Physical systems consisting of an elastic matrix permeated by fluid mixture are ubiquitous, with examples ranging from morphogenesis of a single biological cell to the migration of greenhouse gases in sediments \[1, 2\]. Recent experimental studies show that the presence of the elastic resistance in these systems significantly alters their phase separation response by imposing an energetic cost to the growth of minority-phase droplets \[3\]. However, a quantitative understanding of the role played by elasticity is lacking. Our study bridges this gap by building a comprehensive theoretical framework to analyze the effect of elasticity on the phase separation of a binary mixture in soft nonlinear solids. We employ an energy-based approach that captures both the short-time quasi equilibrium and the long-time evolution of the phase separation, in elastically homogeneous as well as heterogeneous materials. We use this approach to determine the constitutive sensitivities of the phase-separation response. At the short timescale, we predict an arrested phase-separation, resulting in a uniform distribution of the minority-phase droplets. At the long timescale, we predict a long-range migration of the minority phase in heterogeneous materials, which may give rise to a droplet dissolution front. Crucially, we also find a nonlinear effect of elasticity on the dynamics, which challenges the current understanding in the literature. We quantify the thermodynamic driving forces to identify a non-dimensional *dissolution number* that captures the tendency of droplets to re-mix. Based on the dissolution number, we are able to classify the dynamics of the system into diffusion-limited and dissolution-limited regimes. 

This work highlights the importance of elasticity as a potential regulating mechanism for controlling solubility and phase-separation in various physical settings. Tuning the elastic properties of the matrix material can impart control over the stable droplet distribution for industrial applications, it can drive the formation of membraneless organelles in biological settings, and can aﬀect the transport of potent greenhouse gases in soil. Although these systems may diﬀer in lengthscales and diﬀusion properties, given the elastic properties, their long-time evolution can be qualitatively predicted based on the value of their dissolution number.

 

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.  
\[2\] Abegg, Friedrich, and Aubrey L. Anderson. "The acoustic turbid layer in muddy sediments of Eckernfoerde Bay, Western Baltic: methane concentration, saturation and bubble characteristics." *Marine Geology* 137.1-2 (1997): 137-147.  
\[3\] Rosowski, Kathryn A., et al. "Elastic ripening and inhibition of liquid–liquid phase separation." *Nature Physics* (2020): 1-4.

 


Effect of Elasticity on Phase Separation in Heterogeneous Systems

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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