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

Ding, Guang-Yu; Wells, Andrew; Zhong, Jin-Qiang

doi:10.1017/jfm.2019.256

Cited by 4 publications

(9 citation statements)

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“…The construction of the apparatus and the experimental environment have been described in detail in Part 1 (Ding et al 2018). Here we briefly review the experimental procedure, and introduce the experimental components and methods that are relevant to our temperature and concentration measurements.…”

Section: Experimental Methodsmentioning

confidence: 99%

“…A vertically stacked array of thermistors measures temperature T (z, t) at different heights z in the mushy layer, and shadowgraphy images were analysed to infer the mush thickness h(t). See Part 1 (Ding et al 2018) for further details on the configuration, methods used, and procedure for initializing the experiment.…”

Section: Experimental Methodsmentioning

confidence: 99%

“…The dynamical growth of mushy layers in early periods of periodic cooling has been discussed in Part I (Ding et al 2018) revealing modulation of the mushy layer thickness around a background state in the absence of modulation. The experimental data of the mushy-layer thickness h(t) were shown to be broadly consistent with theoretical predictions from a numerical model of mushy-layer growth.…”

Section: The Mushy-layer Growth and The Temperature Distributionmentioning

confidence: 99%

“…Understanding the fundamental physics of a solidifying aqueous binary fluid is important in a wide range of sciences, including geophysics, oceanography, metallurgy and electrical engineering (Loper & Roberts 1983;Hobbs 2010;Chalmers 1964;Rosenberger 1979). When a binary fluid is cooled and solidified from a horizontal plane boundary, the growing solid phase can form a dendritic structure of crystals called a mushy layer (see part I, Ding et al 2018, for a more detailed discussion). Mushy layers are reactive porous materials with interstitial melt that can flow in response to externally applied forces.…”

Section: Introductionmentioning

confidence: 99%

“…In the next section, we summarise the apparatus, experimental methods, and procedures that are described in more detail in Part I (Ding et al 2018), which considered the early time growth characteristics of a mushy layer with the boundary temperature modulated periodically in time. In section 3 we describe experimental measurements of temperature during the corresponding late-time period of mushy layer growth, where the mushy layer is modulated about a nearly steady background state.…”

Section: Introductionmentioning

confidence: 99%

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Solidification of binary aqueous solutions under periodic cooling. Part 2. Distribution of solid fraction

2019

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We report an experimental study of the distributions of temperature and solid fraction of growing $\text{NH}_{4}\text{Cl}$–$\text{H}_{2}\text{O}$ mushy layers that are subjected to periodical cooling from below, focusing on late-time dynamics where the mushy layer oscillates about an approximate steady state. Temporal evolution of the local temperature $T(z,t)$ at various heights in the mush demonstrates that the temperature oscillations of the bottom cooling boundary propagate through the mushy layer with phase delays and substantial decay in the amplitude. As the initial concentration $C_{0}$ increases, we show that the decay rate of the thermal oscillation with height also decreases, and the propagation speed of the oscillation phase increases. We interpret this as a result of the solid fraction increasing with $C_{0}$, which enhances the thermal conductivity but reduces the specific heat of the mushy layer. We present a new methodology to determine the distribution of solid fraction $\unicode[STIX]{x1D719}(z)$ in mushy layers for various $C_{0}$, using only measurements of the temperature $T(z,t)$. The method is based on the phase behaviour during thermal modulation, and opens up a new approach for inferring mushy-layer properties in geophysical and engineering settings, where direct measurements are challenging. In our experiments, profiles of the solid fraction $\unicode[STIX]{x1D719}(z)$ exhibit a cliff–ramp–cliff structure with large vertical gradients of $\unicode[STIX]{x1D719}$ near the mush–liquid interface and also near the bottom boundary, but much more gradual variation in the interior of the mushy layer. Such a profile structure is more pronounced for higher initial concentration $C_{0}$. For very low concentration, the solid fraction appears to be linearly dependent on the height within the mush. The volume-average of the solid fraction, and the local fluctuations in $\unicode[STIX]{x1D719}(z)$ both increase as $C_{0}$ increases. We suggest that the fast increase of $\unicode[STIX]{x1D719}(z)$ near the bottom boundary is possibly due to diffusive transport of solute away from the bottom boundary and the depletion of solute content near the basal region.

