Fluid flows with interactive boundaries

One of the most fascinating and non-intuitive class of problems in fluid mechanics are those involving the interplay between dynamic boundaries and fluid flows. The coupling between the dynamics of the fluid and the kinematics and mechanics of the boundaries in these situations often gives rise to unexpected behaviours that are of paramount importance in many engineering, biological and biomedical contexts. The study of problems involving fluid flows with interactive boundaries have been the focus of the field in the past two decades, to the extent that many examples of such problems have frequently appeared on the cover of recent editions of fluid mechanics journals and textbooks. This relatively new and exciting frontier in fluid mechanics is also highly interdisciplinary and has attracted many engineers and scientists alike.

This special issue of the European Journal of Computational Mechanics is dedicated to selected studies that use theory and numerical simulation to investigate the interaction of flowing fluid with complex and dynamically changing boundaries. The invited contributions cover a wide variety of topics ranging from mucociliary transport, fish locomotion, hydrodynamics of self-propelled particles, and particle motion in acoustic fields to deformation of elastic capsules in shear flows, fluttering of piezoelectric plates, dynamics of wave energy converters, and droplet coalescence on microstructured substrates. However, the selection is not meant to be comprehensive, but rather illustrative of applications of fluid flows with moving boundaries and theoretical and numerical methods used to advance the field. In the following, we outline the main objectives and findings of the articles.

Guo and Kanso examine the performance of beating cilia in healthy and diseased states. Arranged periodically, the cilia are immersed in a two-layer system consisting of a nearly viscous fluid (periciliary layer) at the bottom and a viscoelastic fluid (mucus layer) on the top. An immersed boundary method is employed to resolve the interaction of the cilia with the host fluids. For the sake of simplicity, only one-way coupling is considered, as the kinematics of the cilia beating is assumed to remain unchanged. The simulations are used to examine the effect of the relative thickness of periciliary and mucus layers on the efficiency of mucus transport by cilia. The results indicate that a depletion of periciliary layer (observed in diseased systems) impedes the rate of mucus removal.

Sprinkle et al. simulate the swimming of a fin-plate model of the so-called median/paired fin fish using a constraint-based immersed body method. The authors investigate the implications of the diagonal fin insertion morphology and motility advantages offered by maintaining a rigid body while only undulating the fins. They quantify the energy expenditure per unit distance travelled for different geometries and find that the swimmers that keep a part of their body rigid have a mechanical advantage via minimising the cost of transport.

Gaojin and Ardekani present a two-dimensional numerical study of undulatory swimming near a solid boundary. The authors consider swimming in Newtonian, shear-thinning and viscoelastic fluids. The swimmer is modelled as a slender filament of finite length and the fluid–structure interaction is handled using a distributed Lagrange multiplier method. The undulatory motion is prescribed in the form of a travelling wave with the undulation amplitude either linearly increasing (kicker) or linearly decreasing (burrower) from the head to the tail of the swimmer. The simulations show that, depending on the amplitude of undulations, three modes of swimming exist, which include strong and weak attractions to, and escape from the wall. The authors also find that the shear-thinning viscosity enhances the swimming speed near the wall whereas the fluid elasticity hinders the swimmer’s propulsion. The combination of the two effects, however, is found to boost the speed of swimming and attraction to the wall.

Daghooghi and Borazjani use a sharp-interface immersed boundary method to explore the motion of an undulating rod-like particle under a shear flow. The extra stress generated due to the motion of this active particle is calculated and based on that, the role of the self-propulsion on the effective viscosity of the fluid is determined. The simulations reveal that, under shear, the active particle undergoes a high-frequency kayaking motion, in contrast to its passive counterpart that solely rotates subject to an external shear flow.

Singh and Adhikari develop a combined boundary-domain integral formulation for the motion of an active colloidal particle undergoing Brownian fluctuations in the presence of a confining solid boundary. Using this formulation, the authors calculate the traction forces and torques on the particle and use them to derive Langevin equations for the Brownian motion of active colloids. They also present the corresponding Smoluchowski equations for the probability distribution functions of the position and orientation of the particles. The derivations demonstrate the breakdown of the typical fluctuation-dissipation theorem as a result of particle activity. The breakdown is shown to give rise to non-Gibbsian distribution of active particles near the wall.

Huang et al. present an idealised, simple mathematical model describing the detection and tracking of a two-dimensional chemical trail by male copepods. The authors establish the criteria for successful tracking and propose a detection algorithm for the trackers that are away from the trail based on the run-and-tumble behaviour of bacteria.

Wang et al. analytically study the motion of microscopic particles induced by an acoustic standing wave. Unlike previous studies, the authors take into account the unsteady inertial forces. They also consider the influence of pair interaction on the trajectory of the particles. The analytical solutions for two particles are obtained using the method of reflections. The results of this investigation improve the predictions of particle trajectory in acoustic-based separation devices.

Banaei et al. numerically model the deformation of an elastic capsule with a stiff nucleus in a simple shear flow. The capsule’s thin and impermeable membrane is modelled as a Neo-Hookean shell. A mixed spectral finite-difference approach is adopted to solve the equations governing the dynamics of capsule and fluid flow around it. The fluid-structure coupling in this approach is handled through an immersed boundary method. The authors utilise their hybrid methodology to probe the effects of the stiff nucleus and viscosity ratio on the deformation of the capsule. They show that the presence of the nucleus and bending resistance of the capsule membrane decrease the capsule deformation.

Xia et al. theoretically analyse energy harvesting from the fluid-induced vibration of flexible plates. The authors examine the coupling between the flow of fluid and the electro-mechanics of a piezoelectric plate. They consider a purely local formulation of the fluid forces and continuous distribution of piezoelectric patches placed along the long side of the plate. The patches are responsible for converting the local deformation into electrical currents that powers an output external circuit. The analyses indicate that placing the output resistance near the edges of the plate leads to optimal energy harvesting scenarios. This finding highlights the importance of the proper placement of energy convertors, such as piezoelectric patches, for the purpose of extracting maximum energy from externally-actuated oscillating structures.

Pathak et al. introduce a high-performance computational framework to study the interaction of wave energy converter (WEC) devices with water waves. The framework integrates a volume-of-fluid approach for solving multi-phase Navier-Stokes equations with a fictitious domain method for resolving the fluid–structure interaction. To facilitate the calculations, the computationally expensive Poisson equation for pressure is solved using a fast multigrid preconditioned solver. The authors employ this methodology to investigate the performance of two surface piercing WECs, namely a bottom-hinged cylinder and a flap. The simulations show that, for small-amplitude oscillations, the conventional force decomposition into inertial and viscous contributions can be used to accurately predict the response of full scale WECs from the results of model experiments.

Lastly, Farokhirad et al. employ a three-dimensional multiphase lattice Boltzmann method to examine the coalescence-induced jumping of liquid droplets on superhydrophobic structured substrates. The authors find that the droplets jumping speed and height is greater on superhydrophobic substrates decorated with a periodic array of square pillars than on flat super-hydrophobic surfaces with a 180° equilibrium contact angle. The phenomenon is attributed to the reduced adhesion between the droplet and the pillared substrate. It is further observed that the initial placement of the droplets on pillared substrates significantly influences the evolution of droplets’ dynamics.

In conclusion, we would like to thank the contributing authors as well as the Editor-in-chief, Hamid Bahai, Associate Editor, Reza Mirzaeifar, reviewers, and editorial staff of the journal for their cooperation and support in producing this special issue.

Guest Editors
Hassan Masoud
Department of Mechanical Engineering, University of Nevada, Reno, NV, USA
[email protected]
Arezoo M. Ardekani
School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA
[email protected]