Hysteresis in the freeze-thaw cycle of emulsions and suspensions

TL;DR

This work investigates hysteresis in freeze-thaw cycles using uni-directional experiments on oil-in-water emulsions and polystyrene particle suspensions exposed to a planar solidification front. By tracking the particle-front distance $h(t)$ and the interaction length $l_{ ext{int}}$, and comparing with the theory of Meijer, Bertin & Lohse, the authors reveal that rigid PS particles accumulate net displacement away from their initial positions, while deformable oil droplets tend to return to their starting locations, depending on front velocity $V$ relative to $V_{ ext{crit}}$. The deformation of droplets during encapsulation is reversible, and the thawing process can exhibit additional displacement that is captured by a volume-change term in the theory, extending applicability to oil droplets. The results illuminate how microscopic phase-change flows govern particle transport during freeze-thaw cycles, with implications for templating, cryopreservation, and processing of complex fluids, and suggest directions for extending the theory to more concentrated systems.

Abstract

Freeze-thaw cycles can be regularly observed in nature in water and are essential in industry and science. Objects present in the medium will interact with either an advancing solidification front during freezing or a retracting solidification front, i.e., an advancing melting front, during thawing. It is well known that objects show complex behaviours when interacting with the advancing solidification front, but the extent to which they are displaced during the retraction of the solid-liquid interface is less well understood. To study potential hysteresis effects during freeze-thaw cycles, we exploit experimental model systems of oil-in-water emulsions and polystyrene (PS) particle suspensions, in which a water-ice solidification front advances and retracts over an individual immiscible (and deformable) oil droplet or over a solid PS particle. We record several interesting hysteresis effects, resulting in non-zero relative displacements of the objects between freezing and thawing. PS particles tend to migrate further and further away from their initial position, whereas oil droplets tend to return to their starting positions during thawing. We rationalize our experimental findings by comparing them to our prior theoretical model of Meijer, Bertin & Lohse, Phys. Rev. Fluids (2025), yielding a qualitatively good agreement. Additionally, we look into the reversibility of how the droplet deforms and re-shapes throughout one freeze-thaw cycle, which will turn out to be remarkably robust.

Figures (4)

