Multiple objects interacting with a solidification front

The interaction of objects suspended in a liquid melt with an advancing solidification front is of special interest in nature and engineering sciences. The front can either engulf the object into the growing crystal or repel it. Therefore, the object-front confrontation can have a strong influence on the microstructure and mechanical or functional properties of the solidified material. The past theoretical models and experimental studies have mostly investigated the interaction of isolated, spherical, and hard objects in pure melts. However, the outcome of object-front interactions in complex (more realistic) systems, where multiple objects and solutes are present, is still poorly understood. Here we show the interaction of multiple oil droplets with an ice-water front in the absence and presence of solute effects using in situ cryo-confocal microscopy. We report on how the object size, number of objects, and bulk solute concentration influence the the object-front interaction and the front morphology, as well as the subsequent object spatial distribution. We suggest that the volume fraction of objects suspended in a liquid melt in conjunction with the amount of bulk solute concentration are two important parameters to be incorporated in the development of object-front interaction models.

www.nature.com/scientificreports/ Furthermore, the idealistic assumptions of the theoretical models such as the non-retarded van der Waals forces, absence of solute segregation, and a steady-state planar front interaction are difficult to achieve practically 26 . The advent of accurate finite element models also clearly highlights the disparities in approximations to solidification front shapes and the accuracy of the simulated particle behaviours 27 . The existing theories and experimental evidences have been primarily derived for isolated objects, whereas most real-life applications involve multiple polydisperse particles. This reinforces the importance of investigating the role of particle size distribution, particle-particle interactions and hence, the formation of agglomerates. Progress in studying the spatial distribution, when thousands of particles interact with a solid-liquid front, has been brought about by modern advanced in situ imaging techniques, such as X-ray imaging 28 , confocal microscopy 29 , or the development of numerical modelling techniques, such as molecular dynamics 30,31 . Recently, Saint-Michel et al. 32 proposed a mechanical model on the effects of multiple particle interactions on particle trapping by solidification fronts as depicted in Fig. 1. Their study highlighted the major differences in force equilibrium when considering a multi-particle approach. Their experimental results revealed that the presence of multiple particles can lead to an accumulated particle layer ahead of the solidification front at small growth rates ( V sl < V c ). This particle layer further acts as a porous medium and offers resistance to the fluid flow resulting in an additional frictional force ( F µ ), which facilitates particle engulfment. Hence, the modified force equilibrium for multiple-particles can be given as F η + F µ = F σ . Although, these studies help us to bridge the gap between the single particle models and real-life multi-particle systems, we now need to understand how the presence of multiple particles at the front can locally affect the solidification microstructure.
The presence of solutes, desired or as impurities, impacts the solidification front shape and induces longrange effects (at typical length scales of ≈ D/V sl , where D is the solute diffusion coefficient), which override the short-range thermomolecular forces ( ≤ 10 nm). The existing models, incorporating the role of solute, study their influence on the solid-liquid front shape deformation but not on the nature and equilibrium of the repulsive forces 19,21,[33][34][35] . In general, the solubility of a solute is less in the solid phase than in the liquid phase. As solidification progresses, the solute is rejected by the growing crystal, thereby corresponding to an increasing concentration of solute in the remaining liquid 36 . In the presence of foreign objects, the segregation of solutes at the front is enhanced further by the approaching objects obstructing their diffusion field 21 . This local solute enrichment influences the object environment, (due to local undercooling), and is of particular importance in understanding several mechanisms that can occur at the solid-liquid front. The rejection of additives during the freezing of biological cells can inflict membrane rupture (or cryoinjury) owing to the high osmotic stress gradient from the local solute concentration 3,4 .

Figure 1.
