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Solidification of binary aqueous solutions under periodic cooling. Part 1. Dynamics of mushy-layer growth

Published online by Cambridge University Press:  07 May 2019

Guang-Yu Ding ,
Andrew J. Wells Open the ORCID record for Andrew J. Wells [Opens in a new window]  and
Jin-Qiang Zhong Open the ORCID record for Jin-Qiang Zhong [Opens in a new window]
Guang-Yu Ding
Affiliation:
School of Physics Science and Engineering, Tongji University, Shanghai 200092, China Department of Physics, Chinese University of Hong Kong, Hong Kong, China
Andrew J. Wells
Affiliation:
Department of Physics, University of Oxford, Oxford OX1 3PU, UK
Jin-Qiang Zhong*
Affiliation:
School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
*
†Email address for correspondence: [email protected]
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Abstract

We present studies of the solidification of binary aqueous solutions that undergo time-periodic cooling from below. We develop an experiment for solidification of aqueous $\text{NH}_{4}\text{Cl}$ solutions, where the temperature of the cooling boundary is modulated as a simple periodic function of time with independent variations of the modulation amplitude and frequency. The thickness of the mushy layer exhibits oscillations about the background growth obtained for constant cooling. We consider the deviation given by the difference between states with modulated and fixed cooling, which increases when the modulation amplitude increases but decreases with increasing modulation frequency. At early times, the deviation amplitude is consistent with a scaling argument for growth with quasi-steady modulation. In situ measurements of the mush temperature reveal thermal waves propagating through the mushy layer, with amplitude decaying with height within the mushy layer, whilst the phase lag behind the cooling boundary increases with height. This also leads to phase lags in the variation of the mushy-layer thickness compared to the boundary cooling. There is an asymmetry of the deviation of mushy-layer thickness: during a positive modulation (where the boundary temperature increases at the start of a cycle) the peak thickness deviation has a greater magnitude than the troughs in a negative modulation mode (where the boundary temperature decreases at the start of the cycle). A numerical model is formulated to describe mushy-layer growth with constant bulk concentration and turbulent heat transport at the mush–liquid interface driven by compositional convection associated with a finite interfacial solid fraction. The model recovers key features of the experimental results at early times, including the propagation of thermal waves and oscillations in mushy-layer thickness, although tends to overpredict the mean thickness.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection in porous media Phase change: Solidification/melting
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 121 - 146
Copyright
© 2019 Cambridge University Press 

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Ding et al. supplementary movie

Shadowgraphy movies that show the growth of mushy layers and the flows in the liquid region in three modulation modes with Φ0=0 (left), constant cooling (middle) and Φ0=π (right). Results for A=15K, τ=4000s. The movies display 400 times faster than the real time.

Download Ding et al. supplementary movie(Video)
Video 63 MB