Themo-mechanical analysis of a freezing water-filled capillary tube

Water-filled capillary tubes are a kind of standard component in both life science (e.g., blood vessels, interstitial pores, and plant vessels) and engineering (e.g., MEMS microchannel resonators, heat pipe wicks, and watersaturated soils). Under sufficiently low temperatures, water in capillary tubes undergoes phase transition and exhibits frost heave, which can cause deformation, damage, and even fracture of tube wall. However, the thermomechanical analysis of freezing water-filled capillary tubes remains obscure, particularly regarding the rapid change in water temperature due to thermal transient effects. We develop a thermal model of freezing in a waterfilled capillary tube that is suddenly exposed to cold air flow, with the time domain divided into two regimes, separated by the thermal penetration time tp. The effect of thermal penetration on temperature distribution is solved. Then, a distinction is made between freezing occurring before thermal penetration and those occurring after thermal penetration. We next analyze transient mechanical stresses acting at tube wall, with interfacial tension and frost heave effect accounted for. Results obtained are not only useful for preventing frost heave failure but also provide theoretical guidance for tailoring the freezing resistance of microfluidic devices used in MEMS.