In
fluid and
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of t ...
, the Batchelor scale, determined by
George Batchelor
George Keith Batchelor FRS (8 March 1920 – 30 March 2000) was an Australian applied mathematician and fluid dynamicist.
He was for many years a Professor of Applied Mathematics in the University of Cambridge, and was founding head of the ...
(1959), describes the size of a
droplet
A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the lower end of a tube or other surface boundary, producing a hanging drop called a pendant ...
of
fluid that will
diffuse
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
in the same time it takes the energy in an
eddy
Eddie or Eddy may refer to:
Science and technology
*Eddy (fluid dynamics), the swirling of a fluid and the reverse current created when the fluid flows past an obstacle
* Eddie (text editor), a text editor originally for BeOS and now ported to Lin ...
of size to dissipate. The Batchelor scale can be determined by:
:
where:
*
is the Kolmogorov
length scale
In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot af ...
.
* is the
Schmidt number
Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum diffusivity ( kinematic viscosity) and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convec ...
.
* is the
kinematic viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the int ...
.
* is the
mass diffusivity
Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is enco ...
.
* is the rate of
dissipation
In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy ( internal, bulk flow kinetic, or system potential) transforms from an initial form to ...
of
turbulence kinetic energy
In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by measured root-mean-square (RMS) velocity fluctuat ...
per unit mass.
Similar to the
Kolmogorov microscales
In fluid dynamics, Kolmogorov microscales are the smallest scales in the turbulent flow of fluids. At the Kolmogorov scale, viscosity dominates and the turbulence kinetic energy is dissipated into thermal energy. They are defined by
where
* is ...
– which describe the smallest scales of turbulence before viscosity dominates – the Batchelor scale describes the smallest length scales of fluctuations in scalar
concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', '' number concentration'', ...
that can exist before being dominated by
molecular diffusion
Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of ...
. It is important to note that for , which is common in many liquid flows, the Batchelor scale is small when compared to the Kolmogorov microscales. This means that scalar transport occurs at scales smaller than the smallest eddy size.
References
External links
*
{{DEFAULTSORT:Batchelor Scale
Fluid dynamics
Turbulence