Pressure-drop localization and momentum insulation in liquid-gas coexistence Poiseuille flow

We study pressure-driven Poiseuille flow of a one-component fluid between adiabatic plates in liquid-gas coexistence. The analysis uses Poiseuille flow and Fourier heat conduction in the bulk regions together with particle and energy conservation. From these bulk equations, we identify extremely small dimensionless parameters $A^{\mathrm{L}}$ and $A^{\mathrm{G}}$ describing coexistence Poiseuille flow, whose smallness comes from squared microscopic-to-macroscopic length ratios. In weak driving with macroscopic liquid and gas regions, the pressure difference is concentrated across the interfacial region, and the ordinary Poiseuille particle current is strongly reduced. For equal-temperature reservoirs, this residual particle current produces interfacial cooling.