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Publication# Impact of dipole-dipole interactions on motility-induced phase separation

Résumé

We present a hydrodynamic theory for systems of dipolar active Brownian particles which, in the regime of weak dipolar coupling, predicts the onset of motility-induced phase separation (MIPS), consistent with Brownian dynamics (BD) simulations. The hydrodynamic equations are derived by explicitly coarse-graining the microscopic Langevin dynamics, thus allowing for a mapping of the coarse-grained model and particle-resolved simulations. Performing BD simulations at fixed density, we find that dipolar interactions tend to hinder MIPS, as first reported in [Liao et al., Soft Matter, 2020, 16, 2208]. Here we demonstrate that the theoretical approach indeed captures the suppression of MIPS. Moreover, the analysis of the numerically obtained, angle-dependent correlation functions sheds light into the underlying microscopic mechanisms leading to the destabilization of the homogeneous phase.

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Porosity is one of the major defects in castings because it reduces the mechanical properties of a cast piece [1]. Porosity formation results from the effect of two concomitant mechanisms, namely solidification shrinkage and segregation/precipitation of gases [1]. A model for the prediction of microporosity, macroporosity and pipe shrinkage during the solidification of alloys has been developed at the Computational Materials Laboratory (LSMX-EPFL) [2]. This model has then been improved by taking into account the effect of various alloying elements and gases on porosity formation [3, 4, 5]. However, the modeling of two physical phenomena still needed to be improved: (i) the curvature influence and (ii) the hydrogen diffusion influence on the growth of pores. The effect of pinching, i.e. the pores are forced by the growing solid network to adopt a complex non spherical shape, induces curvature restriction to the pores. This pinching effect can be a limiting factor for the growth of pores and is too simply modeled in the model of Péquet et al. [2]. Several other pinching models exist, but a rigorous experimental study to validate either one of these models is needed. Additionally, Carlson et al. [6] have recently shown that hydrogen diffusion might also be a limiting factor for the growth of pores. In the model of Péquet et al. [2], this effect was not taken into account. This thesis is mainly aimed to (i) provide experimental results that specifically validate the pinching model developed by Couturier et al. [4], (ii) investigate the influence of hydrogen diffusion on the growth of pores and (iii) provide a new model that takes into account the pinching effect and the hydrogen diffusion influence on the growth of pores. At first, pores formed in aluminum-copper (Al-Cu) samples (cast under controlled conditions) have been analyzed using high resolution X-ray tomography. The influence of the alloy inoculant, copper content, cooling rate and initial hydrogen content on the morphology of pores has been investigated. The results show that the curvature of micropores pinched in either non-inoculated or inoculated Al-4.5wt%Cu alloys can be fairly well approximated to that of cylinders. The results also show that the pinching model must be function of (i) the volume fraction of the primary phase gα and (ii) the secondary dendrite arm spacing λ2. However, the influence of the initial hydrogen content appears to be negligible. The pinching model developed by Couturier et al. [4] accounts for these observations and their relation fits fairly well the average mean curvature value of our experimental data. A new model has been developed to calculate an effective hydrogen diffusion coefficient De(gs), that is a function of the volume fraction of solid only. For that purpose, in-situ X-ray tomography has been performed on Al-Cu alloys. For each volume fraction of solid 0.6 ≤ gs ≤ 0.9, a representative volume element of the microstructure has been obtained from the tomography data. Solid and liquid voxels being assimilated to solid and liquid nodes respectively, a hydrogen diffusion equation has then been solved numerically. Calculations have been run until steady-state was reached in order to deduce De(gs) and the simulation results were successfully compared with a new theory based on effective-medium approximations. Both approaches lead to the main conclusion that hydrogen diffusion through the solid phase cannot be neglected, unlike it is assumed in the model of Carlson et al. [6]. Next, using the pinching model of Couturier et al. [4] and the obtained De(gs), a new volume-averaged model has been developed in order to simulate the growth of pores limited by (i) the curvature of the pore phase and (ii) the diffusion of hydrogen. The results show that, although hydrogen diffusion can be a limiting factor for the growth of pores, the pinching effect has a much larger influence. Accordingly, any model for porosity prediction should carefully take into account the influence of curvature and hydrogen diffusion on the growth of pores. In order to ripen this study at a refined scale, a 2D phase-field model has been developed to describe the complex shape of a pore formed within interdendritic liquid channels [7]. The influence of the solid, which can force the pore to adopt a non-spherical shape, is taken into account through the geometry of the domain and appropriate boundary conditions. This model accounts for curvature influence and hydrogen diffusion in the liquid, two of the main aspects governing the growth kinetics of a pore. However, the model still needs to be combined with a description of the liquid flow induced by the pore growth. Basically, this model should serve as a sound basis for further developments that might lead to more sophisticated pinching models. Finally, an experimental study has been conducted in order to track the inoculant influence on the shape of pipe shrinkage. Simultaneously, pipe shrinkage calculations (using the model of Péquet et al. [2]) were performed in order to track the influence of the gs,c parameter on the shape of the pipe shrinkage. This gs,c parameter corresponds to the critical volume fraction of solid at which mass feeding stops. Comparisons between experimental and simulation results show that the gs,c parameter should be set equal to 0.6 or 0.1 for a casting simulation of an inoculated or non-inoculated alloy, respectively.