Force equilibrium to predict engulfment or rejection of objects in the presence of multiple particles. The particle-particle interactions during solidification can result in the formation of a compact layer, which acts as a porous medium. The subsequent resistance offered to the flow of fluid (blue arrows) towards the growing solid results in an additional frictional force F µ , which favors object engulfment. The modified force equilibrium is hence given as F η + F µ = F σ , where F η is an attractive viscous drag force and F σ is a repulsive interfacial force. ∇T = G is the applied temperature gradient and V sl is the imposed growth rate. © (2020) S. Tyagi et al. The objective of our study is to investigate experimentally the solidification dynamics and spatial distribution of objects in multiple particle regimes. We compare our experimental observations with previous theoretical models to comprehend the critical correlations and disparities in the presence of multiple particles. We perform directional solidification experiments with independently regulated solidification velocity ( V sl ) and a linear temperature gradient (G). Both the solidification velocity and the temperature gradient are constant during the entire experiment. The use of freezing emulsions as model system for solidification has been promising 37 and we develop further on this approach using in situ cryo-confocal microscopy. We utilise mono-disperse, bimodal emulsions, and subsequently progress towards realistic poly-disperse systems. We demonstrate several important aspects of multiple particle interactions and its consequences on particle redistribution in the solidified microstructure. We increase the complexity by adding solute to the liquid phase, and examine the effects of increasing poly-dispersity in conjunction with the overriding solute effects. Finally, we illustrate how the systematic approach facilitates to decouple the process parameters impacting the behaviour of an object, while it interacts with a solid-liquid front.

Sample preparation.
We prepared oil-in-water emulsions using a microfluidic setup (microfluidic starter kit, Micronit Microfluidics, Netherlands) with pressure controlled flow pumps (Fluigent LineUP Flow EZ). We used uncoated focused flow droplet generator chips (FF _ DROP, Micronit) with nozzle diameter of 10 μm and 50 μm. These microfluidic chips facilitated the preparation of highly monodisperse droplets with radii of 8 μm ( R 1 ) and 28 μm ( R 2 ), respectively. We ensured a uniform flow rate of oil and aqueous phases using Fluigent Flow Unit S ( 0 − 7 µL · min −1 ) combined with in-line impurity filters (PEEK 2 μm,VWR International). The oil phase consisted of propyl benzoate with 10 −4 M BODIPY to obtain clear imaging of dispersed droplets at 1% laser power. For the aqueous phase, we used 10 −5 M SRhB solution, as self-quenching was reported at concentrations above 2 × 10 −4 M 38 . We added TWEEN 80 ( HLB = 15 39 ), a non-ionic surfactant, to the aqueous phase for stabilising the oil-in-water emulsions. TWEEN 80 (Critical Micellar Concentration = 13 − 15 mg · l −140 ), acted as a model solute as it depresses the freezing point of solutions alike (colligative property). The bimodal emulsions were synthesized by independently mixing the monodisperse emulsions ( R 1 + R 2 ). The polydisperse emulsion was obtained through hand-shaking the aqueous suspension in a 1.5 ml eppendorf vial with 2 vol.% oil phase. The prepared emulsions were filled through capillarity and solidified in a rectangular Hele-Shaw cell (h=100 μm and V=100 µl ). The cell was fabricated using two glass slides (Menzel, 24 × 60 mm , thickness 0.13 − 0.16 mm ), and sealed with nail-polish at one end to prevent evaporation.

Imaging & analysis.
We used Leica TCS SP8 confocal laser scanning microscope (Leica Microsystemes SAS, Germany), equipped with 488 nm (blue) and 552 nm (green) lasers, for image acquisition. In 2D, we utilised the microscope at a scanning speed of 600 Hz , with 1024 × 1024 pixels for imaging 775 × 775 μm, resulting in 1.7 s per frame. In 3D, we used a fast resonant mode with 512 × 512 pixels for a scanning rate of 0.047 s per frame. We used two photodetectors (PMT) to simultaneously image three phases : 1. BODIPY ( ex 493 nm ; em 504 nm ), fluorophore incorporated into the oil droplets. 2. SRhB ( ex 565 nm ; em 586 nm ), fluorophore dissolved in water, to image the aqueous phase and the cells boundaries in ice. 3. Ice, does not fluoresce, as it has very low solubility for solutes 41 and hence, appears black.
The emission spectra of the excited fluorophores was captured using a non-immersive objective (Leica HCX PL APO CS 20× ). The objective working distance of 590 μm along with an insulating foam cladding facilitates the minimization of thermal perturbations on the freezing substrate. We used Fiji 42 for image thresholding in conjunction with Python 43 for image and data analysis.
