# Latest papers in fluid mechanics

### 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

### The role of entrance functionalization in carbon nanotube-based nanofluidic systems: An intrinsic challenge

In this work, experiments, molecular dynamics (MD) simulations, and theoretical analysis are conducted to study ion transport in thin carbon nanotubes (CNTs). Diverse nonlinear relationships between the ionic conductance (G) and the ion concentration (C) are observed. MD simulations show that the distinct G–C dependences are caused by the functionalization of the CNT entrance, which affects the energy barrier for ion transport and changes the ionic conductance. The various G–C relationships are also predicted using the electrokinetic theory by considering the potential generated by the functional groups at the CNT entrance. Practically, the number of functional groups at the CNT entrance is influenced by several factors, including both intrinsic and external effects, which make it difficult to regulate the ionic conductance and pose a challenge to CNT-based nanofluidic systems in practical applications.

### Irreversibility and chaos in active particle suspensions

Author(s): Sergio Chibbaro, Astrid Decoene, Sebastien Martin, and Fabien Vergnet

The collective behavior of active suspensions of microswimmers immersed in a viscous fluid is investigated through numerical studies. It is shown that a bioturbulent state emerges both in suspensions of pushers and of pullers. Which conditions are needed to trigger such phenomenology and what mechanisms underlie such phenomena are discussed. An investigation into whether the difference in puller and pusher dynamics is due to a spontaneous breaking of the hydrodynamics time-reversal symmetry is presented, and the mechanisms underlying such broken symmetry in biological swimmers are examined.

[Phys. Rev. Fluids 6, 013104] Published Tue Jan 26, 2021

### Monotonic instability and overstability in two-dimensional electrothermohydrodynamic flow

Author(s): Yifei Guan, Xuerao He, Qi Wang, Zhiwei Song, Mengqi Zhang, and Jian Wu

Electrothermohydrodynamic convection between parallel electrodes with unipolar injection is investigated using a two-relaxation-time lattice Boltzmann method. The interactions between the stabilizing buoyancy force and the destabilizing electric force lead to either monotonic instability or overstability, depending on the Rayleigh number and the Taylor number. A two-stage bifurcation is observed for overstability near the threshold Rayleigh number with a significant change in phase and amplitude.

[Phys. Rev. Fluids 6, 013702] Published Tue Jan 26, 2021

### Biphase as a diagnostic for scale interactions in wall-bounded turbulence

Author(s): G. Cui and I. Jacobi

Biphase is introduced as a nonlinear alternative to traditional amplitude modulation coefficients for studying the interaction delays between large- and small-scale motions in wall-bounded turbulent flows. The biphase combines energetic and geometric interpretations to provide an integrated diagnostic for the scale interaction problem.

[Phys. Rev. Fluids 6, 014604] Published Tue Jan 26, 2021

### On airborne virus transmission in elevators and confined spaces

The impact of air ventilation systems on airborne virus transmission (AVT), and aerosols in general, in confined spaces is not yet understood. The recent pandemic has made it crucial to understand the limitations of ventilation systems regarding AVT. We consider an elevator as a prototypical example of a confined space and show how ventilation designs alone, regardless of cooling or heating, contribute to AVT. Air circulation effects are investigated through multiphase computational fluid dynamics, and the performance of an air purifier in an elevator for reducing AVT is assessed. We have investigated three different flow scenarios regarding the position and operation of inlets and outlets in the elevator and a fourth scenario that includes the operation of the air purifier. The position of the inlets and outlets significantly influences the flow circulation and droplet dispersion. An air purifier does not eliminate airborne transmission. The droplet dispersion is reduced when a pair of an inlet and an outlet is implemented. The overall practical conclusion is that the placement and design of the air purifier and ventilation systems significantly affect the droplet dispersion and AVT. Thus, engineering designs of such systems must take into account the flow dynamics in the confined space the systems will be installed.

