FDST 8080 Lab 2011

VISCOMETERS We have defined the viscosity of fluid foods in a variety of ways, including: 1. The resistance to flow offered by the fluid. 2. The ratio of shear stress to shear rate: ! = " # =

F / Adu /dy

3. The rate at which momentum is transferred through layers of the fluid 4. The rate that energy is dissipated per volume of fluid. In food science, we are interested in the viscosity of foods for several reasons. First, viscosity is an important sensory attribute of liquid foods. Viscosity correlates with the perceived mouthfeel and thickness of liquid products. Also, our ability to suck liquids through a straw or slurp them off of spoons depends on viscosity. For food processors, fluid viscosity becomes important for determining the size of pump required to move a fluid, whether a material can be extruded, how easily a bottle can be filled, and how much impediment to heat transfer will occur at heat exchanger surfaces. In this lab, we will explore several common devices used to measure food viscosity. This includes the capillary viscometer, the rotational viscometer, falling ball viscometer and the human mouth- the first three being objective physical measurements, the latter a sensory evaluation. We will evaluate several liquid foods by each of these methods and compare results. At this stage, we will assume the liquids are ideal and follow Newtons law

(! = " # ) I. ROTATIONAL VISCOMETRY Rotational viscometers are a common tool in the food industry. A metal cylinder probe is caused to rotate in the sample. The torque required to rotate the cylinder at a given speed is measured. The more viscous the sample, the more torque required to rotate the cylinder. Rotational viscometers are relatively simple to use and can measure a wide range of viscosity values. This latter feature is possible as rotational viscometers usually come with a variety of interchangeable probes: thin probes with small surface areas for viscous materials; larger probes with increased surface area for less viscous liquids. Most can also operate at a variety of rotational speeds, and therefore shear rates. This allows the operator to investigate the shear dependency of the sample. For a concentric cylinder viscometer, the viscosity of a Newtonian fluid is determined by:

FDST 8080 Lab 2011

!

hRb

Rc

! = M4"h#1Rb2

$1Rc2

%

& ' (

) *

where is the angular velocity (RPM), M is the torque, Rb the diameter of the inner cylinder (bob), and Rc the diameter of the sample container. Thus, the rotational speed, measured torque, and consideration of the probe size and shape allow us to determine shear rate and shear stress. The ratio of shear stress and shear rate are give us the apparent viscosity. In practice, these constant factors and measured variables are used by computer software to calculate viscosity. Older instruments may require users to determine multiplication factors for the given spindle. In this lab we will measure an apparent viscosity at a single shear rate. Details of operation depend on the particular instrument. We will use the Brookfield viscometer . Brookfield Pour some sample in a beaker. Insert one of the spindles in the Brookfield and put the end of the spindle in the liquid. Change the rpm/spindles to obtain a reading mid-scale. The particular spindle (with its specific geometry) must be noted.

FDST 8080 Lab 2011

II. FALLING BALL VISCOMETERS One very simple type of instrument is the falling ball viscometer. Here, a glass or metal ball is allowed to fall through the sample. The more viscous the sample is, the longer it takes the ball to reach the bottom. In the simplest case, this may be just a graduated cylinder with a steel ball. Once the ball drops, it will soon reach a terminal velocity once the force of gravity is countered by the frictional forces due to the fluid. By Stokes law: ! = 2("s # "l)gR

2

9$%

& ' (

) *

where is the viscosity, s is the density of the solid ball, l is the density of the fluid, R is the ball radius, g the gravitational constant, and the terminal velocity. The time it takes for the ball to fall a given distance is determined with a stopwatch, and determines the velocity (=x/t).

F = mgg

F = K!"f

FDST 8080 Lab 2011

Research instruments such as the Hoeppler viscometer are also available. These have precision made tubes surrounded by an outer jacket, through which constant temperature water can be circulated. The sample tube can be evacuated to remove air bubbles, then sealed. Here, the tube is tilted at a 10 angle, and the ball is only slightly smaller than the inner diameter of the tube; thus, wall effects are important and incorporated into the analysis. For the Hoeppler viscometer, the absolute viscosity is given by:

!

" = T # (SGs $ SGl) # B where T is the time interval of the falling ball and B is a ball constant. Here SG is the specific gravity (/water)

Type Serial Number

Ball Diam @ 20C (mm)

Wt of Ball (g)