• Figure 1: Interactions during freezing. (a)-(c) Interaction between a silicone oil droplet of size $R \approx 105µ m$ with a water-ice solidification front advancing at different velocities $V$, i.e., (a) $V \approx 1µ m \per s$, (b) $V \approx 0.7µ m \per s$, and (c) $V \approx 0.4µ m \per s$ (see Supplementary Movies 1-3). Images are taken in the frame of reference of the moving front. Depending on the rate of approach, the droplet (a) does barely interact with the front and is rapidly engulfed into the ice, (b) interacts with the front for a certain amount of time $t_{\mathrm{int}}$ before being engulfed, or (c) is repelled by the ice indefinitely. During the encapsulation into the ice the droplet deforms tyagi2022solutemeijer2023thin. The red contours indicate the position where the droplet would have been if the particle-front interaction would have been absent, assuming linear drop/particle motion. Time $t=0$ is defined as the moment in time the center of the particle would have reached the undeformed front. Scale-bars are $100µ m$. (d) Particle-front distance $h(t)$ as a function of time for the three representative cases, i.e., (a) fast engulfment, (b) intermediate rejection, and (c) indefinite rejection. (e) Particle-front interaction time $t_{\mathrm{int}}$ as a function of advancing velocity $V$ for both oil droplets and polystyrene (PS) particles with $R \approx 20µ m$. As $V$ approaches a certain critical value $V_{\mathrm{crit}}$ (dotted lines) the interaction time rapidly increases meijer2024frozen. (f) Aspect ratio $\Gamma(t)$ as a function of time quantifying the deformation dynamics during encapsulation of the droplet corresponding to (b). The inset shows the final extend of the deformation $\Gamma_{\infty}$ as a function of $V$ for oil droplets with $R \approx 50µ m$. tyagi2022solutemeijer2023thin
• Figure 2: Interactions during thawing. (a)-(c) Interaction between a PS particle of size (a) $R \approx 20µ m$ and (b) $R \approx 70µ m$, and a (c) silicone oil droplet of size $R \approx 105µ m$ with a water-ice solidification front retracting at different velocities $V$, i.e., (a) $V \approx -8.9µ m \per s$, (b) $V \approx -0.1µ m \per s$, and (c) $V \approx -0.8µ m \per s$ (see Supplementary Movies 4-6). Images are taken in the frame of reference of the moving front. Depending on the rate of retraction and the type of particle, the object (a) does barely interact with the front and is rapidly expelled by the ice, (b) experiences an additional push by the retracting front, leading to a sudden displacement in the direction opposite of the motion of the front, or (c) is being held back by the front for a certain amount of time. During the extraction out of the ice the droplet regains its spherical shape. The red contours indicate the position where the droplet would have been if the particle-front interaction would have been absent. Time $t=0$ is defined as the moment in time the center of the particle would have reached the undeformed front. The denoted scale-bars are $100µ m$. (d) Particle-front distance $h(t)$ as a function of time for the three representative cases, i.e., (a) fast extraction without interaction, (b) sudden additional displacement opposite the direction of motion of the front for the PS particle, and (c) retardation of the motion away from the front for the oil droplet. (e) Particle-front interaction length $l_{\mathrm{int}}$ as a function of time for the (b) PS particle and (c) oil droplet, highlighting the difference in particle displacement during thawing. (f) Aspect ratio $\Gamma(t)$ as a function of time, quantifying the re-formation dynamics during extraction of the droplet corresponding to (c).
• Figure 3: Reversibility of the freeze-thaw cycle for oil droplets. (a) Particle-front distance $h(t)$ as a function of time for freezing (blue, see Fig. \ref{['fig:1']} (b) & (d)) and thawing (red, see Fig. \ref{['fig:2']} (c) & (d)). The time for the thawing curve (red) has been inverted and then shifted with $t_{\mathrm{int}}$ to let both curves overlap to highlight the effect of hysteresis for this particular case. (b) Deformation (blue, see Fig. \ref{['fig:1']} (f)) and re-formation (red, see Fig. \ref{['fig:2']} (f)) dynamics of an oil droplet with $R = 105µ m$ during one freeze-thaw cycle, with $V \approx 0.7µ m \per s$ for freezing and $V \approx 0.8µ m \per s$ for thawing. The thawing time has again been inverted and shifted to ensure that the start of the deformation and the end of the re-formation match.
• Figure 4: Overall particle displacement during one freeze-thaw cycle. (a) Particle-front interaction length $l_{\mathrm{int}}$ of the PS particle during both freezing (blue, not previously shown) and thawing (red, see Fig. \ref{['fig:2']} (b) & (e)) as a function of time. The thawing time has been shifted for the curve to become continuous. The inset shows the theoretical prediction of the model of Ref.meijer2024frozen. (b) Particle-front interaction length $l_{\mathrm{int}}$ of the oil droplet during both freezing (blue, see Fig. \ref{['fig:1']} (b) & (d)) and thawing (red, see Fig. \ref{['fig:2']} (c) & (e)) as a function of time. The thawing time has been shifted for the curve to become continuous. The inset shows the theoretical prediction of the (slightly adjusted) model of Ref.meijer2024frozen, taking effects of volume expansion into account. (c) Sketch of a spherical particle interacting with an advancing solidification front meijer2024frozen, indicating (among others) the particle-front distance $h(t)$, the distance between the particle's surface and the deformed front $d(\mathbf{x})$, and its radius $R$. The inset shows the quasi-stationary force balance, arising from disjoining pressure $\mathbf{F}_{\Pi}$ and viscous lubrication $\mathbf{F}_{\mathrm{vis}}$, to determine the particle velocity $u(t)$.