Assessment of a Simplified Correlation Between Wettability Measurement and Dispersion/ Coagulation Potency of Oxide Particles in Ferrous Alloy Melt KEIJI NAKAJIMA, WANGZHONG MU , and PA¨RG.JO¨NSSON This article seeks to demonstrate a direct and simplified correlation between the measurement of the wettability and the agglomeration potency of the inclusion particles in liquid ferrous alloy. The established methodology has been validated by the agreement between the calculated coagulation coefficient of Al2O3 particles and the experimental data in the open literature. Subsequently, the coagulation coefficient of Al2O3, MgO, and Ti2O3 particles in ferrous alloy melts was evaluated quantitatively by the proposed method using the actual experimental data of contact angle and surface tension. Meanwhile, the effect of the matrix composition has been investigated by comparing the Hamaker constant and coagulation coefficient between Ti2O3/ pure iron and Ti2O3/low-carbon steel systems. It is noted that the change of coagulation coefficient associated with the contact angle is caused by the formation of a new phase at the oxide/metal interface at the high temperature. The present work aims to provide a deep understanding of the connection between inclusion motion behavior in the liquid alloy and the high temperature interfacial phenomenon. https://doi.org/10.1007/s11663-019-01624-x Ó The Author(s) 2019 I. INTRODUCTION behavior, the experimental studies using both in-situ[11–15] and ex-situ[16–19] methodologies have been PHYSICOCHEMICAL aspects focusing on the performed. However, the current in-situ characterization motion, agglomeration, and detachment behaviors of research by high-temperature confocal laser scanning particles in the liquid or at liquid–gas interface are of microscope (HT-CLSM) limits the inclusion behavior great importance in the different fields including metal- on the liquid steel surface or named steel–gas interface, lurgical engineering. The particles can refer to metal which is a much different mechanism with the case of droplet, aerosol, colloid particle, nonmetallic inclusion inclusion agglomeration at the bulk of the liquid steel. particles in the different engineering fields.[1] Specifically, For the latter case, to the authors’ best knowledge, there the agglomeration of inclusion particles in the liquid is not an available way to characterize this research metal is vital to control the cleanliness of steels.[2,3] In topic directly. Using high-energy X-ray or neutron may addition, their agglomeration behavior relates to the have the chance; however, due to the low density of inclusion size, which is an important factor for inclusion inclusion existed in the liquid steel, the resolution of the roles as a nucleation site to induce intragranular acicular current X-ray, as well as that of the neutron, is not high ferrite nucleation.[4–9] Moreover, there is a concept, enough. Alternatively, the Hamaker constant and coag- inclusion engineering, that deals with the control of the ulation coefficient can be used to support the experi- amount, morphology, size distribution, and composi- mental findings in References 13 through 19. tion of nonmetallic inclusions formed in the liquid steel Besides the experimental work, various simulation during refining and solidification.[10] To better under- studies of the inclusion agglomeration behavior in the stand the mechanism of inclusion agglomeration liquid steel have been carried out by using the turbulent collision rate, which is a function of the coagulation coefficient.[20–23] In some studies, the inclusion has been assumed to be a single phase and the coagulation KEIJI NAKAJIMA, WANGZHONG MU, and PA¨RG. coefficient was set to a constant value of one for the sake JO¨NSSON are with the KTH Royal Institute of Technology, of convenience. As a result, it was not possible to discuss Department of Materials Science and Engineering, Brinellva¨gen 23, quantitatively on the size distribution of different 100 44 Stockholm, Sweden. Contact e-mail: [email protected] [22,23] Manuscript submitted December 27, 2019. inclusion kinds. METALLURGICAL AND MATERIALS TRANSACTIONS B Therefore, the proposed method aims to demonstrate the consideration of the dielectric property of the a simplified but direct correlation between the funda- intervening medium was introduced by Lifshitz.[26] mental study of the wettability measurement and the Visser[27] reviewed the existing approximate equations practical phenomenon of inclusion agglomeration in the for the calculations of the Hamaker constant from liquid steel. First of all, the current methodology experiments, where the methods reported by Frenkel[24] proposed a correlation between the contact angle and and Fowkes[28] based on physical property measure- the Hamaker constant according to Frenkel’s ments were introduced. Actually, there are several method.