Effect of temperature on Viscosity as Determined by Ball-drop Method J. Cayabyab, J.R.L. Cu, A.M.S. Leron Department of Mining, Metallurgical and Materials Engineering University of the Philippines Diliman
[email protected] Abstract The falling ball method makes use of newton’s law of motion of force balance as the falling ball reaches its terminal velocity. In this experiment, experiment, 100%, 75% 75 %, 50 % and 25% of glycerine solution were used. A ball was dropped in every solution while being timed. Timing involved starting the timer when the ball reaches the solution surface then stopping it as it reaches the bottom of the graduated cylinder. It was later proven in the experiment that higher temperatures reduce the viscosity of liquids thus, a smaller velocity value.
1. Introduction Viscosity mainly refers to the fluid resistance to flow. flow. Fluids resist the relative motion motion of immersed objects through them as well as to the motion of layers with differing velocities within them. Viscosity of the fluid is dependent on the intermolecular forces; the stronger the intermolecular forces the higher the viscosity because molecules are closer together and get tangled up and become resistant to flow. There are many ways of measuring viscosity; one of these is the falling ball method. The method involves determining the time it takes for the sphere to reach the bottom of the fluid container. Theory governing this method involve that when a body moves in a fluid, it is acted on by a frictional force opposite the direction of movement. The magnitude of the force depends on the geometry of the body, its velocity and the internal friction of the fluid. Internal friction measurement is given by dynamic viscosity, η. Stokes derived an expression for the frictional force of the falling ball with radius r moving r moving at velocity ω in an infinitely extended fluid of dynamic viscosity η:
At constant velocity, all force acting on the sphere will be in equilibrium (fig 1): frictional force ( F1) F1) + buoyancy force F2 = gravitational force F3 force F3..
Fig 1. Free body diagram of sphere falling through the fluid Where : ρ1 = density of the fluid ρ2 = density of the ball g = gravitational acceleration
Effect of temperature on Viscosity as Determined Determined by Ball-drop Method . Page 1 of 5
Combining expression:
the
forces
ρ2- ρ1)g = 6
arriving
to
the
[1].
Given the initial height of the fluid and recorded time, velocity of the sphere can be computed, which is height/time. Knowing the velocity, viscosity of the fluid can be computed. This experiment aims to compare the viscosities of different glycerine concentrations measured using Falling Ball and determine the effect of increasing temperature in the viscosity of the solutions.
To be able to compute for the viscosity of water, ηwater , velocity vs. concentration was plotted (see appendix, table 1); a linear trend should be observed shown by the graph below. Room Temperature Elevated Temperature Linear (Room Temperature)
2. Methodology 100%, 75%, 50 % and 25% of glycerine solution were prepared. The solutions were placed in graduated cylinder and initial heights were measured using ruler. The ball was drop in each solution and the time it takes for the ball to touch the bottom of the cylinder was recorded. Three trials were performed in each solution. Solutions were then heated at the water bath with temperature of 60oC. Dropping of ball were repeated and it 3 trials were also performed.
3. Results and Discussion In this experiment, the viscosity of the sample, glycerine and the diluting agent, water was determined at two different temperatures, 25°C and 48°C. The experimental viscosity of glycerine, η, can be directly calculated using the modified Stoke’s equation relating the falling ball and the opposing forces. Table 1. Viscosity of 100% glycerine
Temperature 25°C 48°C
Generally for most materials, the trend is as the temperature goes up the viscosity goes down. As you further heat your solution, its tendency is to flow more freely because it makes the molecules mobile thus resistance to flow is harder. [2]
ηexpt’l ηtheo [1] 3.2900 Pa·s 1.4200 Pa·s 2.6863 Pa·s 0.2800 Pa·s
) 150.0000 s / m 100.0000 c ( y t i c 50.0000 o l e v
0.0000
0
5
10
concentration (M)
Figure 1. Velocity vs. concentration graph at room and elevated temperatures
The computed values of the viscosity of pure water through interpolation at 0 concentration of glycerine is shown in Table 2 below. Table 2. Vicosity of pure water
Temperature ηexpt’l ηtheo [2] 25°C 0.1812 Pa·s 8.91 x 10- Pa·s 48°C 0.1258 Pa·s 5.66 x 10- Pa·s
From Tables 1 and 2, a very large deviation from theoretical values is observed. This experiment greatly relies on the accuracy and reaction time of the time keeper and also of the type of timer used, and the time is takes for the ball to fall from the point it touches the surface of the solution up to t he bottom of the cylinder
Effect of temperature on Viscosity as Determined by Ball-drop Method . Page 2 of 5
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is just a fraction of a second, human error is very hard to eliminate.
4. Conclusion and Recommendation The temperature and viscosity was shown in this experiment to have a inverse proportional relationship. Higher temperatures makes the glycerine solution less viscous at all concentrations. Hence, the ball would drop faster. It can also be concluded that viscosity was highly dependent on the concentration of the solution wherein, higher concentrations yield more viscous solutions. [4] Due to errors in the experiment because of inaccurate timing, it is highly recommended to have a ball drop viscometer which is an automated and standardized instrument to measure viscosity.
5. Reference [1]
D.R. Rohendra etal., Europian J. Phys. Vol. 33, pp. 1457, (2012)
[2]
Elert, G. (n.d.). Viscosity. Retrieved January 23, 2012, from The Physics Hypertextbook: http://physics.info/viscosity
[3]
ThermExcel. (2003, June). Physical characteristics of water (at atmospheric pressure). Retrieved January 23, 2013, from ThermExcel: http://www.thermexcel.com/english/ta bles/eau_atm.htm
[4]
CM. Scarfe, Viscosity-Temperature relationships of melts at 1atm in the system diopside-albite American Mineralogist V 71, pp767-771, 1986
Effect of temperature on Viscosity as Determined by Ball-drop Method . Page 3 of 5
Appendix Table 1. Gathered Data % conc
Concentration (M)
vol (mL)
100% 75% 50% 25%
13.6497 10.2372 6.8249 3.4124
76 67 79 82
100% 75% 50% 25%
13.6497 10.2372 6.8249 3.4124
84 65 78 82
ht (cm)
t1 (s)
t2 (s)
t3 (s)
tave
Room Temperature (25°C) 14 3.07 2.67 3.18 2.9733 12.2 0.38 0.38 0.34 0.3667 14.2 0.28 0.26 0.26 0.2667 14.9 0.23 0.22 0.19 0.2133 Elevated Temperature (48°C) 15.2 2.69 2.58 2.37 2.5467 11.2 0.29 0.26 0.25 0.2667 14.1 0.16 0.16 0.22 0.1800 14.9 0.14 0.16 0.15 0.1500
mass (g)
density (g/mL)
v (cm/s)
95.532 77.2816 88.1345 87.9827
1.2570 1.1535 1.1156 1.0730
4.7085 33.2727 53.2500 69.8438
98.0612 75.4216 87.1682 87.1281
1.1674 1.1603 1.1175 1.0625
5.9686 42.0000 78.3333 99.3333
Sample calculations
1. Calculation of concentration (M) of glycerine
2. Density of the solution
3. Velocity of the falling ball at experimental concentrations
4. Viscosity of glycerine at purity
Effect of temperature on Viscosity as Determined by Ball-drop Method . Page 4 of 5
5. Viscosity of pure water
Effect of temperature on Viscosity as Determined by Ball-drop Method . Page 5 of 5
