High-Reynolds-number droplets: the internal flow instability and its link with path instability

Pengyu Shi is a fresh FNRS Postdoctoral Researcher at the TIPs lab, working under the supervision of Prof. Benoit Scheid. His current research focuses on surfactant effects in microfluidics, in particular on how surfactants influence droplet generation and cross-stream migration.
Pengyu obtained his PhD from Technische Universität Dresden, Germany, in 2021, where he studied the behaviour of bubbles and particles in inhomogeneous flows. He then continued as a postdoctoral researcher at the Institut de Mécanique des Fluides de Toulouse (IMFT), France, investigating the flow and path instabilities of single droplets using direct numerical simulations. He will be the speaker of the seminar.

This seminar will present key results from his recent work at IMFT Toulouse, where he investigated how internal flow dynamics influence the buoyancy-driven rise trajectories of droplets.
Bubbles, droplets, and particles with axisymmetric shapes may follow various non-vertical paths when rising or falling freely in a fluid otherwise at rest. One of the key causes of path instability is the flow instability that occurs beyond a critical Reynolds number, even if the body is translating with constant speed and orientation. For bubbles and particles, the flow inside the body is either irrelevant or absent, and flow instability typically originates in the near wake. For droplets—particularly those with a viscosity ratio of O(1)—the internal and external flow fields are strongly coupled, and asymmetry may originate and grow initially inside the droplet before it breaks the axisymmetry of the entire flow. This scenario, which we refer to as an internal flow instability, is the central theme of this talk.

The talk consists of two parts. In Part 1, I will discuss the identification of this internal flow instability by considering a uniform flow past a fixed spherical droplet. The results, obtained using the JADIM code developed at IMFT Toulouse in France, allow us to examine the time evolution of the flow structure following the onset of instability, its influence on the drag and lift forces acting on the droplet, and the parametric conditions under which the instability may arise.

In Part 2, I will show the connection between the internal flow instability and the path instability when the droplet is free to move. This is achieved by studying a toluene droplet rising freely in water, with simulations performed using the Basilisk code and its built-in adaptive mesh refinement. We show that as the droplet radius RRR increases, the first path instability sets in at a critical radius RcR_cRc​ that coincides with that of the internal flow instability. Detailed examination of the temporal evolution of the three-dimensional flow field inside and around the freely rising droplet further confirms the close link between the two instabilities.