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Section: Experimental Methodsmentioning

confidence: 99%

Section: Experimental Methodsmentioning

confidence: 99%

Section: The Mushy-layer Growth and The Temperature Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solidification of binary aqueous solutions under periodic cooling. Part 2. Distribution of solid fraction

2019

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Structure of mushy layers grown from perfectly and imperfectly conducting boundaries. Part 1. Diffusive solidification

Hitchen,

Wells

2025

J. Fluid Mech.

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We model transient mushy-layer growth for a binary alloy solidifying from a cooled boundary, characterising the impact of liquid composition and thermal growth conditions on the mush porosity and growth rate. We consider cooling from a perfectly conducting isothermal boundary, and from an imperfectly conducting boundary governed by a linearised thermal boundary condition. For an isothermal boundary we characterise different growth regimes depending on a concentration ratio, which can also be viewed as characterising the ratio of composition-dependent freezing point depression versus the temperature difference across the mushy layer. Large concentration ratio leads to high porosity throughout the mushy layer and an asymptotically simplified model for growth with an effective thermal diffusivity accounting for latent heat release from internal solidification. Low concentration ratio leads to low porosity throughout most of the mushy layer, except for a high-porosity boundary layer localised near the mush–liquid interface. We identify scalings for the boundary-layer thickness and mush growth rate. An imperfectly conducting boundary leads to an initial lag in the onset of solidification, followed by an adjustment period, before asymptoting to the perfectly conducting state at large time. We develop asymptotic solutions for large concentration ratio and large effective heat capacity, and characterise the mush structure, growth rate and transition times between the regimes. For low concentration ratio the high porosity zone spans the full mush depth at early times, before localising near the mush–liquid interface at later times. Such variation of porosity has important implications for the properties and biological habitability of mushy sea ice.

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Dynamics of melting in a slab under harmonic heating and convective cooling boundary conditions

Shamberger

Hoe

Deckard

et al. 2020

Journal of Applied Physics

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The dynamics of steady periodic melting-solidification in finite thickness slabs are relevant for numerous natural and engineered systems, including for the thermal management of pulsed power devices. Despite this, the characteristic thermal response and temperature rise at the heated surface of a slab resulting from a simple harmonic heating under convective cooling boundary conditions on the opposing side has not been investigated in detail. This configuration is critical for understanding the frequency regime under which a reversible endothermic transformation (e.g., melting/solidification) in a slab serves to effectively buffer temperature rise at a device surface. This study presents a numerical investigation of steady periodic melting-solidification in a slab due to conductive heat transfer, focusing on the resulting temperature rise and phase lag at the heated surface. The internal temperature distribution within the slab closely follows the transient thermal response of a single-phase material, with the exception of a perturbation within a localized region of frequency and amplitude of the harmonic heating. Within this regime, the melt front exhibits antiresonance with the harmonic heating, resulting in a phase lag and a depression in the peak observed temperature on the heated surface. The peak frequency and amplitude at which this antiresonance occurs decrease as the heat transfer coefficient on the cooling side of the slab decreases. This analysis reveals the interaction between material parameters, the system geometry, and the nature of the boundary conditions and is critical for designing systems that are appropriately tuned to particular heating profiles.

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

Cited by 4 publications

References 40 publications

Solidification of binary aqueous solutions under periodic cooling. Part 2. Distribution of solid fraction

Solidification of binary aqueous solutions under periodic cooling. Part 2. Distribution of solid fraction

Structure of mushy layers grown from perfectly and imperfectly conducting boundaries. Part 1. Diffusive solidification

Dynamics of melting in a slab under harmonic heating and convective cooling boundary conditions

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