Mathematical Approaches to Interfacial Dynamics in Complex Fluids (17w5057)

Arriving in Banff, Alberta Sunday, June 25 and departing Friday June 30, 2017


(Purdue University)

(Penn State University)


The general objective of this workshop is to bring together the leading and up-and-coming researchers in soft matter and interfacial dynamics, across several disciplines, to foster awareness and the cross-disciplinary transfer of ideas.

The problem of interfacial dynamics in complex fluids is clearly multi-disciplinary. But so far the work done by mathematicians, engineers, physicists and biologists has largely been independent of one another. The sharp-interface methods have been used extensively by physicists and engineers, while the interface regularization methods have been developed mostly by mathematicians. Experimentalists, on the other hand, have documented the physical and biological processes and identified the most important problems that need to be solved. However, researchers across the disciplines have so far seldom had the chance to interact and learn of each other's work. This is at least partly owing to the lack of a forum that can attract the full range of researchers tackling such problems from different angles and within different scientific communities. For instance, few mathematicians and fluid dynamicists attend rheology and biology meetings regularly where many practical applications are discussed. Conversely, engineers, rheologists and material scientists rarely participate in applied mathematics conferences and workshops dealing with moving internal boundaries.

The two organizers recognize this disconnect because they come from very different backgrounds. Chun Liu is an applied mathematician who is familiar with the state-of-the-art of the mathematical developments on moving boundary problems and complex fluids. Jie Shen specializes in numerical analysis and algorithm development, and has contributed to the recent advances in diffuse-interface theories. Recent visits and discussions among us brought about the realization that a tremendous advantage can be gained in the area of interfacial dynamics in complex fluids if researchers from different backgrounds are brought together, and shown the wide range of problems and newly developed methods. Linkage can then be developed between mathematical tools and applied problems, probably after adaptation and fusion with other ideas and techniques. Thus, interfacial dynamics in complex fluids clearly forms an important subject ripe for a coordinated theoretical, numerical and experimental effort. Interaction and collaboration among researchers in diverse disciplines will greatly catalyze this effort. In this sense, the proposed workshop is particularly timely.

Toward the above objective, we have designed the scope of the workshop to contain both a mathematical and an applied component. The former will address 3 aspects of mathematics:
* Analysis, e.g. singularity regularization, convergence, sharp interface limit
* Modeling, e.g. boundary conditions, wall-interface interaction, Q-tensor theory, multi-scale modeling, multi-component models
* Computation, e.g. phase-field, volume-of-fluid and level set algorithms, Cahn-Hilliard-Navier-Stokes solvers, error analysis, parallelization and optimization

On the applied side, the workshop will feature experts on a diverse array of problems, including
* Viscoelastic interfacial flows, including capillarity
* Electrokinetic flows on liquid interfaces and solid surfaces
* Magnetic and ferrofluids: interfacial dynamics under external fields
* Transport of charged particles through plasma membranes
* Liquid crystallinity in soft matter, including biological tissue
* Interfaces in living matter, including cells, tissues and self-propelled suspensions

We expect the following concrete outcomes from the workshop:

(1) To survey the state of the art on "Interfaces in Complex Fluids", and highlight it as an important emerging area in mathematics and applied science. Experimentalists will describe recent observations and measurements on processes such as moving contact-lines, interfacial rheology, Marangoni flows and self-assembly on interfaces. Theoreticians and numerical analysts will summarize the predictive capabilities of their models, including fixed- and moving-grid numerical methods, incorporating continuum and molecular theories. We will encourage the two sides to "compare notes" and come up with a common understanding of our current knowledge in this area.

(2) To identify the most pressing scientific issues. Experimentalists will underscore phenomena that cannot be readily rationalized or explained. These might include interfacial stretching and rupture, thermally or chemically modulated tip-streaming and surface-directed self-assembly. Modelers and simulators will define the limitations of various theoretical and numerical methods, and explore multi-scale modeling for singular events such as moving contact-lines and topological changes.

(3) To develop promising research strategies for the future. The workshop will expose application-oriented people to rigorous theories and computational tools that can be adapted for their specific problems, and to introduce theorists to puzzling observations and complex engineering issues and challenge them to develop a framework to understand these phenomena. We hope this effort will result in a list of problems recommended for concerted theoretical, numerical and experimental investigations.

(4) To facilitate the pursuit of these strategies by initiating inter-disciplinary collaborations. We envision broad and lively discussions of all the theoretical analysis, modeling and computational methodologies, experimental discoveries and new and existing applications. Out of the discussions, we hope, collaborations will naturally grow between researchers with complementary skills and expertise. In particular, younger scientists will benefit from direct interactions with more established experts, and from the opportunity to integrate or distinguish themselves in this exciting multi-disciplinary community. We have compiled a stellar and diverse roster for the workshop. We have invited the mathematical experts on each class of methods as well as leading physicists, engineers and biologists known for their expertise in complex fluids and interfacial dynamics. In the meantime, we have also included a significant number of younger researchers, with the aim of providing them with essential tools and techniques that they would not normally encounter within their own institutions and research groups. So far 36 invitees have tentatively accepted the invitation, pending on determination of the workshop's timing. In the event that time conflict prevents some from attending, we have also compiled a “waiting list” of a dozen people. We are confident that this workshop will gather an exceptionally strong group of scientists and achieve the objectives outlined above.