[24] Subsequently the relationship between the mechanisms of collision-coagulation other than vdW Hamaker constant and the coagulation coefficient based force that can also contribute to the particle agglomer- on the turbulent coagulation model is established. ation. For instance, liquid bridge force, cavity bridge Thereafter, this integration method is verified by the force, and capillary force are also the reason. However, experimental data of the Al2O3 particles in liquid iron. the focus of this work is vdW force, which only relates to Finally, the difference between the coagulation coeffi- the Hamaker constant and coagulation coefficient. The cient and the Hamaker constant among Al2O3, MgO, applicability of the Hamaker constant has been reported [27] and Ti2O3 particles in the liquid iron/low-carbon steel is in the colloid chemistry. Meanwhile, Taniguchi compared. The success of the applicability of the et al.[29] utilized this concept in the physical model, proposed method will let the industrial community which simulates the particle motion behavior in the assess the inclusion elimination efficiency rapidly steelmaking. It is noted that these Hamaker constant according to the experimental database of the physical values obtained from the surface tension measurement property measurement from the academic community. agreed well with other methods at room temperature, We challenge it here. such as graphite, polystyrene, polymers, SiO2, and TiO2 in water solution.[20,27,29] Regarding the Hamaker con- stant application at high temperature, Lin and Shimme[30] have tried to estimate the Hamaker constant II. METHODOLOGY [28] for Al2O3 in an iron melt, based on Fowkes’s method. A. Calculation of Hamaker Constant However, it might not be a perfect estimation since this The flowchart of the calculation proposed in this value was used for the adhesion between Al2O3 and work is presented in Figure 1. Prior to the calculation of liquid iron at 1600 °C. Alternatively, the selected the coagulation coefficient, it is important to introduce Hamaker constant of Al2O3 is at room temperature. the calculation method of Hamaker’s constant using the From the viewpoint of its applicability to particle physical measurement data. According to the history of dispersion/coagulation phenomena and the simplicity [25] using physical property at high temperature, the original this parameter, Hamaker was the pioneer who [24] reported that the adhesion force, London-v.d. Waals equation by Frenkel was adopted. Subsequently, the interaction (vdW), exists between two small particles. Hamaker constant is viewed as a system-specific phys- The vdW of two spherical particles can be calculated as ical constant for a system in which the intervening media a function of the diameters and the distance separating is iron/steel melt (M) and the two adjacent particles are them. Moreover, it is reported that the vdW force could oxide inclusions (I). However, it depends apparently on split into a geometrical part associated with a parameter the temperature and time because the composition of the called the ‘‘Hamaker constant.’’ The basic equation to intervening medium and the particle changes slightly with the temperature as well as with the holding time. calculate this factor is provided in Reference 25. [24] Subsequently, a description of the vdW interaction with According to Frenkel’s method, the interfacial adhesion energy between two particles with a plate shape is expressed as À2cIM per unit area. On the other hand, the van der Waals interaction free energy between 2 two particles with a plate shape is ÀAIMI/12pa per unit area. Thus, using the van der Waals adsorption approx- imation, the following equations can be obtained as Eqs. [1] and [2], and the details can be seen in References 13 and 14. 2 AIMI ¼ 24p a cIM ½1 cIM ¼ cI À cM cos hIM ½2 where AIMI is the Hamaker constant (J); a is the ionic radius, which is 2.8 9 10À10 for the oxides and À10 3.4 9 10 for the nitrides (m); cI is the surface 2 energy of oxide (J/m ); cM is the surface tension of 2 iron/steel melt (N/m, equivalent to J/m ); and cIM and 2 hIM are the interfacial free energy (J/m ) as well as the Fig. 1—Flowchart of the present calculation process. METALLURGICAL AND MATERIALS TRANSACTIONS B pffiffiffiffiffiffiffiffiffiffiffiffiffiffiÀÁ 3 contact angle (degrees) between iron/steel melt and the bT ¼ 1:3a pq e=l r þ r ½3 oxide substrate. Thus, the Hamaker constant at high ij t f i j temperature, AIMI, can be obtained from the contact angle data (hIM). cIM is the interfacial free energy "# À0:242 between iron/steel melt and oxide. 3 1=2 lri ðÞqfe=l at ¼ 0:727 ½4 AIMI B. Relationship Between Hamaker Constant and Coagulation Coefficient where ri and rj are radii of the inclusion particles (m), 3 It is speculated that the viscous drag force and the van qf is the density of iron/steel melt (kg/m ), e is the tur- bulent energy dissipation rate (0.01 m2/s3), and l is the der Waals force act on the particles in the liquid metal. À3 See the schematic illustration in Figure 2. At the time of viscosity of iron/steel melt (6.92 9 10 Pa s).