The Solution Equivalent of the Navier-Stokes Equation in HPLC

Author(s)

Abstract
The Navier-Stokes equation is generally considered the ultimate mathematical expression for the dictates of the Laws of Nature which pertain to transport phenomena in the field of fluid dynamics. It is written and typically discussed, however, in the form and jargon of advanced mathematics. This makes it very difficult for any nonmathematician to understand, and this, in part, is why it remains unsolved for most applications. The essence of the equation, however, has nothing to do with mathematics and everything to do with the underlying physics surrounding the fluid transport mechanisms involved in any given fluid flow embodiment. Accordingly, it is the non-mathematical “solution equivalent” of the N-S equation that is important to the practitioner of fluid dynamics. In the case of HPLC (High Pressure Liquid Chromatography), for instance, this means the physics underlying fluid flow through conduits packed with partially porous solid particles. Recently, 2019, a new fluid flow model (QFFM) was published which contains, embedded in its framework, the “solution equivalent” for the N-S equation in chromatographic columns. This novel fluid flow model teaches that an empty HPLC column is a special case of the same column packed with solid particles. In fact, one is the mirror image of the other. The difference between the two is defined by the choice of independent variables. Thus, by setting the value of three independent variables in the QFFM, the complexity of the advanced mathematics in the Navier-Stokes equation can be avoided. If one considers “matter” and “anti-matter” to be the mirror image of one another, however, one can easily rationalize the rules of engagement which underlie this phenomenon in the context of the Navier-Stokes equation. In this paper we will explain how the QFFM rationalizes the fundamental issues of the Navier-Stokes equation, providing the “solution equivalent”, in the jargon of classical mechanics, as opposed to that of advanced mathematics, for fluid flow through HPLC columns.

Keywords
Conduit Porosity; Hypothetical Q particles; Particle porosity: Packed beds; Column Permeability.

Cite this paper
Hubert M. Quinn, The Solution Equivalent of the Navier-Stokes Equation in HPLC , SCIREA Journal of Mechanics. Volume 4, Issue 1, February 2023 | PP. 1-34. 10.54647/mechanics130034

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