Related Experiment Video
Updated: Jun 12, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Communications: The fractional Stokes-Einstein equation: application to water
1School of Physical, Environmental and Mathematical Sciences, University College, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia. k.harris@adfa.edu.au
The Journal of Chemical Physics
|June 25, 2010
Summary
The fractional Stokes-Einstein relation accurately describes liquid behavior across temperatures and densities. Water exhibits a distinct transition in this relation, differing from confined water studies.
Area of Science:
- Physical Chemistry
- Materials Science
- Thermodynamics
Background:
- The fractional Stokes-Einstein relation (FSE) has been shown to describe the relationship between self-diffusion coefficients and viscosity in various liquids.
- Previous studies demonstrated the applicability of FSE to model liquids like the Lennard-Jones fluid and a range of molecular and ionic liquids.
- Water, both normal and heavy, exhibits FSE behavior with distinct transitions in the supercooled region at atmospheric pressure.
Purpose of the Study:
- To extend the high-temperature applicability of the fractional Stokes-Einstein relation (FSE) for water isotopomers.
- To analyze the FSE behavior of water along its saturation line up to higher temperatures.
- To compare the FSE transition temperatures in bulk water with those reported for confined water systems.
Main Methods:
- Utilized recent self-diffusion data for water isotopomers along the saturation line.
- Applied the fractional Stokes-Einstein relation (D/T = (1/eta)^t) to analyze the data.
- Extended the temperature range of FSE fitting to 623 K for both normal and heavy water.
Main Results:
- The fractional Stokes-Einstein relation was successfully extended to 623 K for water along the saturation line.
- The high-temperature exponent 't' for water was found to be consistent with previous findings.
- The FSE transition temperature in bulk water was observed to be significantly higher than values reported for confined water.
Conclusions:
- The fractional Stokes-Einstein relation provides a robust framework for understanding liquid dynamics over extended temperature and density ranges, including water.
- Water exhibits a clear transition in FSE behavior, with the transition temperature being sensitive to the physical state (bulk vs. confined).
- The findings highlight the importance of considering phase and confinement effects when applying transport property relations in liquids.
Related Concept Videos
01:25Poisson's And Laplace's Equation
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
01:24Stokes’ Theorem and Its Applications
Stokes’ Theorem provides a fundamental connection between the circulation of a vector field along a closed boundary and the cumulative rotational behavior across the surface it encloses. For a smooth three-dimensional surface with an oriented boundary curve, this theorem offers a unified way to relate motion along the edge to local rotational effects distributed over the surface.Mathematical FormulationThe theorem states that the circulation of a vector field along a closed curve is equal to...
01:20Stokes' Law
Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves through a liquid, viscous forces drag it in the opposite direction. The force's magnitude depends on the solid's shape and size, as well as its speed and the liquid's coefficient of viscosity, density and temperature.
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only for low Reynolds...
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only for low Reynolds...
01:21Partial Differential Equations
A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...
01:28Euler's Equations of Motion
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
01:28Navier–Stokes Equations
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...