Phase separation is observed across scales and in a variety of physical processes that range from the fields of biology to metallurgy. Liquid-liquid phase separation and subsequent species migration is understood to be a crucial mechanism for regulating the normal bodily functions of a cell. For instance, P-granule assembly is believed to employ phase separation as a mechanism to polarize the cell along its anterior-posterior axis as a precursor to cell differentiation [1]. The dynamics of this process is dependent on the cytoplasm and its properties. Similarly, phase separation phenomena are commonly observed in metals [2,3]. In the case of metals, elastic fields in the matrix are well known to affect the phase transitions; they can either inhibit or promote the growth of precipitates [4]. While important work has been carried out, both experimentally and theoretically, in understanding the elastic effects on phase separation and species migration in soft-material systems, a quantitative understanding of the dynamics of these processes still presents many challenges. In practical applications, the matrix properties are often heterogeneous, and the phase separation process is sensitive to these non-uniformities. In this talk, we will present the theory of phase separation with nonlinear elastic effects and apply it to provide quantitative predictions for the phase separation of a binary liquid mixture in a crosslinked polymer. We will discuss how elasticity arrests phase separation in such a system, leading to a distribution of uniform-sized droplets in the polymer. Over a longer timescale, this distribution becomes unstable in a heterogeneous sample, resulting in a propagating droplet mixing front (as experimentally reported in [5]). We will discuss how elasticity controls the droplet size and the speed of the front, a potentially important mechanism for biological systems like cells to actively control rate of material transport.

References

[1] Brangwynne, Clifford P., et al. "Germline P granules are liquid droplets that localize by controlled dissolution/condensation." Science 324.5935 (2009): 1729-1732.
[2] Rao, C. N. R., P. V. Vanitha, and Anthony K. Cheetham. "Phase separation in metal oxides." Advances In Chemistry: A Selection of CNR Rao's Publications (1994‚Äì2003). 2003. 37-44.
[3] Edwards, Peter P., and M. J. Sienko. "Phase separation in metal solutions and expanded fluid metals." Journal of the American Chemical Society 103.11 (1981): 2967-2971.
[4] Johnson, W. C. "On the elastic stabilization of precipitates against coarsening under applied load." Acta Metallurgica 32.3 (1984): 465-475.
[5] Rosowski, Kathryn A., et al. "Elastic ripening and inhibition of liquid‚Äìliquid phase separation." Nature Physics (2020): 1-4.


DYNAMICS OF PHASE SEPARATION WITH NONLINEAR ELASTIC EFFECTS

The Virtual Technical Meeting of the Society of Engineering Science 2020 is the first fully virtual meeting of the SES community to envision and connect during the hiatus created by Covid-19, providing a platform for the exchange of ideas, and to showcase the latest research in the field of engineering science.

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