Freezing stage. We conducted unidirectional solidification experiments, translating the sample cell along a constant linear temperature gradient (G), using the cryo-confocal stage described in detail previously 29 . We imposed the temperature with two Peltier modules, and controlled it with high precision ( < 0.01 °C) using TEC-1122 Dual Thermo Electric Cooling Temperature Controller from Meerstetter Engineering, Switzerland. The Peltier elements were separated by a distance ( 2 mm ) to establish a linear temperature gradient along x . We utilised the VT-80 translation stage (Micos Pollux Drive PI, USA) to impose the rate at the which the sample cell is pulled ( V sl ). The rate of translation was verified to be in agreement with the measured solidification velocity using posterior image analysis ( error < 1 % ). Thus, we can control independently the solidification velocity ( V sl ) and the thermal gradient (G) in our system. We carried out the experiments in the velocity range of 1 ≤ V sl ≤ 10 µm · s −1 , with sufficient waiting time to establish thermal equilibrium along the sample depth ( z ). The in situ observation of object interaction with the solid-liquid front was captured using a confocal microscope placed vertically over the gap ( 2 mm ) between the two Peltier modules. Hence, the solidification front tends to appear immobile in the frame of observation, however, in the sample frame, it is the ice solidifying (along x ) at the velocity imposed by the pulling rate of the motor.

Results
Front morphology. We study the directional solidification of oil-in-water emulsions, translated at a velocity V sl along a linear temperature gradient G, using a confocal microscope, as shown in Fig. 2. A typical confocal image, as shown in Fig. 3, enables us to distinguish the dark solid phase (ice) from the bright aqueous phase (water). Ice, like most solids, has extremely low solubility for dissolved solutes and rejects them in the remaining liquid as solidification progresses 41 . The coexisting solid-liquid phases are delimited by the solidification front, corresponding macroscopically to an isotherm at bulk melting temperature T m . In directional solidification, the advancing solid-liquid front can have predominantly three morphologies; planar, cellular, and dendritic (Fig. 3). The stability and morphology of a front are essentially controlled by the growth rate, the underlying temperature gradient, and the solute concentration in the melt. The major advantage of our system is that we can independently regulate and accurately maintain a constant solidification velocity ( V sl ) as well as temperature gradient (G) over the experimental time-scales. This ensures a steady-state solidification front under a constant cooling rate with the absence of thermal destabilisation.
To establish the domains of the different front morphologies, we performed experiments using a constant thermal gradient G of 10 4 K · m −1 , as shown in Fig. 4. We observe three distinct front morphologies (Figs. 3,4), in the absence of suspended objects, while solidifying the aqueous phase in a velocity range of 1 ≤ V sl ≤ 10 µm · s −1 with varying concentrations of solute. In Fig. 4, the steady-state planar front is thermodynamically favorable at  www.nature.com/scientificreports/ low growth velocities ( V sl ≤ 5 µm · s −1 ) for small solute concentrations ( ≤ 10 −1 wt.%). As we increase the front velocity or the solute concentration, the steady state planar front develops local growth instabilities with a few cells boundaries, which remain stable during experimental time scales ≈ 40 − 60 min . At the higher velocities and solute concentrations, the front eventually destabilises into a cellular front morphology. The uniformly spaced lamellae are generated owing to the propagation of a Mullins-Sekerka instability during the solid-liquid phase transformation 44 . The solute rejected by the growing ice front builds up a steep concentration gradient with the bulk solution, over a length scale ( ≈ D/V sl ) 21,23 . Since growth from solutions depends on the concentration gradient of solutes, the liquidus temperature of the melt in the vicinity of the front differs from the liquidus temperature of the bulk liquid far from the front. As the solute segregates, the liquidus temperature further decreases. This change in liquid composition alters its transformation temperature, referred to as constitutional undercooling 36 . This constitutional undercooling is a necessary criterion for the destabilization of a planar front into a metastable or cellular front 44 . Theoretically, for steady-state planar front growth the solute concentration gradient in the melt scales as ∇C ∝ e −V sl x/D , where x is the distance from the solidification front 36 . Therefore, an increasing growth rate leads to a strong increase of the solute concentration gradient. This explains why the critical bulk solute concentration for the destabilization of a planar front decreases with an increasing growth rate, as reported in Fig. 4.
