Gases macroscopic/microscopic length scales

Electrolytic gas evolution can be discussed on two scales of length. The macroscopic or process scale is important to the overall design of equipment and includes modeling the overall distribution of gas in the reactor and the effects of gas bubbles on the gross electrolyte flow pattern. The microscopic scale is where the details of bubble events and their consequences are found. In this review, I concentrate on the latter, microscopic scale. 

On the continuum level of gas flow, the Navier-Stokes equation forms the basic mathematical model, in which dependent variables are macroscopic properties such as the velocity, density, pressure, and temperature in spatial and time spaces instead of nf in the multi-dimensional phase space formed by the combination of physical space and velocity space in the microscopic model. As long as there are a sufficient number of gas molecules within the smallest significant volume of a flow, the macroscopic properties are equivalent to the average values of the appropriate molecular quantities at any location in a flow, and the Navier-Stokes equation is valid. However, when gradients of the macroscopic properties become so steep that their scale length is of the same order as the mean free path of gas molecules,, the Navier-Stokes model fails because conservation equations do not form a closed set in such situations. 

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