# Latest papers in fluid mechanics

### On formation of dry spots in heated liquid films

Here, the phenomenon of food sticking when frying in a frying pan is experimentally explained. Thermocapillary convection causes a dry spot formation in the center of the frying pan upon heating of the sunflower oil film. It is shown that the speed of formation of a dry spot is similar to the speed of receding motion of the edge of a droplet upon impact and spreading on a solid surface. This allows theoretical determination of the speed of dewetting. For the thin liquid film flowing vertically over a solid surface, the critical volumetric flow rate qcr partitions two regimes: metastable or subcritical, when small perturbation of the film free surface results in the film rupture (q < qcr) and stable or supercritical at q > qcr. For the falling thin liquid film, the critical volumetric flow rate qcr partitions two regimes: metastable or subcritical (q < qcr) and stable or supercritical at q > qcr. At q < qcr, small deformations of the film free surface result in the film rupture. For the case of the temperature distribution in the form of a unit step function, the fundamental solution G1(x) describing the deformation of the film free surface has been derived by the perturbation technique. This solution is important by itself since it describes the most “dangerous” film surface profile at a prescribed value of the temperature drop. For an arbitrary surface temperature distribution θ (ξ), the convolution of G1(ξ) and θ ′(ξ) yields the film thickness profile.

### Squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids

Author(s): Santiago G. Solazzi, Beatriz Quintal, and Klaus Holliger

Mechanical waves, which are commonly employed for the noninvasive characterization of fluid-saturated porous media, tend to induce pore-scale fluid pressure gradients. The corresponding fluid pressure relaxation process is commonly referred to as squirt flow and the associated viscous dissipation ca...

[Phys. Rev. E 103, 023101] Published Mon Feb 01, 2021

### Delaying leading edge vortex detachment by plasma flow control at topologically critical locations

Author(s): Johannes Kissing, Bastian Stumpf, Jochen Kriegseis, Jeanette Hussong, and Cameron Tropea

Leading edge vortices on flapping wings induce high transient lift during their growth phase and increase maneuverability at low flight speeds. A hypothesis is developed and experimentally validated that the vortex growth phase on a pitching and plunging airfoil can be prolonged with dielectric barrier discharge plasma actuators. This is demonstrated for various airfoils and for different motion dynamics and kinematics.

[Phys. Rev. Fluids 6, 023101] Published Mon Feb 01, 2021

### Control of viscous fingering: From the perspective of energy evolution

Author(s): Hongzhi Ma and Quanzi Yuan

An energy model is developed to describe the linear viscous fingering (VF) phenomena from the perspective of evolution paths of energy dissipation rate. By means of the variational method, rate-altering control schemes with different scaling laws are constructed in the energy model to control whether the VF instability develops or is suppressed. Furthermore, a stable and continuous forward movement of the fluid-fluid interface is achieved through a periodic suppression scheme. The effectiveness of the energy model and all control schemes are well verified by our experiments.

[Phys. Rev. Fluids 6, 023901] Published Mon Feb 01, 2021

### Phase separation of an ionic liquid mixture assisted by a temperature gradient

Author(s): Marc Pascual, Arthur Poquet, Alexandre Vilquin, and Marie-Caroline Jullien

To aid in the recycling of ionic liquids, a method that takes advantage of capillary phenomena at small scales is presented. The phase separation is performed in a temperature gradient by the joint effects of sedimentation and thermocapillary actuation. This gives rise to a complex three-dimensional flow structure, which is quantitatively captured by our model.

[Phys. Rev. Fluids 6, 024001] Published Mon Feb 01, 2021

### Role of viscoelasticity on the dynamics and aggregation of chemically active sphere-dimers

The impact of complex media on the dynamics of active swimmers has gained a thriving interest in the research community for their prominent applications in various fields. This paper investigates the effect of viscoelasticity on the dynamics and aggregation of chemically powered sphere-dimers by using a coarse-grained hybrid mesoscopic simulation technique. The sphere-dimers perform active motion by virtue of the concentration gradient around the swimmer’s surface, produced by the chemical reaction at one end of the dimer. We observe that the fluid elasticity enhances translational and rotational motion of a single dimer; however, for a pair of dimers, clustering in a particular alignment is more pronounced. In the case of multiple dimers, the kinetics of cluster formation along with their propulsive nature is presented in detail. The key factors influencing the enhanced motility and the aggregation of dimers are the concentration gradients, hydrodynamic coupling, and the microstructures present in the system.

