Coupled Membrane Mechanics and Tensile Metastability of Fluids Under Large Pressure Differences

AbstractA large pressure difference between a fluid and its surroundings can produce two physically distinct but coupled effects: stress in a confining membrane or shell, and tensile states within the fluid. These effects must not be conflated.A pressure difference loads the boundary; the resulting shell stress depends ongeometry, thickness, material response, and stability. A liquid may also sustainpressure below its liquid–vapor equilibrium pressure as a metastable state, butthe attainable tension depends strongly on nucleation sites, impurities, interfaces,temperature, loading rate, and confinement.This paper develops a unified theoretical framework using continuum mechanics,thin-shell equilibrium, elastic constitutive relations, thermodynamics of metastableliquids, classical nucleation theory, and fluid–structure interaction. Governingrelations are presented for cylindrical and spherical membranes and generalized tocurved shells. A coupled formulation is then outlined for fluid compressibility, shellcompliance, dynamic response, and cavitation probability. Dimensionless groupsare introduced to distinguish membrane strength, shell buckling, fluid–structurecompliance, and nucleation exposure.The framework is a synthesis of established theories rather than a claim thata new universal material law has been experimentally established. It provides abasis for analysis and test design. Practical pressure-boundary design still requiresapplicable codes, material data, imperfection-sensitive stability assessment, andvalidation against experiments.