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In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected [clarification needed] connection revealed independently by William Sutherland in 1904, [1] [2] [3] Albert Einstein in 1905, [4] and by Marian Smoluchowski in 1906 [5] in their works on Brownian motion.
The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on a wall in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
For instance, a 20% saline (sodium chloride) solution has viscosity over 1.5 times that of pure water, whereas a 20% potassium iodide solution has viscosity about 0.91 times that of pure water. An idealized model of dilute electrolytic solutions leads to the following prediction for the viscosity μ s {\displaystyle \mu _{s}} of a solution: [ 57 ]
The viscosity of water is about 10 −3 Pa·s or 0.01 poise at 20 °C (68 °F), and the speed of sound in liquid water ranges between 1,400 and 1,540 metres per second (4,600 and 5,100 ft/s) depending on temperature.
In this way Einstein was able to determine the size of atoms, and how many atoms there are in a mole, or the molecular weight in grams, of a gas. [13] In accordance to Avogadro's law, this volume is the same for all ideal gases, which is 22.414 liters at standard temperature and pressure.
Intrinsic viscosity [] is a measure of a solute's contribution to the viscosity of a solution.If is the viscosity in the absence of the solute, is (dynamic or kinematic) viscosity of the solution and is the volume fraction of the solute in the solution, then intrinsic viscosity is defined as the dimensionless number [] = It should not be confused with inherent viscosity, which is the ratio of ...
Consequently, if a liquid has dynamic viscosity of n centiPoise, and its density is not too different from that of water, then its kinematic viscosity is around n centiStokes. For gas, the dynamic viscosity is usually in the range of 10 to 20 microPascal-seconds, or 0.01 to 0.02 centiPoise. The density is usually on the order of 0.5 to 5 kg/m^3.
The free variables in the two equations above, also indicates that specific constitutive equations for shear viscosity will be quite different from the simple defining equation for shear viscosity that is shown further up. The rest of this article will show that this is certainly true.