Micro fluidic : Knudsen Number

Micro fluidic : Knudsen Number

By: Mohd Faizal Abd Rahman (PhD Student)

This article will discuss about the Knudsen number, an important parameter determining what type of region that any micro fluidic flow will fall into. According to Wikipedia, Knudsen Number is defined as a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. It is useful to determine whether the flow is in continuum, slip, transition or free molecular region or more simply, the Knudsen number is how many times its own diameter a particle will travel on average before hitting another particle.

When we zoom into molecular stage, we know that fluids are composed of discrete molecules that collide with one another and solid objects. The continuum flow assumes fluids to be continuous, not discrete molecules. Properties likes density, pressure, temperature, and velocity are assumed to vary continuously from one point to another. The fact that the fluid is made up of discrete molecules is ignored. The continuum hypothesis is basically an approximation, therefore this hypothesis can lead to results which are not of desired accuracy. That said, under the right circumstances, the continuum hypothesis produces extremely accurate results. This is why the Knudsen Number calculation is important, to determine whether the continuum or statistical mechanics will be used for problem solving.

The parameter is given by:

This parameter sometimes can be related to other important micro fluidic parameter, Reynolds number which will be discussed in future issue. Knudsen number characterise the flow regime by three categories such as:

1) Small value, for Kn < 0.01: the flow is in continuum model, where the above assumption is applied. 2) Intermediate value, Kn1, the flow is in transition region, where the Boltzmans transport equation influence the molecules transport (kinetic model)[2]. 3) Large value, Kn>100, the flow is in molecular free region, where the kinetic model is still appropriate with collision term being small[2]. Problems with Knudsen numbers at or above unity are best evaluated using statistical mechanics for reliable solutions.

References:

[1] T. Hsu, MEMS and Microsystems: Design and Manufacture, McGraw Hill, 1ST edition,2002 [2] The effect of Knudsen Number on Transient Time during Chemical Vapor Depostion M.T. Gobbart and T.S. Cale [3] R.W. Barber, D.R. Emerson, The influence of Knudsen number on the hydrodynamic development length within parallel plate microchannels, Advances in Fluids Mechanics IV, UK 2002, 207-216.

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Micro fluidic : Knudsen Number

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