# Viscosity

Viscosity is a physical measure of how a fluid moves when a shear stress is applied to it. Viscosity is caused by a fluid's internal frictional forces.

## Quotes

* In connexion with the experimental determinatination of viscosity it should be noted that the flow of liquid is influenced in a very marked way by the driving pressure that is used. Bose and Rauert have made measurements at pressures from 0.005 to 2 kilograms per sq. cm., and find that whilst Poiseuille's Law holds for low pressures, very marked deviations are found when the pressure is increased, and in some instances the relative rates of flow are reversed, the more viscous of two liquids flowing more readily and becoming the less viscous at high pressure.
** Albert Ernest Dustan and Ferdinand Bernard Thole: The Viscosity of Liquids. Longmans, Green and Company. 1914. p. 4.
* The viscosity of blood has long been used as an indicator in the understanding and treatment of disease, and the advent of modern viscometers allows its measurement with ever-improving clinical convenience. However, these advances have not been matched by theoretical developments that can yield a quantitative understanding of blood’s microrheology and its possible connection to relevant biomolecules (e.g., fibrinogen). Using coarse-grained molecular dynamics and two different red blood cell models, we accurately predict the dependence of blood viscosity on shear rate and hematocrit.
** Dmitry A. Fedosov, Wenxiao Pan, Bruce Caswell, Gerhard Gompper, and George E. Karniadakis (2011). "Predicting human blood viscosity in silico". Proceedings of the National Academy of Sciences 108 (29): 11772–11777. DOI:10.1073/pnas.1101210108.
* ... To describe the motion of a fluid, we must give it properties at every point ... We will write the force density as the sum of three terms. We have already considered the pressure force per unit volume, –$\nabla$p. Then there are the “external” forces which act at a distance—like gravity or electricity. When they are conservative forces with a potential per unit mass, $\phi$, they give a force density –$\rho \nabla \phi$. (If the external forces are not conservative, we would have to write ƒ$_{ext}$ for the external force per unit volume.) Then there is another “internal” force per unit volume, which is due to the fact that in a flowing fluid there can also be a shearing stress. This is called the viscous force, which we will write ƒ$_{visc}$. Our equation of motion is $\rho \times$(acceleration) = –$\nabla$p –$\rho \nabla \phi$+ƒ$_{visc}$ ... When we drop the viscosity term, we will be making an approximation which describes some ideal stuff rather than real water. John von Neumann was well aware of the tremendous difference between what happens when you don’t have the viscous terms and when you do, and he was also aware that, during most of the development of hydrodynamics until about 1900, almost the main interest was in solving beautiful mathematical problems with this approximation which had almost nothing to do with real fluids. He characterized the theorist who made such analyses as a man who studied “dry water.” Such analyses leave out an essential property of the fluid.
** Richard Feynman: (1964). 40–2. The equations of motion in Chapter 40. The Flow of Dry Water, The Feynman Lectures on Physics, Volume II, Mainly Electromagnetism and Matter
* Taking now for granted that instability arises generally even in those cases in which the inviscid equation allows only a neutral solution, the question arises how viscosity can cause instability. From simple arguments one would expect damping rather than amplifying. But here one should remember that an inviscid fluid is a system of an infinite number of degrees of freedom, which normally interact so that the energy is dissipated among all modes of vibration. It is only for very special geometrical conditions that this transfer of energy does not take place. Therefore, if a neutral disturbance is possible in the inviscid fluid, the viscosity may easily change the phases of vibration in such a manner that the transfer of energy begins, which then means amplification of the vibration.
** Werner Heisenberg: "On the stability of laminar flow". Proc. Intern. Math. Congress, Cambridge, Mass. 1950. vol. 2. pp. 292–296. (quote from p. 295)