the measurement. If the concentric cylirider viscometer is used with very viscous fluids at high shear rates, temperature rise due to shear heating can be troublesome. This effect is neglected here, but is considered further in the discussion, section 5. 


2.4.3. Departure from circular flow 

In concentric cylinder arrangements, fast moving fluids near to the inner cylinder try to move outwards due to the centripetal force. Such a movement is impossible for the liquid as a whole, so local circulation occurs [ref 4]. These 'Taylor vortices' are only formed above a certain rate of rotation, as in figure 2. This secondary flow is still regular but complex, and the relations derived above no longer apply. At still higher speeds the flow becomes turbulent For Newtonian fluids, the 'Reynolds number' is defined as 
Re = O R (R2 - R2) / v 
where R is the radius of the moving cylinder, and the other variables are as before.  For inner cylinder rotation, Taylor [ref. 5] found that vortices occurred for 
Re > 41.3 (R2 / (R2 - R1)) ^ l/2 
At a rotation rate of 300 rpm, and with inner and outer cylinders of radius 1 and 2 cm respectively, the  corresponding minimum kinematic viscosity which may measured is 0.005 cst. The current viscometer will not handle such low viscosities. 

2) Operation Principle of pH-meters

Understanding pH measurement 

In the process world, pH is an important parameter to be measured and controlled. The pH of a solution
indicates how acidic or basic (alkaline) it is. The formal mathematical definition of pH is the negative logarithm
of hydrogen ion activity. In most cases, hydrogen ion activity can be approximated by the hydrogen ion
concentration, and the formula becomes pH = - log10 [H+]. On the pH scale, which varies from 0-14, a very
acidic solution has a low pH value, a very basic solution has a high pH value, and a neutral solution has a pH
of approximately 7.

A pH measurement loop is made up of three components, the pH sensor, which includes a measuring electrode, a reference electrode, and a temperature sensor; a preamplifier; and an analyzer or transmitter. A pH measurement loop is essentially a battery where the positive terminal is the measuring electrode and the negative terminal is
the reference electrode. The measuring electrode, which is sensitive to the hydrogen ion, develops a potential (voltage) directly related to the hydrogen ion concentration of the solution. The reference electrode provides a stable potential against which the measuring electrode can be compared. 

When immersed in the solution, the reference electrode potential does not change with the changing hydrogen ion concentration. A solution in the reference electrode also makes contact with the sample solution and the measuring electrode through a junction, completing the circuit. Output of the measuring electrode changes with temperature (even though the process remains at a constant pH), so a temperature sensor is necessary to correct for this change in output. This is done in the analyzer or transmitter software. The pH sensor components are usually combined into one device called a combination pH electrode. The measuring electrode is usually glass and quite fragile. Recent
developments have replaced the glass with more durable solid-state sensors. The preamplifier is a signal-conditioning device. It takes the high-impedance pH electrode signal and changes it into a low
impedance signal which the analyzer or transmitter can accept. The preamplifier also strengthens and stabilizes the signal, making it less susceptible to electrical noise. Keeping the system up and running 

A system’s pH electrodes require periodic maintenance to clean and calibrate them. The length of time
between cleaning and calibration depends on process conditions and the user’s accuracy and stability expectations. Over time, electrical properties of the measuring and reference electrode change. Calibration in known-value pH solutions called buffers will correct for some of these changes. Cleaning of the measuring sensor and reference
junction will also help. However, just as batteries have a limited life, a pH electrode’s lifetime is also finite. Even in the "friendliest" environments, pH electrodes have to be replaced eventually. 

The sensor’s electrical signal is then displayed. This is commonly done in a 120/240 V ac-powered analyzer
or in a 24 V dc loop-powered transmitter. Additionally, the analyzer or transmitter has a human machine
interface for calibrating the sensor and configuring outputs and alarms, if pH control is being done.

Keep in mind, application requirements should be carefully considered when choosing a pH electrode.
Accurate pH measurement and the resulting precise control that it can allow, can go a long way toward
process optimization and result in increased product quality and consistency. Accurate, stable pH
measurement also controls and often lowers chemical usage, minimizing system maintenance and expense

Operation Principle of pH-meters (pH: Corning Model 440 pH Meter)
The principle of electrometric pH is the determination of the activity of the hydrogen ions by potentiometric measurement using a glass pH indicating electrode coaxially joined to a silver/silver chloride reference electrode. When immersed in solution, the reference electrode makes contact with the sample through the junction, completing Electrical contact between the reference electrode, sample and pH indicating electrode.