# Overview of Solidification of a binary solution system

### From Thermal-FluidsPedia

Solidification of multicomponent PCMs has been investigated due to its importance in the fields of metallurgy (Viskanta, 1988), crystal growth (Bardsley et al., 1979), oceanography (Hobbs, 1974), and modeling (Beckermann and Wang, 1995; Bennon and Incropera, 1987a, b; Zeng and Faghri, 1994a, b), as well as many others. It is characterized by the presence of a variety of microscopically complex interfacial structures; as a result, the macroscopic solid-liquid interface is not smooth, as is the case in the solidification of single-component PCMs. The most popular microstructure is known as the dendrite, which can exist in either cocolumnar or equiaxed forms (Beckermann and Wang, 1995). From the heat transfer point of view, the microscopic region where solid and liquid coexist is considered a mushy zone that exists between pure solid and pure liquid phase. The temperature at the interface between the mushy zone and the liquid region is the liquidus line temperature, while the interfacial temperature between the solid and the mushy zone is the solidus temperature (see Fig. 2.11). Therefore, phase change of multicomponent PCMs can be considered to occur over a range of temperatures. The presence of a mushy zone in solid-liquid phase change system not only characterizes the phase change of multicomponent mixtures, but also poses the primary challenge in analyzing and modeling of binary and multicomponent solid-liquid phase change systems.

As indicated in Table 1.10, melting and solidification of multicomponent PCMs can be viewed as dispersed phase. Therefore, the volume-averaged governing equations presented in Chapter 4 can be used to describe the transport phenomena in the mushy zone (Beckermann and Wang, 1995). Some mathematical models have been developed to describe the solidification process of a binary system. In general, such models can be divided into two classes: phase-averaged (multi-fluid model) and overall mass- or volume-averaged (mixture or homogeneous) models. Since the mushy zone can be described as a dispersed phase region, the phase-averaged models (multi-fluid model in Chapter 4) develop a set of conservation equations for each phase, as well as the coupled relationship between the phases (Beckermann and Wang, 1995). The advantage of phase-averaged model is that the nonequilibrium between the two phases can be addressed. The disadvantage is that they require modeling of the interface exchange terms that are related to the microstructure in the mushy zone. The volume-averaged model (homogeneous or mixture model in Chapter 4), on the other hand, reduces the general system of two-phase flow equations to a set of continuum conservation equations that can be applied to the entire solidification domain, including the solid, liquid, and mushy zones (Bennon and Incropera, 1987a, b; Zeng and Faghri, 1994a, b). Using the phase-averaged model, computational studies have identified important features such as liquidus interface irregularity, remelting channeling in the mushy zone, and double diffusive convection in the liquid.

An experimental investigation was presented by McDonough and Faghri (1993) concerning the solidification of an aqueous sodium carbonate solution around a vertical cylinder. The liquid-mushy and mushy-solid interface locations are determined by the pulse-echo ultrasonic measurement technique. Ultrasonically measured interface locations were compared with visual observations of the liquid-mushy interface, and temperature measures of the mushy-liquid interface. The ultrasonically measured liquid-mushy interface was shown to be in good agreement with visual observations. High attenuation and scattering of the ultrasonic pulse in the mushy region made the location of the mushy-solid interface difficult to determine ultrasonically.
Many researchers conduct experiments using a transparent PCM, such as NH_{4}Cl-H_{2}O solution, because its solidification is quite similar to the solidification of alloys and is easy to observe.

## References

Bardsley, W., Hurle, D.T.J., and Mullin, T.B., 1979, *Crystal Growth: A Tutorial Approach*, North-Holland, Amsterdam.

Beckermann, C., and Wang, C.Y., 1995, “Multi-Phase/-Scale Modeling of Transport Phenomena in Alloy Solidification," *Annual Review of Heat Transfer*, Vol. 6, pp. 115-198.

Bennon, W.D., and Incropera, F.P., 1987a, “A Continuum Model for Momentum, Heat and Species Transport in Binary Solid-Liquid Phase Change Systems – I: Model Formulation,” *International Journal of Heat and Mass Transfer*, Vol., 30, pp. 2161-2170.

Bennon, W.D., and Incropera, F.P., 1987b, “A Continuum Model for Momentum, Heat and Species Transport in Binary Solid-Liquid Phase Change Systems – II: Application to Solidification in a Rectangular Cavity,” *International Journal of Heat and Mass Transfer*, Vol. 30, pp. 2171-2178.

Faghri, A., Zhang, Y., and Howell, J. R., 2010, *Advanced Heat and Mass Transfer*, Global Digital Press, Columbia, MO.

Hobbs, P.V., 1974, *Ice Physics*, Clarendon Press, Oxford.

McDonough, M. W., and Faghri, A., 1993, “Ultrasonic Measurement of Interface Positions During the Solidification of an Aqueous Sodium Carbonate Solution around a Vertical Cylinder,” *Experimental Heat Transfer Journal*, Vol. 6, pp. 215-230.

Viskanta, R., 1988, “Heat Transfer During Melting and Solidification of Metals,” ASME *Journal of Heat Transfer*, Vol. 110, 1205-1219.

Zeng, X., and Faghri, A, 1994a, “Temperature-Transforming Model for Binary Solid-Liquid Phase-Change Problems Part I: Physical and Numerical Scheme,” *Numerical Heat Transfer*, Part B, Vol. 25, pp. 467-480.

Zeng, X., and Faghri, A., 1994b, “Temperature-Transforming Model for Binary Solid-Liquid Phase-Change Problems Part II: Numerical Simulation,” *Numerical Heat Transfer*, Part B, Vol. 25, pp. 481-500.