The Uhlenbeck-Ford model in two dimensions: Reference system for fluid-phase free-energy calculations
Related Experiment Video
Updated: Oct 25, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
Samuel Cajahuaringa1, Rodolfo Paula Leite2, Maurice de Koning2,3
1Dipartimento di Fisica, Università di Trieste, I-34151 Trieste, Italy.
Abstract:
We investigate the Uhlenbeck-Ford (UF) model as a reference system for free-energy calculations in two-dimensional (2D) fluids. The 2D virial coefficients are computed exactly up to the tenth order and combined with molecular simulation data to construct highly accurate numerical representations of the equation of state and the excess Helmholtz free energy. We then determine the phase diagram of the model in order to establish the thermodynamic stability limits of the fluid phase and thereby identify the range of applicability of the UF model as a fluid reference system. In the course of this analysis, we identify the solid, hexatic, and fluid phases and show that the fluid remains the only thermodynamically stable phase, independent of density, for scaling parameters up to p ≲ 70. Finally, we demonstrate the practical applicability of the 2D UF model as a reference system through thermodynamic integration calculations of the free energy of a two-dimensional Lennard-Jones fluid.
Related Concept Videos
Typical Model Studies
Modeling and Similitude
Dimensionless Groups in Fluid Mechanics
Two-Dimensional Force System: Problem Solving
The first step to solving a two-dimensional force system problem is to draw a free-body diagram of the object under consideration. This diagram helps identify all the external forces acting on the object, including their...
Newtonian Fluid: Problem Solving
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
Euler's Equations of Motion