The spatial distribution of the objects in the solidified material is determined by the advancing front morphology obtained at the given experimental conditions 23,45 . In ice-templating, a cellular front is used to segregate the dispersed colloids between the arms of the growing ice crystals 9 . In contrast, the growth of single crystals demands a planar front to ensure a homogeneous structure 7 . We thus feel it is important to investigate the systematic impact of object size, solute concentration, and inter-object interactions on the solidified microstructure with planar and meta-stable fronts. To do so, we modify only the bulk solute concentration, while keeping a constant growth rate of 1 µm · s −1 and a constant temperature gradient of 10 4 K · m −1 during our experiments.
Interaction of the front with monodisperse objects. We first examine the interaction of monodisperse oil-in-water emulsions with the solid-liquid front at a growth rate of V sl = 1 µm.s −1 and a temperature gradient of G = 10 4 K · m −1 , as depicted in Fig. 5. The corresponding droplet size and bulk solute concentration used for the experiments are given in table 1. www.nature.com/scientificreports/ In Fig. 5A, we observe that the 8 µm ( R 1 ) oil droplets with 0.01wt.% solute concentration are continuously repelled by the ice growing from the bulk suspension, forcing them to build-up as a compacted layer. In our experiment, the height of the close-packed layer increases until ≈ 80 µm and subsequently, the droplets get engulfed by the growing solid. Interestingly, the droplets are engulfed as single layers and fabricate a texture parallel to the solid-liquid front. The droplets, albeit closely packed in the liquid ahead of the front, get separated as they are captured by the growing ice crystal. We believe the lateral gap ( y ) between the engulfed droplets in ice is created owing to the elongation induced during their capture. The increase in diameter parallel to the temperature gradient ( x ) is compensated by the decreasing width in the lateral direction ( y ) and hence, the close-packed droplets get separated in the frozen solid. In contrast to the smaller R 1 droplets (Fig. 5A), the engulfment of the larger R 2 ( 28 µm ) droplets is instantaneous and we observe no subsequent compact layer formation (Fig. 5B). The elongation induced owing to the droplet-front interaction is visually prominent during the solidification of the R 2 droplets. The deformation of droplets during solidification will be addressed in a separate communication and is not in the scope of the present study. The steady-state planar front remains stable and does not destabilise neither from the formation of the close packed layer nor during the capture of the different size objects (Fig. 5A,B).
The presence of a similar particle agglomerated layer has been reported previously 32,46,47 , where its steadystate thickness (h) depends primarily on the solidification velocity ( h ∝ V −1 sl ) . It was shown that the complex scenario of multiple particles can be partly understood by building on the single-particle models. At 0.01wt.% concentration, the solute does not play a dominating role and hence, we shall compare this system to the previous theoretical models derived for single isolated objects. We consider the Rempel-Worster (RW) model 16 , which considers the balance between repulsive van der Waals forces and attractive viscous forces, to estimate the critical particle size ( R c ), at a given solidification velocity V sl , below which particles are rejected by the front and above which particles are captured by an advancing front. The critical particle size R c , can be given as where σ sl is the ice-water interfacial tension, A ow is the oil-water Hamaker constant, and η is the dynamical viscosity. We obtain a R c of 9 µm with the typical parameter values (see Table 2) for an object in the ice-water system. Hence, using the RW model we can account for the initial repulsion of the 8 µm droplets ( R 1 < R c ) and an instantaneous engulfment of the 28 µm ( R 2 > R c ) droplets.
Isolated droplets are rejected at the ice-water front when their size is smaller than the critical size ( R 1 < R c ). In concentrated systems, the droplets being pushed get accumulated ahead of the front and eventually interact with the other droplets, thereby forming a dense object layer (see Fig. 1). Recently, Saint-Michel et al. 32 have derived a modified force equilibrium for multi-particle systems, and suggested that an additional frictional force, generated by the friction of the fluid flowing through the compact particle layer, toward the ice-water front, favors engulfment above a critical thickness of the packed particle layer. The existence of this critical layer thickness induces periodic repulsion-engulfment transitions as we observe in our study. Thus, we suggest that this additional frictional force, which grows with the height of the compact layer, results in the periodic engulfment of droplets for a critical layer thickness of ≈ 80 µm.