### Computational fluid-structure interaction of a restrained ogive-cylindrical body with a blunt elliptical base at a high incidence

Author(s): Mark Ishay, Oded Gottlieb, and David Degani

The fluid-structure interaction of an elastically restrained inclined tangent ogive-cylindrical body with a blunt elliptical base is investigated numerically. The flow is three-dimensional, compressible, and laminar, and the slender body is allowed to yaw at high incidence. The resulting response exhibits an intricate bifurcation structure that includes bistable periodic (finite amplitude) and nonstationary (small amplitude) limit cycles for moderate angles of attack, and nonstationary (finite amplitude) oscillations for high angles of attack.

[Phys. Rev. Fluids 6, 014401] Published Fri Jan 29, 2021

### Roughness, inertia, and diffusion effects on anomalous transport in rough channel flows

Author(s): Seonkyoo Yoon and Peter K. Kang

Fluid flow and mass transport in rough channels are ubiquitous phenomena occurring in numerous engineering applications and natural processes. Comprehensive numerical simulations and stochastic upscaling elucidate how the complex interplay between channel roughness, inertia, and diffusion controls solute transport in channel flows. A mechanistic link between the complex interplay and anomalous transport in rough channel flows is successfully established.

[Phys. Rev. Fluids 6, 014502] Published Fri Jan 29, 2021

### Semi-conditional variational auto-encoder for flow reconstruction and uncertainty quantification from limited observations

We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The proposed model is a version of a Conditional Variational Auto-Encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty quantification of the prediction. We show that in our model, conditioning on measurements from the complete flow data leads to a CVAE where only the decoder depends on the measurements. For this reason, we call the model semi-conditional variational autoencoder. The method, reconstructions, and associated uncertainty estimates are illustrated on the velocity data from simulations of 2D flow around a cylinder and bottom currents from a simulation of the southern North Sea by the Bergen Ocean Model. The reconstruction errors are compared to those of the Gappy proper orthogonal decomposition method.

### An engineering application of Prosperetti and Lezzi equation to solve underwater explosion bubbles

The dynamic behaviors of underwater explosion bubbles differ for different explosives. The explosive characteristic parameters will result in a greater impact on the motion characteristics of the bubbles. Based on the bubble dynamics equation established by Prosperetti and Lezzi [“Bubble dynamics in a compressible liquid. Part 1. First-order theory,” J. Fluid Mech. 168, 457âĂŞ-478 (1986); “Bubble dynamics in a compressible liquid. Part 2. Second-order theory,” J. Fluid Mech. 185, 289âĂŞ-321 (1987)], we proposed an initial condition and an equation of state (EOS) form applicable for calculating the underwater explosion bubble dynamics of different explosives. With the assumption of instantaneous detonation and initial shock wave formation at the gas–liquid boundary, we calculated the initial state of the bubble boundary and established the initial condition for calculating explosion bubbles. Using the Jones–Wilkins–Lee EOS for different explosives, we constructed an isentropic EOS with a polytropic exponent that varied with density. We calculated and analyzed the differences in the initial expansions and the subsequent oscillations of underwater explosion bubbles with different explosives as well as the effects of different explosive parameters on the explosion bubble dynamics. This study showed that the proposed initial condition and the EOS form with a polytropic exponent that varied with density yielded good calculation accuracy and achieve close association of the underwater explosion bubbles with the properties of the explosive detonation and the characteristics of the detonation products. In addition, the explosion bubbles differed in the initial expansion, where the bubbles produced by explosives with higher densities and greater detonation velocities expanded more rapidly.

### Axisymmetry breaking, chaos, and symmetry recovery in bubble film thickness profiles due to evaporation-induced Marangoni flows

Understanding the dynamics of evaporating thin liquid films is of practical and fundamental interest. Practically, this understanding is crucial for tuning bubble stability, while fundamentally thin films are an excellent platform to study the characteristics of evaporation-driven two-dimensional (2D) flows. Here, we experimentally study, across a wide range of volatile species concentrations (c0), the spatial and temporal dynamics of film thickness profiles [h(r, θ, t)] over bubbles in binary liquid mixtures subjected to evaporation-induced Marangoni flows. Initially, we probe the spatial structure and show that the spatial symmetry of the film thickness profiles is non-monotonic functions of volatile species concentration with profiles being axisymmetric for both very low (∼1%) and very high (∼90%) concentrations. The temporal evolution of the film thickness fluctuations reveals a similar non-monotonic dependence between the species concentration and the spatial prevalence of fluctuation stochasticity. At a tested intermediate species concentration of 50%, we observe a complete breakdown in spatial symmetry and obtain film thickness fluctuations that are chaotic everywhere in space with spatially invariant fluctuation statistics and rapidly decaying spatial correlation. The observed non-monotonic behavior is a result of the system sensitivity to ambient perturbations scaling as Δγc0(1 − c0)/μ, where Δγ is the difference in equilibrium surface tension between the two species in the mixture and μ is the dynamic viscosity. These insights along with the reported experimental setup serve as an excellent platform to further investigate evaporation-driven 2D chaotic flows.

