Solute effects on dynamics and deformation of 1 emulsion droplets during freezing 2

13 Soft or rigid particles, suspended in a liquid melt, interact with an advancing 14 solidification front in various industrial and natural processes, such as fabrica15 tion of particle-reinforced-composites, growth of crystals, cryopreservation, frost 16 heave, and growth of sea ice. The particle dynamics relative to the front de17 termine the microstructure as well as the functional properties of the solidified 18 material. The previous studies have extensively investigated the interaction of 19 foreign objects with a moving solid-liquid interface in pure melts while in most 20 real-life systems, solutes or surface active impurities are almost always present. 21 Here we study experimentally the interaction of spherical oil droplets with a 22


Introduction 2.2 Sample Preparation
We prepared the oil-in-water emulsions using a microfluidic setup, as explained 147 in our previous study [15]. The monodisperse droplets have radii (R 1 , R 2 ) of 148 either 7.2 ± 0.4 µm or 30.9 ± 1.2 µm, as shown in Fig.1 solidified in a rectangular Hele-Shaw cell (height =100 µm and volume =100 µl). 173 We fabricated the Hele-Shaw cell using two glass slides (Menzel, 24 × 60 mm,    Figure 3: Cryo-confocal microscope setup to perform in situ solidification experiments. A Hele-Shaw cell containing an oil-in-water emulsion is pulled at a constant velocity (V sl ) through a constant linear temperature gradient (G), established by two Peltier elements. In steady-state, the solidification interface is at a constant position under the microscope objective. In the sample frame, the interface is moving at a solidification velocity of V sl , imposed by the motor. c (2020) S. Tyagi

Droplets in water 250
We track the trajectories of the oil droplets which enables us to deduce the   corresponds to the range of interaction between the droplets and the interface. 281 We find that the droplets get repelled over distances ranging between 10 and 282 100 µm, often larger than their diameter, especially for the largest surfactant

295
In Fig.9 we present the droplet displacement δ due to their repulsion by the 296 front (defined in Fig. S1), which represents the distance moved by the droplets 297 during the interaction time. We again observe that increasing the surfactant 298 concentration leads to higher displacements while increasing the growth rate 299 leads to a lower displacement.

300
The results described so far emphasize that an increasing amount of surfac- where C L is the solute concentration at a distance x from the interface, C 0  in Fig.11. The droplets can elongate permanently as they get engulfed in the 372 growing ice (Fig.11A), the droplets may deform transiently (t = 13 s) at the 373 ice-water interface and subsequently relax to their original spherical shape as 374 they move further into the ice phase (Fig.11B), or the droplets remain mostly 375 spherical during their engulfment by the growing crystal (Fig.11C). We notice 376 that the deformation behaviour depends on the droplet size R, the imposed 377 growth rate V sl , and the bulk surfactant concentration. Therefore, we need to 378 systematically study the effect of these solidification parameters to understand 379 the different types of deformation observed.

380
The droplet deformation is estimated from the analysis of 2D shape elonga-381 tion, as shown in the schematic in Fig.11A, taking the ratio of droplet diameters 382 along x and y. In Fig.12, we depict the mean elongation profiles calculated for  is located at a distance of 2R × Elongation. Once the droplets are completely 393 engulfed in the ice, their shape does not evolve any more (Fig.12A,B). Interest-394 ingly, we notice that the elongation reduces with an increasing growth rate for 395 both the droplet sizes investigated. However, the maximum elongation for the 396 smaller R 1 droplets is lower as compared to the larger R 2 droplets at the given 397 0.01 wt.% solute concentration.

398
In Fig.12C, we report the transient deformation of the oil droplets as they 399 confront the ice-water interface with 1 wt.% bulk solute concentration. Here, 400 the oil droplets undergo elongation at the interface (distance =0 µm) but even-401 tually recover their shape as they are completely engulfed in the ice. In contrast, 402 from Fig.12D we notice that the larger R 2 droplets do not undergo any type

496
In the second section, we have shown that the deformation of droplets at 497 the ice-water interface depends strongly on the growth rate (V sl ) and the cor-498 responding bulk solute concentration (C 0 ). Furthermore, the addition of solute 499 increases the thickness of the observable premelted films, which appears to act 500 as a protection mechanism against the interface initiated droplet deformation. In conclusion, we report that the oil droplets undergoing directional solidifi-  Figure S1: Measurement of interaction time and apparent droplet velocity U in the observation frame. In the observation frame, far from the solid-liquid interface in water the droplet moves at the imposed growth rate U = V sl , as the droplet approaches the interface it gets repelled U = V sl , and as the droplet is engulfed in the ice it doesn't get repelled anymore, thereby recovering U = V sl . The interaction time is the total duration over which a droplet gets repelled by the solidification interface. Relative time is zero when the front edge of the droplet hits the solidification front. Experimental conditions for which the curve was recorded: V sl = 3 µm · s −1 , G = ∇T = 10 4 K · m −1 , Droplet size R 1 = 7.2 ± 0.4 µm. c (2020) S. Tyagi et al.  Figure S2: Deducing the isolated droplet velocity U r and the mean droplet velocity U in the sample frame. In the sample frame, the isolated droplet velocity U r is zero far from the interface, it increases and reaches a maximum when the droplet gets repelled by the interface and subsequently, reduces to zero as the droplet is engulfed in the ice. Experimental conditions for which the curve was recorded: V sl = 3 µm·s −1 , G = ∇T = 10 4 K ·m −1 , Droplet size R 1 = 7.2±0.4 µm. c (2020) S. Tyagi et al.