(1) Table 1. Droplet radius (R) and bulk solute concentration (wt.%) in the aqueous phase for the monodisperse oil-in-water emulsions.   Table 2. Typical solidification parameters for an object in front of an ice-water solidification front. σ sl adapted from Rempel et al. 16 . www.nature.com/scientificreports/ We will now discuss the droplet-front interactions with 1wt.% solute in solution. The 8 µm ( R 1 ) droplets in the presence of 1wt.% solute are pushed by the growing ice and subsequently organise into close-packed clusters (Fig. 5C). The droplet clusters formed are rather non-uniform in their distribution and are heterogeneously scattered over the front in the lateral direction ( y ). The droplet clusters are eventually engulfed and incorporated in the growing crystal, while getting textured perpendicular ( x ) to the solid-liquid front. This spatial distribution is hence opposite to the parallel mono-layers (along y ) obtained in the presence of 0.01wt.% solute concentration (Fig. 5A). In contrast, the 28 µm ( R 2 ) droplets get engulfed without repulsion (Fig. 5D), and represent similar behaviour as the corresponding large droplets at 0.01wt.% solute concentration (Fig. 5B). We thus observe a distinct variation in the droplet spatial distribution only in the presence of small R 1 droplets.

Parameters Nominal value
We believe the formation of these heterogeneous clusters is owing to the local destabilization of the ice front and therefore, instigated by the rejected solute segregation. The presence of multiple droplets further enhances the local solute concentration by obstructing the solute diffusion field in the bulk liquid 13,21,33,34 . Highly fluorescent zones in the vicinity of the droplets can be clearly seen at the front (Fig. 5C,D). These zones are formed owing to the segregation of the fluorescent dye, which is rejected by the growing ice. We expect that the solute, although not fluorescent yet having a similar diffusion coefficient as the dye, segregates in an identical manner at the front. The solute invokes severe constitutional undercooling in the premelted films behind the droplets, thereby inducing a concave curvature of the front 48 .
The extensive concave cusping eventually transforms into a pocket with the droplet build-up and results in subsequent entrapment of droplets along the crystal growth direction ( x ). Such solute enriched pockets have also been reported by Chang et al. 49 during the directional freezing of biological cells. The premelted films are highly sensitive to the concentration of solute and surround the droplets engulfed by the ice, while the interface heals and rebounds to the horizontal isotherm ( T m ). The presence of solute premelted films with thickness of the order ≈ 5 µm leads us to believe that the solute plays a dominating role at such high concentration 50 . In the absence of solute effects, premelted films of thickness ≈ 10 nm have been predicted in the particle-front gap by the past studies 15-17 . Our results depict that an augmentation of solute does not seem to influence the previously predicted value (RW model) of critical radius R c for droplet engulfment. Similar to the R 1 droplets in the presence of 0.01wt.% solute concentration, we report an initial repulsion of the R 1 droplets with 1wt.% solute in solution. A few analytical models 20,21,33,34 and numerical simulations 19,35,49 studying the object-front interactions in the presence of solute effects have been derived previously. In theory, the magnitude of van der Waals force, responsible for pushing the particle, is regulated by the particle-front gap. The high concentration of segregated solute increases the particle-front gap by constitutional undercooling and hence, significantly reduces the effect of repulsive van der Waals force. This implies that for a given growth rate, smaller objects can be engulfed much more easily in solutions, in contrast to pure melts ( R solution c < R pure melt c ). Thus, the theoretical models predict a critical radius ( R c ) of magnitude much smaller for binary solutions as compared to the pure melts, which is not what we observe experimentally (i.e. R solution c ≈ R pure melt c ). Therefore, we deduce from our experimental observations that R 1 < R c < R 2 is still a valid criterion with 1wt.% solute in solution.
Interaction of the front with bimodal objects. We have discussed so far the interaction of monodisperse objects, exhibiting distinct radii ( R 1 , R 2 ), with an approaching solid-liquid front. Yet, in many applications, such as fabrication of metal/ceramic matrix composites, we can have a distribution of object sizes. Thus, it is essential in such scenarios to comprehend and predict, the segregation or sorting of particles, during solidification. In light of these uncertainties, we conducted horizontal unidirectional solidification with the same set of droplets (radii R 1 = 8 µm and R 2 = 28 µm ) composed together, at a solidification velocity V sl of 1 µm · s −1 and a constant linear temperature gradient G of 10 4 K · m −1 . To understand the novel scenarios observed, we compare the modes of interactions in bimodal emulsions to the monodisperse regimes at their corresponding solute concentrations ( 0.01, 1wt.%). We also depict the associated descriptive schemes in absence (Fig. 6A-D) and presence (Fig. 7A,B) of dominating solute effects.
