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# VISCOSITY

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1. VISCOSITY

2. Definitions • Fluid: a material that flows when subject to a force (liquids and gases) • Solids: may be deformed by a force, but do not flow • Semi-solids: exhibit characteristics of both solids and liquids • Viscosity: property by which fluids offer resistance to objects moving through them

3. Liquids Solids Semi-solids

4. Suspensions: mixtures in which solid matter is suspended in a fluid medium • Emulsions: mixtures in which small liquid droplets are dispersed in another liquid • Glasses: amorphous materials which behave as solids due to high viscosity

5. Emulsion Suspension

6. Glassy States: a solid or a very, very viscous liquid?

7. Viscosity • Viscosity is the resistance that a fluid offers to flow when subject to a shear stress Isaac Newton: “the resistance which arises from the lack of slipperiness of the parts of a fluid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from each other”

8. Force A Closer Look • In an ideal liquid there would be no viscosity, as there would be no forces acting between layers of a fluid

9. In reality, fluid layers interact through “frictional” forces. Each layer of fluid will drag the next layer to some extent

10. Describing Viscosity:The Model (Fastest moving layer of fluid) (fluid is still at lower surface) Velocity gradient at y1: g = (shear rate) . du dy

11. Shear Stress: t = F/A Shear stress is the force delivered parallel to an area of fluid surface Force Area A

12. Newton’s Law • Shear stress and shear rate are related by the proportionality constant h (known as the viscosity)

13. Laminar Versus Turbulent Flow • Newtons description applies to laminar flow fluids. • Laminar Flow: “streamline” flow. Fluid moves in a straight line with the applied force. Layers slide by with no swirls. • Turbulent Flow: disorderly flow. Small packets of fluid moving in all directions and all angles to normal line of flow.

14. Reynolds Number The Reynolds number describes the degree of turbulence Laminar Flow: [Re] < 2000 Turbulent Flow: [Re] > 3000 Turbulent fluids have viscosity, but we usually measure viscosity in laminar flow

15. Molecular Basis of Viscosity • Viscosity represents the internal friction between molecules in a fluid. The origin is net transfer of momentum between layers of fluid moving at different velocities in parallel flow by the mechanism of molecular collisions.

16. MOMENTUM = p = mv Newton’s Second Law

17. A “layer” of fluid subject to a force has m=ADxr, velocity v1, momentum=mv1 • Adjacent layers are not subject to the force, yet they move with a speed v<v1 • Thus, momentum is “transferred” to other layers of fluid Dx Area A v1 v2

18. Viscosity in Foods • Determines mouth feel, body of fluid foods, perceived thickness, and ease of swallowing • Influences pourability, how well batters stay on • Determines pumping needs of juice, milk, and other fluid foods

19. Emulsion and suspensions

20. Heterogeneous foods

21. Viscosity and Temperature • For liquids, temperature decreases viscosity • The way in which it varies depends on the fluid • It is critical to know the temperature at which viscosity is measured • Arrhenius model often applies

22. Ea is the “activation energy”, that is, the energy barrier to flow • As a molecule moves it will experience minimum and maximum intermolecular forces with its neighbors. The difference represents the activation energy

23. Ea Energy Direction of Flow

24. Williams-Landel-Ferry Model: applies to very viscous systems • where C1 and C2 are constants, Tg is the glass transition temperature, and hg is the viscosity at Tg (~1012 Pa.s).

25. Other empirical equations may apply . . . and many more

26. Transfer Processes • Shear stress is considered as momentum flux

27. Viscosity Units • Viscosity has the dimensions of ML-1T-1 • In units • CGS: poise or centipoise (cp) • SI : Pa.s = 1000 m Pa.s • kinematic viscosity in centistokes (cSt) • Conversions • 1000 m Pa.s = 1 Pa.s = 1Ns/m2 • 100 cP = 0.1 Pa.s = 100 m Pa.s =1 dyne.s/cm2

28. Types of Viscosity • Dynamic or absolute viscosity

29. Other descriptions of viscous forces • Fluidity: the inverse of dynamic viscosity. f = 1/h • Kinematic Viscosity: absolute viscosity divided by the density of the fluid: u = h/r Kinematic viscosity is measured by capillary viscometers

30. Often used for polymer solutions. When a polymer is added to a solvent, there is a noticeable increase in the viscosity. • If h is the viscosity of the solution, and ho the viscosity of only the solvent, then the following definitions apply: