Capturing Liquid-Liquid Phase Separation Through a Continuum Model
Research Summary: We developed a continuum reaction–diffusion model that connects microscopic interactions with macroscopic liquid-liquid phase separation, revealing mechanisms governing droplet formation, growth, coarsening, and spatial organization.
Researcher Spotlight
Dr. Nayana Mukherjee is a mathematician and researcher working on mathematical modelling, nonlinear dynamics, reaction–diffusion systems, and interdisciplinary applications of mathematics in physical and biological sciences.
Linkedin: https://www.linkedin.com/in/nayana-mukherjee-01b83647/
Instagram: https://www.instagram.com/09nayana90/
Lab PI name: Dr. Jagannath Mondal
University: Tata Institute of Fundamental Research (TIFR) Hyderabad
Lab social media: https://www.tifrh.res.in/~jmondal/people/
Dr. Pushpita Ghosh
University: IISER Thiruvananthapuram
What was the core problem you aimed to solve with this research?
Liquid-liquid phase separation (LLPS) is a fundamental process through which a homogeneous mixture separates into distinct dense and dilute phases. It plays an important role in biological systems, including the formation of membraneless cellular compartments, as well as in a variety of materials and chemical systems.
A major challenge is to understand how molecular-level interactions translate into the large-scale spatial patterns and dynamics observed during phase separation. Existing models can capture important aspects of LLPS, but there is a need for computationally efficient continuum frameworks that can incorporate multiple interacting components and capture experimentally relevant spatial structures.
Our aim was to develop such a continuum framework and use it to understand the mechanisms governing the formation and evolution of phase-separated droplets.
How did you go about solving this problem?
We formulated a multi-component continuum reaction–diffusion model to describe the coupled evolution of dilute and dense phases. The model incorporates diffusion, interconversion between different phases, nonlinear interactions, and stochastic fluctuations.
We then systematically explored how parameters such as diffusivity and interconversion kinetics influence nucleation, droplet growth, coarsening, and spatial organization. Numerical simulations were used to map the different dynamical regimes and identify the conditions under which distinct phase-separated structures emerge.
This approach allowed us to connect microscopic interaction mechanisms with macroscopic patterns without requiring computationally expensive simulations at molecular scales.
“Our model connects microscopic interactions with macroscopic phase separation, offering a transparent framework to understand and control complex condensate dynamics.” – Dr. Jagannath Mondal & Dr. Pushpita Ghosh
How would you explain your research outcomes (Key findings) to the non-scientific community?
Imagine a mixture that initially looks completely uniform but gradually separates into droplets, much like oil separating from water. Our model helps explain how these droplets appear, grow, interact, and eventually reorganize over time.
We found that the rate at which molecules move through the dilute phase can strongly influence droplet formation. We also found that faster exchange between dilute and dense phases can accelerate the growth of large droplets at the expense of smaller ones.
One particularly interesting result was that our model naturally produced ring-like dilute regions around the dense droplets. We also found that random fluctuations, or “noise”, can accelerate phase separation.
What are the potential implications of your findings for the field and society?
The work provides a mathematical framework for understanding LLPS at experimentally relevant spatial and temporal scales while retaining information about the underlying interactions.
Because LLPS is relevant to biological organization, biomolecular condensates, chemical systems, and advanced materials, a better understanding of the mechanisms controlling phase separation may ultimately help researchers understand and control these processes in different applications.
Our framework may also provide a useful computational tool for exploring how changes in diffusivity, reaction kinetics, and fluctuations influence phase-separated structures. The model is intended primarily as a theoretical and computational framework, and further experimental validation would be required before applying specific predictions to particular biological or materials systems.
What was the exciting moment during your research?
One of the most exciting moments was when the simulations produced the ring-like dilute-phase shells around the dense condensates. This was particularly interesting because such structures emerge naturally from the multi-component interactions in our model and are not captured by conventional single-field phase-separation models.
Seeing the model generate such a nontrivial spatial structure from the underlying equations was a particularly rewarding moment in the study.
Paper reference/citation (with link): Mukherjee, N., Wasim, A., Mondal, J. & Ghosh, P. (2026). Capturing the essence of liquid–liquid phase-separation at macroscopic scales via a continuum model. Physical Chemistry Chemical Physics, 28, 18025–18039. https://doi.org/10.1039/D6CP01106C
