LIFD Colloquium

Event Schedule

12:00-12:10 Opening

12:10 -12:35 ECR talk1: Droplet dynamics on heterogeneous surfaces. Jiatong Jiang, University of Leeds.

12:35-13:00 ECR talk2: An investigation of the fluid structure interaction arising in articular cartilage across disparate scales. Emily Butler, University of Leeds.

13:00-14:00 Lunch

14:00-15:00  Invited speaker: Problems in viscous fingering. Draga Pihler-Puzovic, University of Manchester.

Draga Pihler-Puzovic from Manchester Center for Nonlinear Dynamics at the University of Manchester. - "Problems in viscous fingering”

Abstract

Growth of complex fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation.  This problem is quasi-two-dimensional and its key information is encapsulated in the interface, so it is relatively simple to study both experimentally and theoretically compared to many other nonlinear phenomena. In this talk we consider two variants of this system.
Firstly, we consider the fingering between plates which are subject to a time-dependent (power-law) plate separation. We demonstrate that in this system the interface can evolve in a self-similar fashion such that the interface shape at a given time is simply a rescaled version of the shape at an earlier time. These novel, self-similar solutions are linearly stable but they only develop if the initially circular interface is subjected to unimodal perturbations. Conversely, the application of nonunimodal perturbations (e.g., via the superposition of multiple linearly unstable modes) leads to the development of complex, constantly evolving finger patterns similar to those that are typically observed between rigid stationery plates. Secondly, we study viscous fingering within a collapsed, compliant channel - a model for pulmonary airway reopening. Depending on the imposed flow rate, we observe a wide variety of finger-tip morphologies, which occur persistently or evolve transiently as the finger propagates. We identify different regimes of finger propagation, dominated by viscous or elastic forces, and highlight the importance of multistability and transient evolution in this system.
We discuss the findings from both systems in the context of understanding disordered front propagation more generally, and their implications for practical problems, such as multiphase flows through multi-generational branching networks with elastic components.