1. Mer331 Lab – Week 2 - Viscosity Background: Viscosity n A fluid is a state of matter that does not permanently resist shear and the resistance to deformation (shear stress) is a function of the rate of deformation (shear rate) n Rheology = science of deformation n Viscometry = measurement of rheological properties n Viscosity is the property of a fluid that resists deformation: u molasses vs water, u molasses in January vs molasses in July. n Newton Law of Viscosity (for Newtonian fluids)

2. Shear stress as a function of deformation Background: Viscosity Shear Thickening

3. Background http://en.wikipedia.org/wiki/Bartholome w_and_the_Oobleck http://www.youtube.com/watch?v=yHlAcASsf6U Oobleck : shear thickening http://io9.com/5715076/non+newtonian-fluids-the- weirdest-liquids-youve-ever-seen

4. Background Ketchup, Toothpaste : shear thinning http://www.youtube.com/watch?v=GX4_3cV_3Mw Leaping Shampoo! Versluis M, Blom C, Meer D, Weele K, Lohse D (2006) Leaping Shampoo and the Stable Kaye Effect. Journal of Statistical Mechanics: Theory and Experiment 2006P07007.

5. Absolute (or Dynamic) Viscosity,  Units: 1 Poise = 1 g/(cm sec) 1 Pa sec = 1 kg/(m sec) = 1 N sec/m 2 1 Poise = 100 cP = 0.1 Pa sec Kinematic Viscosity: =  /ρ Units: 1 stoke = 1 cm 2 /sec = 0.0001 m 2 /sec Background: Viscosity Units

6. Techniques for Measuring Viscosity n Capillary Viscometers n Rotary Viscometers n Falling “Object” Viscometers n And many others….

7. Capillary Viscometers n Capillary Viscometers u Measure the flow rate of a fixed volume of fluid through a small orifice u From laminar flow theory we can relate the flow rate, pressure drop to viscosity = K*time K is a calibration constant Time is measured in seconds is given in cSt

8. Rotary Viscometers n Use the torque on a rotating shaft to measure a fluids resistance to flow  = F * torque F is a calibration constant which you look up in the instrument manual

9. Falling “Object” Viscometers n Apply F=ma n At terminal speed a=0 F G = F B + F D F G = mg  D 3 g/6 F B =  fluid  D 3 g/6 The drag on a sphere depends on the flow field: …. F B = Buoyancy F D =Drag F G = Weight

10. Falling “Object” Viscometers The drag on a sphere depends on the flow field: Reynold’s Number: For Stokes Flow: Re < 0.1 Therefore: Restrictions: terminal velocity, Re < 0.1

11. Gilmont Viscometer  = Kt(  ball -  fluid ) K = 35  ball,ss = 8.02 (gm/ml)  ball,glass = 2.53 (gm/ml)  in Cp t in minutes

12. Lab Write Up You will write a full lab report. Review the information on the course webpage: http://engineering.union.edu/~andersoa/mer331/MELabReports.htm Include detailed information on the uncertainty analysis: u Table of uncertainty values for each thing you measure (i.e. mass, volume etc). u Report all data with an uncertainty value u Include (hand written) derivation of uncertainty equations with a sample calculation in an appendix. u See handout on lab report expectations.