Thin-Film-Mediated Deformation of Droplet during Cryopreservation

Freezing of dispersions is omnipresent in science and technology. While the passing of a freezing front over a solid particle is reasonably understood, this is not so for soft particles. Here, using an oil-in-water emulsion as a model system, we show that when engulfed into a growing ice front, a soft particle severely deforms. This deformation strongly depends on the engulfment velocity $V$, even forming pointy-tip shapes for low values of $V$. We find such singular deformations are mediated by interfacial flows in nanometric thin liquid films separating the nonsolidifying dispersed droplets and the solidifying bulk. We model the fluid flow in these intervening thin films using a lubrication approximation and then relate it to the deformation sustained by the dispersed droplet.

Figure 1

Schematic of the experimental setup. The red arrow indicates the direction of sliding of the Hele-Shaw cell over the copper block.

Figure 2

(a)–(d) Top-view snapshots capturing the engulfment of a 5 cSt silicone oil droplet submerged in water by an advancing solidification front ($V=0.4\mathrm{\mu }\mathrm{m}{\mathrm{s}}^{-1}$), i.e., ice, first approaching and then passing over the droplet (Supplemental Movie 1). At $t=0$ the drop makes first contact with the front. The applied temperature gradient $G$ is about $10\mathrm{K}{\mathrm{cm}}^{-1}$. The droplet remains deformed in the solidified bulk after engulfment throughout the entire experiment (typically $\sim 4\mathrm{h}$).

Figure 3

(a) Aspect ratio $\mathrm{\Gamma }(t)$ as a function of time $t$ for advancing velocities $V=(bluefilledcircle)0.2\mathrm{\mu }\mathrm{m}{\mathrm{s}}^{-1}(pinkfilledcircle)0.4\mathrm{\mu }\mathrm{m}{\mathrm{s}}^{-1}(yellowfilledcircle)0.6\mathrm{\mu }\mathrm{m}{\mathrm{s}}^{-1}$. The solidification front makes first contact with the droplet at $t=t_0$. The inset shows the universality of the engulfment process, where $\xi =(\mathrm{\Gamma }(t)-1)/({\mathrm{\Gamma }}_{\infty }-1)$ and $\overline{t}=(t-t_0)V/R$. (b) Final aspect ratio ${\mathrm{\Gamma }}_{\infty }$ of the deformed droplet in the solidified bulk as a function of the solidification front advancing velocity $V$ for two kinematic viscosities $\nu =(orangefilledsquare)5\mathrm{cSt}$ and (blue filled diamond) 50 cSt.

Figure 4

(a) Experimental image capturing the engulfment of an oil drop (Supplemental Movie 2). (b) The schematics visualizes the competition between the disjoining pressure $\mathrm{\Pi }$ and Marangoni effects that mediate the flow profile within the liquid film with varying $H(X)$. Depending on the profile of the thin film, the pressure in the film $p_{\mathrm{film}}$ varies, which determines the local curvature of the oil-water interface and eventually the overall shape of the drop.

Figure 5

Experimental snapshots of three deformed 5 cSt silicone oil droplets that were engulfed at different velocities $V=0.2\mathrm{\mu }\mathrm{m}{\mathrm{s}}^{-1}$, $0.4\mathrm{\mu }\mathrm{m}{\mathrm{s}}^{-1}$, and $0.6\mathrm{\mu }\mathrm{m}{\mathrm{s}}^{-1}$. The applied temperature gradient $G$ is about $10\mathrm{K}{\mathrm{cm}}^{-1}$ and the corresponding final aspect ratios ${\mathrm{\Gamma }}_{\infty }$ of their final shapes are also indicated. The lines overlayed in red are the shapes generated by the pendant drop model [39] with corresponding values of the deformation parameter $\mathcal{E}$.