### Droplet breakup and coalescence of an internal-mixing twin-fluid spray

Droplet breakup and collision dynamics of an internal-mixing twin-fluid (air-assisted) spray were investigated experimentally. Time-resolved spray morphological evolutions were obtained by employing a high-speed spray visualization system, while droplet size and velocity were measured by using a phase-Doppler particle analyzer. The results show that the air-assisted spray is composed of a bulk of tiny droplets entrained by high-speed gas-phase flow. Droplets with a diameter of less than 5 µm account for the majority of samples on the basis of the distribution function. The calculated Stokes numbers of selected tracer droplets (0 µm–5 µm) show that these droplets tend to follow the air flow faithfully and thus can be used to estimate the local air flow velocity. By comparing with the critical Weber number, we found that droplet shear breakup is absent, but some droplets may undergo turbulent breakup. A theoretical analysis accounting for the effects of the turbulent dissipation rate on both droplet breakup and coalescence was performed, and the critical equilibrium length of breakup and coalescence is found to be less than 3.0 mm. In terms of droplet collision dynamics in the spray far-field, coalescence dominates droplet collision outcomes; therefore, the droplet size increases linearly as the spray downstream distance X increases. Particularly, the influence of the droplet size ratio [C. Tang, P. Zhang, and C. K. Law, “Bouncing, coalescence, and separation in head-on collision of unequal-size droplets,” Phys. Fluids 24, 022101 (2012)] was adopted to quantify the droplet coalescence probability. When compared to the n-octane spray, the n-dodecane spray accounts for more droplet bouncing (II) since n-dodecane possesses a relatively larger bouncing (II) region.

### Dynamic permeability of fluids in rectangular and square microchannels: Shift and coupling of viscoelastic bidimensional resonances

Pulsatile dynamics of Newtonian and Maxwellian fluids is exactly solved by theoretical analytical means when confined within rectangular microchannels subject to oscillatory driving forces. The analytical solution exhibits a complex behavior caused by the fluid dynamics along the smallest and the secondary confinement dimensions. For Newtonian fluids, the maximum and average flow velocities within the microchannel differ considerably from the ones predicted by simplified one-dimensional models when fluids are subject to moderate and high driving force frequencies. This is caused by the stagnation of flow velocity in the vicinity of the channel walls at the secondary confinement dimension. For Maxwellian fluids, the secondary confinement incorporates flow resonances that are coupled to the ones caused by the smallest confinement, leading to a shift of the main resonance and the arising of resonances when bidimensional vibration modes are excited. These effects depend on the aspect ratio between channel width and height and on the magnitude of the driving force frequency, compared to the characteristic viscous frequency of the microchannel. The theoretical results are compared with recent experimental results in the literature in pulsatile microfluidics for hyaluronic acid solutions with viscoelastic properties, as well as for water. In both cases, an agreement is found between theoretical and experimental results.

### Numerical study of droplet motion on discontinuous wetting gradient surface with rough strip

The self-transport of a droplet on a wetting gradient surface is of great importance in understanding the mechanism of surface coating and the design of numerous functional surfaces. Although it is known that the wetting gradient and surface condition are the main factors that influence the droplet transport, the effect of roughness on the motion on a discontinuous wetting gradient surface is worth further study. In this work, a numerical model based on the front tracking method was utilized to investigate the droplet’s motion on such surfaces. The capillary number Ca and the mass center [math] were recorded to scale the transient speed and trace the motion, respectively. The self-transport under two regimes of driving forces for different smooth strip lengths is analyzed, and it is found that the roughness has a significant influence on the transport velocity and stability of the motion. Regimes of droplet crossing states are plotted for the roughness η and the wettability difference Δθ between two adjacent regions. The regime plot shows that the transport modes for droplets on discontinuous wetting gradient surfaces depend on the surface roughness.

