경막결정화에서 경막결정층의 유효열전달계수와 불순물 분포 현상

김광주, Joachim Ulrich*

한국화학연구원 화학공정연구센터 결정화공정연구실

(과학기술부 국가지정연구실)

* Martin-Luther-Universitaet Halle-Wittenberg, Germany

Impurity Distribution and Effective Thermal Conductivity of Crystalline Layers in Layer Melt Crystallization

Kwang-Joo Kim, Joachim Ulrich*

National Research Laboratory for Crystallization Process & Engineering,

Chemical Process Engineering Center,

Korea Research Institute of Chemical Technology

* Martin-Luther-Universitaet Halle-Wittenberg, Germany

Introduction

Layer melt crystallization has been applied in the wide fields of separation and purification of chemicals. The layer melt crystallization is based on the growth of a crystalline layer on a cooled surface[1,2]. The profiles of temperature and concentration near the solid-liquid interface affect the growth rate of the layer, which has an influence on the structure of the layer and the distribution of inclusions of impurities in the layer. The impure liquid inclusions are trapped in crystal layers during its growth and at the same time migrate towards the warm surface due to the temperature gradient developed over the solid phase between the cooled surface and the S-L interface [3,4].  The important parameters to determine the impurity behavior during growth of crystalline layer are profiles of temperature and concentration in boundary layer near the S-L interface. The previous results presented that the behavior of the impurities was estimated by mathematical simulation [5].

Experimental and theoretical studies on the effective thermal conductivity are focused on metal melts and frost formation [3-6]. However, even entrapment of inclusions and migration of inclusions were found during layer crystallization by the investigators [1-3], it is interesting to note that most of the earlier works on the layer crystallization were never considering the effective thermal conductivity. All previous studies on the layer melt crystallization are based on constant thermal conductivity, which is assumed to the same as that of the pure material. It means that the inclusion fraction was neglected in growing the layer with operating time. However, the interfacial distribution coefficient and inclusion fraction varies with growth of the crystalline layer and the elapsed time.

In the present work, the effective thermal conductivity of the crystalline layer during the crystal growth period is studied.

Measurements

In order to investigate the influence of the 5 major parameters on layer crystallization: melt composition, cooling temperature, cooling rate, hydrodynamic condition and melt temperature, a test equipment was built. The apparatus consists of the layer crystallizer, thermostatic bath, circulators with temperature programming controllers, data acquisition and image analysis system. The thermostatic bath was composed of a 500 ml vessel containing liquid melt and was equipped with an agitator and an outside jacket. The crystallizer is a cylindrical tube type equipment with a diameter of 26.5 mm and a length of 150 mm. A water  ethylene glycol mixture is used as a coolant. Flow rate of the coolant inside the tube crystallizer was set as 230 cc/sec. The agitation rate was set to 400 rpm.

A homogeneous mixture of water and sodium chloride was prepared and a total of about 300 ml was charged into the bath. The solution was heated above its saturation temperature and then the desired melt temperature was set. When the temperature of the cylindrical tube was constant, the tube was immersed in the melt, the crystalline layer started to appear on the crystallizer surface. Measurements were made during the growth of layer.

Model for layer crystallization

A simple model has been considered in which the crystalline layer is assumed to consist of crystals and inclusions. The following assumptions are made for this model:

- Crystalline layer during growth consists of crystalline and liquid inclusion parts due to an eutectic mixture.

- The temperature of the crystalline layer at a cross section Dr is the same as that of the inclusion part at this position and varies with radial direction.

- The composition of inclusions at any cross section corresponds to the saturation concentration at that temperature.

- Heat transfer from the S-L interface to the cooling surface is a one-dimensional heat transport.

- Concentration of the crystalline layer formed at nucleation point is the same as that of feed mixture due to high constitutional supercooling.

- Migration of inclusions entrapped occurs simultaneously with the growth. Migration is driven by diffusion with partial melting and partial recrystallization.

A model shown in Fig. 1 was selected in which the crystalline layer is assumed to have one-dimensional growth. The process of growth of the crystalline layer on the heat transfer surface is a very slow and unsteady process. However, because this process is very slow, it is treated as a quasi-steady state.

In the crystalline layer, heat transfer is controlled by the heat conduction in the layer.

Fig. 1. Energy balance in the crystalline layer.

[eqn: PARTIAL over {PARTIAL r } LEFT ( k_cl` r {PARTIAL T}over{ PARTIAL r} RIGHT ) =0]                             (1)

Where kcl is the thermal conductivity of the crystalline layer.

The crystalline layer consists of crystal and inclusions. The inclusions trapped inside the layer migrate by diffusion transport during the growth of the crystalline layer. An energy balance in a differential segment as shown in Fig. 1 yields:

[eqn: -A_{i n}~ rho _l ~nu _mig {dH_l}over dr - A_{i n}~ rho _l ~ lambda {d nu_mig }over dr -A_s {dQ_s}over dr - A_{i n} {dQ_{i n}} over dr =0]         (2)

The first term is the enthalpy change in migration by convection, the second term is enthalpy change by phase change (like recrystallization and remelting) in migration, the third term is the energy change by conduction in the solid phase, and the final term is energy change by conduction in the inclusion phase.

Fig. 2. Interfacial temperature variation

with time for cooling temperatures.

Fig. 3. Comparison between calculated

and experimental thermal conductivity.

Results and discussion

Fig. 2 shows a typical variation of interfacial temperature with time for various cooling temperatures at Co=0.97 and Tm=272 K. At the beginning of the layer growth the interfacial temperature increases rapidly and slows down approaching the melt side temperature. The increase of the surface temperature of the layer is due to the increase of the thermal conductive resistance of the layer, which results from the rapid growth of the layer with high amount of inclusions due to large subcooling with decreasing cooling temperature. Figs. 3 shows examples of a comparison between calculated and experimental values of the effective thermal conductivity for Co=0.94 and Co=0.94 at Tm=272 K, respectively. The model equation was concluded from the experimental data and used to estimate the effective thermal conductivity.

Conclusion

At higher impurity level in the melt phase, constitutional supersaturation become more pronounced and unstable growth morphologies occur more easily. The predictions of effective thermal conductivity agree with the experimental data. The model were applied to estimate the thermal conductivities of the crystalline layer during layer melt crystallization.

References

[1] J. Ulrich, Melt Crystallization, Handbook of Industrial Crystallization, Ed.       A.S. Myerson, Butterworth-Heinemann, Oxford.

[2] J. Ulrich, J. Bierwirth and S. Henning, Separation and Purification             Methods 25(1), 1, (1996).

[3] K. J. Kim, J. Ulrich, Proc. 14 ISIC, Cambridge, UK, (1999).

[4] R. Scholz, Ph.D. Thesis University of Bremen, Germany, (1992).

[5] K. J. Kim, J. Ulrich, J. Phys. D: Appl. Phys. 34, 1, (2001).

[6] K. J. Kim, J. Ulrich, Powder Technology, in print, (2001).