Stress accumulation by confined ice in a temperature gradient

Abstract

When materials freeze, they often undergo damage due to ice growth. Although this damage is commonly ascribed to the volumetric expansion of water upon freezing, it is usually driven by the flow of water toward growing ice crystals that feeds their growth. The freezing of this additional water can cause a large buildup of stress. Here, we demonstrate a technique for characterizing this stress buildup with unprecedented spatial resolution. We create a stable ice–water interface in a controlled temperature gradient and measure the deformation of the confining boundary. Analysis of the deformation field reveals stresses applied to the boundary with O (micrometers) spatial resolution. Globally, stresses increase steadily over time as liquid water is transported to more deeply undercooled regions. Locally, stresses increase until ice growth is stalled by the confining stresses. Importantly, we find a strong localization of stresses, which significantly increases the likelihood of damage caused by the presence of ice, even in apparently benign freezing situations. Ultimately, the limiting stress that the ice exerts is proportional to the local undercooling, in accordance with the Clapeyron equation, which describes the equilibrium between a stressed solid and its melt. Our results are closely connected to the condensation pressure during liquid–liquid phase separation and the crystallization pressure for growing crystals. Thus, they are highly relevant in fields ranging from cryopreservation and frost heave to food science, rock weathering, and art conservation.

Effect of particle trapping on frost heaving soils

“…During in situ freezing flow in premelted films at colder locations can also occur (secondary frost heave) [38]. At short laboratory timescales the magnitude of secondary frost heave is relatively small [39] and ice lenses grow without penetrating the warmer pores [15].…”

Ice segregation efficiency theory of frost heave

“…The freezing temperature T f of the soil is given by the Clapeyron equation [37,38], and in general there exists a region of soil of depth d f between the freezing front and the 0 • C isotherm.…”

“…Numerical simulations by O'Neill and Miller [49], Fowler et al [33,34] and Rempel [51] show that after an initial transient period the heave varies approximately linearly with time, in qualitative agreement with the high-overburden pressure h(t) data in figure 3. Gerber et al [38] have shown recently that experimental flow rates during secondary frost heave in a model soil are relatively slow, and mechanisms for increasing the flow rates were discussed. One possibility mentioned was the presence of hydrogels or other colloidal media, which allow larger amounts of unfrozen water to be present at sub-zero temperatures.…”

Polycrystalinity enhances stress build-up around ice

“…Now, water can flow away as ice grows, preventing any pressure build-up during ice's initial growth. However, if the ice is below its freezing temperature, and in contact with an unfrozen supply of water, it will subsequently suck water back into the pore, causing the ice to grow [6,9,10]. Then, the ice can push open the pore, causing pressure to build up with a maximum pressure of about 1 MPa per degree of undercooling [1, 5,9,[11][12][13][14].…”

“…However, if the ice is below its freezing temperature, and in contact with an unfrozen supply of water, it will subsequently suck water back into the pore, causing the ice to grow [6,9,10]. Then, the ice can push open the pore, causing pressure to build up with a maximum pressure of about 1 MPa per degree of undercooling [1, 5,9,[11][12][13][14]. Importantly, the expansion of the pore due to cryosuction can theoretically be unbounded, provided enough unfrozen water is available.…”