### Numerical and experimental investigation into the dynamics of a bubble-free-surface system

Author(s): N. Bempedelis, J. Zhou, M. Andersson, and Y. Ventikos

The interaction between an oscillating bubble and a free surface is experimentally and computationally investigated. The evolution of the free surface is characterized by measuring the surface area and the volume of the jets that are formed at the free surface.

[Phys. Rev. Fluids 6, 013606] Published Thu Jan 28, 2021

### Erratum: “Oscillation of a bubble in a liquid confined in an elastic solid” [Phys. Fluids 29, 072101 (2017)]

### Velocity of suspended fluid particles in a low Reynolds number converging flow

We studied a pressure-driven, low Reynolds number fluid flow through a planar channel whose spanwise width along the flow varied inversely as the streamwise coordinate such that the extensional rate on the centerline was near constant. The effect of the near constant extensional rate on an immiscible droplet of silicone oil was studied by tracking its deformation. The droplet rapidly deformed into an ellipsoid and displayed a consistent lag velocity compared to the single phase background flow at the same point. The observations were attributed to the flow induced deformation of the immiscible droplet, which was a function of the magnitude of the initial capillary number. The streamwise component of the single phase velocity along the centerline of the converging flow was also estimated as leading order using lubrication theory. The estimated velocity is compared favorably with numerical simulations; validation with experimental measurement of the flow of castor oil through the channel by tracking tracer particles is performed. The accuracy of the determination of the velocity field by the lubrication theory allowed for the careful measurement of the velocity difference between the drop and suspended fluid velocities. This research validated lubrication theory predictions of the flow velocity through a converging channel and provided an experimental insight into the behavior of a suspended phase.

### Effect of liquid depth on dynamics and collapse of large cavities generated by standing waves

The effect of fluid depth on the collapse of large cavities generated by over-driven axisymmetric gravity waves in a 10 cm diameter cylindrical container has been studied. At a large fluid depth in a viscous glycerine–water solution, the collapse of the cavities is inertia dominant at the initial phase with the time-dependent cavity radius (rm) obeying rm ∝ τ1/2; τ = t − t0 being the time remaining for collapse, with t0 being the time at collapse. However, enhanced damping at a low liquid depth turns the late stage of the transition into the viscous regime (rm ∝ τ) at some critical depth beyond which a singular collapse (transition from non-pinch-off and pinch-off collapse) is impossible. At a shallow depth, the change in cavity radius follows a flip of the power law, i.e., rm ∝ τ at the initial stage of collapse followed by a transition to rm ∝ τ1/2, suggesting a viscous–inertial transition. For fluids with relatively lower viscosity but similar surface tension, here water, a smoother cavity with damped parasitic waves at a small liquid depth collapses at a smaller radius. The surface jet velocity due to the collapse of the cavity monotonically decreases with the decrease in the depth, whereas in the case of water, it increases with the depth reaching a maximum at a critical depth followed by a decrease again. The self-similarity, exhibited by the cavity up to the critical depth, is lost due to the axial movement restriction by the bottom wall.

### Vapor condensation in Rayleigh–Bénard convection

In this work, the condensation process in the Rayleigh–Bénard convection is studied by a combination of theoretical analysis and numerical simulations. Depending on the domain size, three different patterns, namely, no condensation, critical condensation, and periodic condensation, are identified. By applying the order analysis to the energy equation, we show that the heat fluctuation is responsible to overcome the energy barrier of condensation and thus propose a new dimensionless number to describe the critical condition of condensation, which corresponds to zero value of the heat fluctuation. In addition, through the order analysis, a scaling law is established to quantify the condensation period when periodic condensation occurs. The scaling relations derived from the order analysis are well validated by the hybrid lattice Boltzmann finite difference simulations, where the Rayleigh number and the Prandtl number vary over the ranges of 104 ≤ Ra ≤ 106 and 1 ≤ Pr ≤ 10, respectively.

### Mixing and unmixing induced by active camphor particles

Author(s): Clément Gouiller, Florence Raynal, Laurent Maquet, Mickaël Bourgoin, Cécile Cottin-Bizonne, Romain Volk, and Christophe Ybert

Small colloidal floaters are poured at the air-water interface of a tank stirred by many camphor swimmers. The system rapidly reaches a statistically stationary state, resulting in competition between (i) efficient stirring by the disordered motion of the swimmers and (ii) unmixing promoted by the chemical cloud attached to each individual self-propelled disk.

[Phys. Rev. Fluids 6, 014501] Published Wed Jan 27, 2021