As far as I know they show variations,
especially the volume and pressure values change to exponential terms.
But as I have seen the calculation of the reynolds number is still valid.
By the way you can perform microfluidic simulation for macro and micro scales in COMSOL, and then compare the results....
I am gonna investigate the squeeze film damping effect on nanowires and I am interested to know if the governing compressible equation of Reynold would change or not, the dimension of problem is about 10nm to 1micrometer. I am wondering if the continuum mechanic can be embedded or not and if the following equation work in this scale or not.
in micro scale the equation is as follow:
Where w is deflection of micro-plate and d is the gap distance of plate and substrate.
in this problem as the gap distance decrease , I am not sure that the fluid would be continuous or not.
Just to makes sure, are you talking about liquid or gas fluid medium?
In the case of a liquid such as water, which can be assumed incompressible, the classical Navier-Stokes equation apply down to a few nanometer.
Moreover, at the length scale that you consider, I would be surprise to see high Reynolds number occurring.
You could check one of my publication about electrohydrodynamic flow in nanochannels for more insight, as it reviews a number of paper in that respect:
Article Modeling and simulation of electrostatically gated nanochannels
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