Capturing the kinematics and dynamics of fluid fronts

Joseph Thalakkottor^1*Kamran Mohseni²

• ¹South Dakota School of Mines and Technology, Rapid City, United States
• ²University of Florida, Gainesville, United States

Gibbs was the first person to represent a phase interface by a dividing surface. He defined the dividing surface as a mathematical surface that has its own material properties and internal dynamics. In this paper, an alternative derivation to this mathematical surface is provided that generalizes the concept of dividing surface to fluid fronts beyond that of just a phase or material interface. Here, this extended definition of dividing surface is referred to as the extended dividing hypersurface (EDH), as it is not just applicable to a surface front but also to a line and a point front. This hypersurface represents a continuum approximation of a diffused region, where fluid properties and flow parameters vary sharply but continuously across it. This paper shows that the properties and equations describing an EDH can be derived from the equations describing the diffused region by integrating it in the directions normal to the hypersurface. This is equivalent to collapsing the diffused region in the normal direction. Hence, ensuring that the EDH is both kinematically and dynamically equivalent to that of the diffused region. Various canonical problems are examined to demonstrate the EDH's ability to accurately represent different types of fluid and flow fronts, including static and dynamic interfaces, shock fronts, and vortex sheets. These examples emphasize the EDH's capability to represent various functionalities within a front, the relationship between the flux of quantities and hypersurface quantities, and the importance of considering the mass of the front and associated dynamics.