Francesco Romanò

Tracking particles in flows near invariant manifolds via balance functions

Particle moving inside a fluid near, and interacting with, invariant manifolds is a common phenomenon in a wide variety of applications. One elementary question is whether we can determine once a particle has entered a neighbourhood of an invariant manifold, when it leaves again. Here we approach this problem mathematically by introducing balance functions, which relate the entry and exit points of a particle by an integral variational formula. We define, study, and compare different natural choices for balance functions and conclude that an efficient compromise is to employ normal infinitesimal Lyapunov exponents. We apply our results to two different model flows: a regularized solid-body rotational flow and the asymmetric Kuhlmann–Muldoon model developed in the context of liquid bridges. To test the balance function approach, we also compute the motion of a finite size particle in an incompressible liquid near a shear-stress interface (invariant wall), using fully resolved numerical simulation. In conclusion, our theoretically developed framework seems to be applicable to models as well as data to understand particle motion near invariant manifolds.

Limit cycles for the motion of finite-size particles in axisymmetric thermocapillary flows in liquid bridges

The motion of a small spherical particle of finite size in an axisymmetric thermocapillary liquid bridge is investigated numerically and experimentally. Due to the crowding of streamlines towards the free surface and the recirculating nature of the flow, advected particles visit the free surface repeatedly. The balance between centrifugal inertia and the strong short-range repulsive forces a particle experiences near the free surface leads to an attracting limit cycle for the particle motion. The existence of this limit cycle is established experimentally. It is shown that limit cycles obtained numerically by one-way-coupled simulations based on the Maxey–Riley equation and a particle–surface interaction model compare favorably with the experimental results if the thickness of the lubrication gap between the free surface and the surface of the particle is properly taken into account.

The Lid-Driven Cavity

The lid-driven cavity is an important fluid mechanical system serving as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes which are driven by the tangential motion of a bounding wall. A comprehensive review is provided of lid-driven cavity flows focusing on the evolution of the flow as the Reynolds number is increased. Understanding the flow physics requires to consider pure two-dimensional flows, flows which are periodic in one space direction as well as the full three-dimensional flow. The topics treated range from the characteristic singularities resulting from the discontinuous boundary conditions over flow instabilities and their numerical treatment to the transition to chaos in a fully confined cubical cavity. In addition, the streamline topology of two-dimensional time-dependent and of steady three-dimensional flows are covered, as well as turbulent flow in a square and in a fully confined lid-driven cube. Finally, an overview on various extensions of the lid-driven cavity is given.

Oscillatory switching centrifugation: dynamics of a particle in a pulsating vortex

The dynamics of a small rigid spherical particle in an unbounded pulsating vortex is considered, keeping constant the particle Stokes number St and varying the particle-to-fluid density ratio

Numerical investigation of the interaction of a finite-size particle with a tangentially moving boundary

\varrho

Particle–boundary interaction in a shear-driven cavity flow

and the pulsation frequency of the vortex

Smoothed-profile method for momentum and heat transfer in particulate flows

\omega

Topology of three-dimensional steady cellular flow in a two-sided anti-parallel lid-driven cavity

. We show that the asymptotic dynamics of a particle of given St and

Cellular flow in a partially filled rotating drum: regular and chaotic advection

\varrho

Finite-size Lagrangian coherent structures in thermocapillary liquid bridges

can be controlled by varying