In the presence of 0.01wt.% solute (Fig. 6), we notice two peculiar behaviours of the inter-droplet interaction with the solid-liquid front as follows: First, as shown in Fig. 6C,E the small droplets ( R 1 < R c ) form a compacted layer at the planar front as seen in monodisperse emulsions (Fig. 6A), which further acts as a barrier layer and provokes the repulsion of a larger droplet ( R 2 ). The latter is pushed ahead for t ≈ 200 s before getting eventually trapped by the growing ice. This suggests that a droplet with a radius greater than the critical value ( R 2 > R c ) can still be repelled if it does not interact with the solidification front immediately. In contrast, isolated monodisperse large droplets get engulfed instantaneously without undergoing repulsion-trapping, as shown schematically in Fig. 6B and experimentally in Fig. 5C.
The second observation (see Fig. 6D,F) depicts the repulsion-trapping transition of the compacted layer ( R 1 < R c ), instigated by the presence of 3 large droplets ( R 2 > R c ), labelled as 1, 2, 3 in Fig. 6F. We also notice the relative repulsion of droplet 2 as compared to droplet 1, similar to Fig. 6C, manifested by the decreasing horizontal distance between t ≈ 0 s and t ≈ 274 s . The droplet 2 encounters a compacted layer in the vicinity of the front, while droplet 1 undergoes instant engulfment owing to its large size ( R 2 > R c ) and an immediate interaction with the solidified crystal. The height (h) of the compacted layer is ≈ 90 µm at the instance of the repulsion-trapping transition in the two observations stated above (Fig. 6E,F). Interestingly, this corresponds closely to the height of ≈ 80 µm , observed in Fig. 5A with monodisperse small droplets. The trapping of droplets, for a sufficiently large thickness of the compacted layer, prevents their accumulation and thereby ensures a constant steady-state layer thickness 32 . This clearly demonstrates the importance of multiple-particle interactions with a solid-liquid front on the development of a solidified microstructure. www.nature.com/scientificreports/ We now investigate the dynamics of bimodal droplet size distribution with 1wt.% solute in solution. The large droplet ( R 2 = 28 µm ) as shown in Fig. 7B,C provokes a concave curvature ( t = 0 s ), thereby diminishing the crystal growth rate behind it. The pocket created in the ice proceeds with the engulfment of the large droplet surrounded by a relatively high concentration of solute ( t = 100 s ). The temporary opening, at the solid-liquid front, entices a cluster of smaller droplets ( R 1 = 8 µm ) behind the large droplet ( t = 135 s ). The droplet cluster, initially isolated, is trapped at the fermeture of the pocket and gets textured perpendicular to the front ( x ). This orientation is reminiscent of a solidifying monodisperse emulsion depicted schematically in Fig. 7A. The lateral growth of the ice crystals, transverse to the temperature gradient, pushes the droplets together and results in a close-packed microstructure. Thus, a small increase in the amount of solute added has again a drastic impact on the solidification microstructure.
Interaction of the front with polydisperse objects. In the last section, we look at the behaviour of polydisperse oil-in-water emulsions. The low interfacial tension of the oil (propyl benzoate) with water enables us to obtain relatively small polydisperse droplets, varying in size from 5 < R < 30 µm . We utilize in situ cryo-confocal microscopy to acquire 2D and 3D evolution of the microstructure at V sl = 1 µm · s −1 and G = 10 4 K · m −1 . Previously, we have reported on the monodisperse and bimodal size particle interactions between the growing solid and the droplets, which is considerably different from the nature of interactions between the front and an isolated object. To attain a better understanding of complex (more realistic) systems, we will now investigate the confrontation of polydisperse droplets with an advancing solidification front. The emulsions are prepared with 0.01wt.% and 1wt.% solute in solution.
