Viscous drag forces in gas operated pressure balances

Abstract

Accurate determination of all forces acting on the piston in the gas operated pressure balance is a long-standing problem in high precision pressure measurements. A major contribution, responsible for the difference between the actual and the effective areas of the piston, is due to the drag force on the piston, and at a fundamental level surprisingly little is known about this force. We present here a first detailed analysis of the hydrodynamics shear forces acting at the gas–piston interface on a molecular level, using effective intermolecular potential functions and a large-scale non-equilibrium molecular dynamics simulation to model the flow of several gases. We show using the hydrodynamic approach that the drag force on the piston for force-driven plane steady-state flow is exactly one half of the external driving force independent of the boundary conditions, justifying a widely accepted assumption in pressure balance theory, and verify this result in computer simulation for a range of gas densities. The natural fall rates using different gases as the pressure transmission medium were measured experimentally for a range of generated pressures and estimated from computer simulation using force-driven Poiseuille flow. Both results, which are in excellent agreement, show pronounced species dependence. This, however, cannot explain the gas species dependence of the effective area.