SGB @ 20C

Ball Constant

A2 8440 15.9051 4.6958 2.2290 ---------- C33 8665 15.8059 4.6088 2.2291 0.009529 F6 8269 15.6300 4.4516 2.2266 0.077944 H8 8058 15.5512 15.5447 7.8939 0.13630 K10 8114 14.9846 13.9058 7.8933 1.2691 M12 6869 13.4933 10.1712 7.9071 10.804 Where possible, use the falling ball viscometer to measure the viscosity of the same liquids you measured in the rotational viscometer. If the liquid is too opaque, this may not be possible. Record the time it takes for the ball to pass from the first marker to the final one. We will also need to record the specific gravity of the liquid. III. Zahn Cup-Type Viscometer The Zahn cup is an easy-to-use device for assessing the viscosity of oils, paints, syrups, batters and other liquids. The cup is filled to the top and the liquid allowed to flow through an opening in the bottom. The viscosity of the liquid is measured in Zahn number, that is, the time in seconds for a known volume of liquid to flow out of the cup. For thin fluids, a cup with a small orifice is used; for more viscous mixtures, a cup with a larger whole is used. Although easy to use, the geometry and driving force for flow are difficult to describe. Thus, no exact formulas exist to convert viscosity measurements in Zahn numbers into absolute viscosity. However, it is common practice to report the viscosity in Zahn numbers. Some empirical formulas have been developed, however, to relate Zahn number to kinematic viscosity. For the Boekel brand cups:

FDST 8080 Lab 2011

Zahn Cup# Formula T, Zahn Seconds Range

1 / = 1.1(T-29) 45 - 80 2 / = 3.5(T-14) 25 - 80 3 / = 14.8(T-5) 20 - 75 4 / = 11.7(T-7.5) 20 - 80 5 / = 23(T-0) 20 75

Specifications Zahn Cup # 1 2 3 4 5 Orifice Diameter (in) .078 0.108 0.148 0.168 0.208 Zahn Range (s) 45-80 25-80 20-75 20-80 20-75 Centistoke Range* 18-56 40-230 150-790 220-1100 460-1725+ Application Very thin

oil Thin oil Medium

oil Heavy

mixture, Batter, syrup

Very heavy mixture,

Heavy syrup

*Centistoke is a measure of kinematic viscosity = absolute viscosity (cP)/density (gcm-3)

FDST 8080 Lab 2011

Measure the temperature of the liquid prior to measurement. The Zahn cup is provided with a bracket to hold a thermometer. Prior to measurement, raise the bracket so the thermometer stem is out of the cup. Place a finger in the ring, lift the viscometer completely out of the liquid and start the stop watch when the top edge of the cup breaks the surface. Stop the watch when the steady flow of the liquid from the orifice breaks. Repeat until consistent results are obtained. Express viscosity in Zahn seconds. IV. Capillary Viscometry Capillary viscometers are relatively simple and inexpensive instruments for measuring fluid viscosity, and when used properly, give very accurate measurements of viscosity. In this approach, gravity causes a fluid to drop between two marks in a capillary tube. The time required for the fluid level to fall a given distance measures the viscosity.

The Hagen-Poiseuille equation shows that the flow rate Q is related to the pressure drop (P=gh), the tube radius R, the tube length L, and the viscosity : Q = ! ("P)R

4

8#L

It can be shown that the kinematic viscosity is just

!"=#ghR48LV t = kt

FDST 8080 Lab 2011

That is, the ratio of viscosity to density is proportional to the time it takes for the liquid to drop between the marks. The absolute viscosity can be determined by separately measuring the fluid density. In some cases it is interesting to determine the intrinsic viscosity of a sample [], as this can be related to the molecular weight of a dissolved solute. Capillary viscometers are of limited use in food systems, as particulate systems can clog the capillary tube. Also, dependence of viscosity on shear rate or shear history is more difficult to study. It can be very useful, however for studying clear juices, beverages, or solutions of food macromolecules such as proteins or carbohydrates. The time in seconds for the fluid to fall between the two markers is recorded. When multiplied by the capillary constant k, this gives the kinematic viscosity /. V. Juice Viscometer A variant of the capillary viscometer is the AOAC capillary viscometer for juices (AOAC 37.1.108). It Is more appropriate for fruit nectars and juice products, which may have bits of pulp and particulates that would clog a precision capillary viscometer.

FDST 8080 Lab 2011

To use, the viscometer should be maintained at 24C. The instrument is first calibrated with water. Water is filled to the top while the flow is stopped by placing your finger at the lower end. The top is leveled off with a spatula. Remove the finger and begin timing. A line is scribed on the side to indicate the level reached by water in 13 s. Clean and dry the instrument. Add the juice sample and let flow until steady flow is attained. Place finger over the capillary tube to stop the flow. Fill the tube util almost full and check for air bubbles. Remove an bubbles with a stir rod. Fill the tube to the top, then level off with a spatula. Remove finger and begin timing. Record the time to nearest 0.1 s needed for the juice to reach the calibration line. Obtain at least 2 or more readings. TO DO: Lab reports are to be done on a spreadsheet, both text and calculations. Show an example calculation in the text. A. Make a table showing the sample and the following information: Brookfield Viscometer: Spindle #, rotational speed, correction factor, viscosity Falling Ball: Ball#, SGB, SGL, Time(s), viscosity Zahn Viscometer: Cup#, time (Zahn seconds), density, viscosity Capillary Viscometer: Viscometer model, viscometer constant, time, density, viscosity Juice Viscometer: Time for water, juice, relative viscosity, juice viscosity B. How do the results of the different measurements compare? Are they well correlated? C. What advantages or disadvantages do the various approaches offer?