When an object interacts with a solid-liquid front it can be engulfed immediately, pushed irreversibly, or repelled for a certain distance and then engulfed 15 . These behaviours are encountered owing to a critical velocity ( V c ), inversely proportional to the particle radius ( V c ∝ R −α ), above which an object is engulfed ( V sl > V c ), while below it the object is pushed by the front ( V sl < V c ). Conversely, for a given growth rate V sl , there should exist a critical radius R c , where the objects smaller than the critical size should be pushed and vice-versa. Thus, in our experiments with different object sizes one would expect a range of critical velocities or a range of critical radii at www.nature.com/scientificreports/ the imposed growth rate. Ideally, we expect the engulfment of objects with R y > R c and rejection of objects with R x < R c , where the critical radius is 9 µm for our experimental parameters. However, we observe the repulsion of miscellaneous droplets irrespective of their radii ( R x < R c < R y ), as seen in Fig. 8, in the absence of longrange solute effects. The droplet clusters form at the front with the primary layer occupied by the small droplets ( R x < R c ), which further creates a barrier and facilitate the repulsion of relatively larger droplets ( R y > R c ). For planar front solidification in the presence of solute, the previous models 19,21,33,34 deduce a critical engulfment velocity which in most cases is an order below the critical velocity for isolated objects in pure materials. The models suggest either an absence of pushing-engulfment transition, or a destabilisation of the steady-state planar front prior to engulfment. In both scenarios, rapid engulfment of the object is suggested as the most favorable outcome, facilitated by an increase in the viscous drag forces. However, the presence of multiple-particle   www.nature.com/scientificreports/ interactions is not incorporated in these models. The experimental evidence are difficult to correlate with owing to varying process parameters and often suggest contradictory results 4,23-25 . Körber et al. 4 have reported no impact of solute on critical velocity in water-NaMnO 4 solution, in contrast to the theoretically expected decrease in V c (from pure melts) owing to the impurity effects. On the contrary, Sekhar & Trivedi 23 have demonstrated strong impacts of impurity leading to particle trapping in the directional solidification of succinonitrile-acetone system. In our experiments, we report a pushing-engulfment or repulsion-trapping transition in the presence of dominating solute effects. From Fig. 9A, we observe the presence of droplet clusters generated both at (inset 1,2,3,4 in Fig. 9A) and ahead of the front (inset box in Fig. 9A). The 3D time-lapse evolution depicts the small droplet (inset arrow Fig. 9A) being pushed by the front for ≈ 400 s . Consequently, the droplets (inset 1,2,3,4 in Fig. 9A) are blocked and form a close-packed cluster, eventually engulfed at t = 808 s . We illustrate this scenario in Fig. 9B with a model schematic. The morphology of the front does not undergo a transformation in the presence of droplets, as suggested previously 23,51,52 , and remains as depicted in the absence of objects (Fig. 4). The formation of the cluster ahead of the front is still not clear but we believe the solute phoretic phenomenon such as diffusiophoresis can be at the genesis of such long-range displacement 37 . Although, we require more experiments to conclude effectively the origin of such close-packed clusters.

Conclusions
The size, presence of multiple objects, complex front morphology, and high concentration of solute significantly alter the microstructure developed during directional solidification. We performed solidification experiments to study the droplet rearrangement of monodisperse, bimodal, and polydisperse distributions in the solidified matrix. We have tried to highlight the correlations and disparities of multiple-particle regime with previous isolated single object models 16,19 as well as recent multi-particle models 32 , computed both in the absence and presence of solute effects. We have successfully demonstrated in our experiments the distinct behaviour when the size of droplets adheres to the criterion of R 1 < R c < R 2 . Furthermore, we have observed no change in critical radius ( R c ) in the presence of solute effects contrary to the predictions of the theoretical models. The critical radius ( R c ) or critical velocity ( V c ) is modified by the presence of inter-droplet interactions. We depict that the presence of multiple objects can lead to the formation of a segregated microstructure, while the initial suspension is homogeneous. We illustrate for the first time a pushing-engulfment or repulsion-trapping transition in the presence of overriding solute effects. We report no change in the morphology of the solidification front owing to the presence of objects in the melt. We suggest that the volume fraction of objects in the melt is an important criterion to be considered for predicting the object distribution in the solidified microstructure. The solidification of controlled oil-in-water emulsions can help us visualize and model a variety of microstructures by utilizing different colonies of droplets in the presence or absence of solute effects.

Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request. www.nature.com/scientificreports/ Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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