Dendritic Growth Model Involving Interface Kinetics for Supercooled Water

Abstract

The dendritic growth of ice in supercooled water droplets is studied theoretically and experimentally. The measured dendritic growth velocity of ice shows a good agreement with the prediction of the Langer and Muller-Krumbhaar (LM-K) growth model at supercoolings less than 7 K, whereas an increasing overestimation in the latter is observed as the droplets are further supercooled. Therefore, the LM-K dendritic growth model is modified by considering the influence of interface kinetics. In the modified model, a dendrite grows in the limit of marginal stability coupled with diffusion at the liquid−solid interface, and the interface kinetics supercooling is introduced to predict the dendritic growth velocity. The interface kinetics factor is determined by fitting the experimental dendritic growth velocity within the framework of the modified model. This modification to the LM-K model well describes the dendritic growth of ice in water supercooled up to 25 K. It provides a solution to the dendritic growth of ice in the high-supercooling regime and can serve as a reliable input for studies on icing problems in engineering fields.

Nanoscale “Earthquake” Effect Induced by Thin Film Surface Acoustic Waves as a New Strategy for Ice Protection

“…For the SAW devices with a larger wavelength and/or applied with higher SAW power (e.g., 100 µm with 0.25 W; 200 µm with 0.15 W; and 300 µm with 0.07 W), a different icing phenomenon (often called supercooled icing phenomenon) [ 35,36 ] appeared in the droplets as shown in the second row in Figure 2. For the device with 300 µm wavelength and 0.07 W power, the droplet was kept supercooled without any icing occurring during the initial stage.…”

A Novel Crystal Growth Model with Nonlinear Interface Kinetics and Curvature Effects: Sensitivity Analysis and Optimization

“…The idea was pioneered by Papapetrou and later formalized by Ivantsov . The literature ,, shows, however, that the kinetic and curvature effects start dominating the dendritic morphology and growth rate for supercooling greater than 4–5 °C. This study includes the effects of thermal diffusion, interface kinetics, and curvature to model the growth rate and interfacial undercooling to incorporate a wider supercooling range.…”

“…The recalescence stage is followed by an equilibrium freezing stage where the phase-change process is controlled by the type of boundary condition at the droplet surface. , After solidification, the solid subcooling stage causes the temperature of the solidified droplet to lower further until the droplet is in thermal equilibrium with the surroundings. ,, The recalescence stage plays a critical role in ascertaining the morphology of the crystal formed, its growth rate, and thermodynamics of the freezing process. Even though the recalescence stage has been a subject of experimental, theoretical, and numerical studies since the early 20th century, ,− it still has numerous open research avenues in terms of different physical, electrical, and kinetic phenomena that govern the process of crystal growth. ,− During the recalescence stage, both the morphology and growth rate have been demonstrated to be a strong function of a solid–liquid interface temperature and humidity in the surrounding medium . The morphological classification is broadly illustrated in the literature as Nakaya diagrams, which characterize the crystal shapes in the temperature and humidity space.…”

“…Hence, at higher supercooling, the kinetic effects on dendritic growth cannot be neglected. Two pervasive theories in the literature to incorporate the kinetic effects within the dendritic growth rate framework are linear kinetic theory , and the Wilson–Frenkel model. ,, While both theories consider the effect of attachment kinetics in their formulation, the Wilson–Frenkel model has been demonstrated to predict the growth rates well for liquids with Lennard-Jones potential such as water. , The Wilson–Frenkel theory posits that the atomic diffusion process controls the net rate of attachment of molecules from supercooled liquid to a solid crystal structure which, in turn, determines the dendritic growth rate. Self-diffusivity and the interface kinetic parameter play a critical role in governing the accuracy of the Wilson–Frenkel model.…”

Numerical Simulation of Supercooled Water Droplets Impacting Ice with Rapid Crystal Growth Taken into Consideration

“…Generally, the dendritic growth velocity in supercooled water, which depends on supercooling, is an input in the determination of Ω D ( t ), and can be obtained from experiments ,, or theory . In this article, the dendritic growth velocities at different supercoolings are determined using the dendritic growth model of supercooled water developed by Wang et al The dendritic growth velocity is calculated by simultaneously solving three independent equations, including a modified Ivantsov equation, Wilson–Frenkel equation, and marginal stability equation . The calculated dendritic growth velocities in all cases are shown in Table in the next section.…”