Two-fluid plasma equations in terms of Macfarlane quaternions

In this paper, stimulated by the existence of a correspondence between the variables of electromagnetism and fluid mechanics, an alternative mathematical model based on Macfarlane quaternions has been proposed to formulate the two-fluid plasma equations compactly and elegantly. This work extends the previous effort based on the hyperbolic quaternion formulation of electromagnetism to reflect the hydrodynamic description of plasma. It has also been proved that when the electromagnetic contributions in the plasma equations are eliminated, the gas dynamic equations in terms of Macfarlane quaternions for each species are obtained.