### On airborne virus transmission in elevators and confined spaces

The impact of air ventilation systems on airborne virus transmission (AVT), and aerosols in general, in confined spaces is not yet understood. The recent pandemic has made it crucial to understand the limitations of ventilation systems regarding AVT. We consider an elevator as a prototypical example of a confined space and show how ventilation designs alone, regardless of cooling or heating, contribute to AVT. Air circulation effects are investigated through multiphase computational fluid dynamics, and the performance of an air purifier in an elevator for reducing AVT is assessed. We have investigated three different flow scenarios regarding the position and operation of inlets and outlets in the elevator and a fourth scenario that includes the operation of the air purifier. The position of the inlets and outlets significantly influences the flow circulation and droplet dispersion. An air purifier does not eliminate airborne transmission. The droplet dispersion is reduced when a pair of an inlet and an outlet is implemented. The overall practical conclusion is that the placement and design of the air purifier and ventilation systems significantly affect the droplet dispersion and AVT. Thus, engineering designs of such systems must take into account the flow dynamics in the confined space the systems will be installed.

### Expansion and combustion of droplets that contain long-chain alcohol alternative fuels

This paper studies the expansion, micro-explosion, and combustion behaviors of base fuels blended with long-chain alcohols. Diesel, biodiesel, and aviation kerosene are chosen as the base fuels, while n-butanol and n-pentanol are representative long-chain alcohols. Upon addition of a long-chain alcohol, deformation of the blended-fuel droplet becomes more violent. Expansion and ejection of internal liquid and gas occur throughout the process; larger proportions of long-chain alcohols lead to larger ejection holes. The degree of expansion first increases and then decreases with the proportion of alcohol. The effect of the alcohol type on d* (normalized droplet diameter) is substantial at low φ (volume fraction of long-chain alcohol) but negligible at high φ. The aviation kerosene-based fuel exhibits the smallest changes in d*. The effects of φ and the alcohol type on the micro-explosion delay time are also analyzed. The ignition delay time of the diesel-based fuel decreases monotonically with the increasing alcohol proportion and that of the biodiesel-based fuel first decreases and then increases, while that of the aviation kerosene-based fuel increases and then decreases. The combustion rate of a pure base fuel accelerates upon addition of alcohol. The ignition delay time is greatly shortened at higher temperatures, and the combustion duration shortens significantly at temperatures lower than 800 °C. The biodiesel-based fuel offers the shortest ignition delay time and the longest combustion duration, while aviation kerosene exhibits the opposite characteristics. Finally, the micro-explosion and comprehensive combustion indices are proposed to estimate the comprehensive micro-explosion and combustion performances, respectively, of blended fuels.

### Experimental analysis of supercritical-assisted atomization

Supercritical CO2 is used in supercritical-assisted atomization (SAA) systems to promote the atomization of nanoparticle suspensions in powder generation in pharmaceutical, electronics, and coating applications. Due to the sensitivity of the mixture properties to the operational conditions, the SAA process is not fully resolved to date. This study experimentally investigates the underlying mechanisms behind SAA utilizing CO2 or N2 as the assisted-atomization fluid (CO2-A or N2-A) using high-speed imaging and laser diffraction techniques. The effects of injection temperature, pressure, and gas-to-liquid ratio (GLR) are explored, and empirical droplet size models are developed. It is found that the primary breakup of CO2-A is governed by the emergence of the near-nozzle gas bubbles originated from the dissolved CO2, which expand radially and squeeze the liquid due to the inertial forces. As a result, the edges of the liquid core become thinner and deform into relatively long ligaments that further break up into droplets. CO2-A exhibited a shorter liquid length, wider spray angle, and smaller droplet size compared to N2-A. The discrepancies observed in the breakup process are mainly attributed to the higher solubility of CO2 in water and lower surface tension of the CO2–water system. The smallest droplet size distribution and the narrowest droplet size distribution are detected for CO2-A injected at the critical pressure of the CO2–water binary system where the solubility of CO2 in water significantly rises. Linear instability analysis indicates that both shear and acceleration that indirectly incorporate the experimentally observed bubble expansion are the main factors driving the instabilities.

### Probing the high mixing efficiency events in a lock-exchange flow through simultaneous velocity and temperature measurements

Gravity currents produced by a lock-exchange flow are studied using high-resolution molecular tagging techniques. Instead of employing salt to produce density stratification, an initial temperature difference is introduced in the system to generate the ensuing gravity currents. The experiments focus on the interface between the hot and cold fluids to characterize the resultant mixing across the interface. The present measurements spatially resolve the flow to smaller than the Kolmogorov scale and close to the Batchelor scale. This enables reasonably accurate estimates of velocity and density gradients. The measured density (temperature) distribution allowed estimation of the background potential energy of the flow that is used to quantify mixing. These measurements yield a mixing efficiency of about 0.13 with a standard deviation of 0.05 for the present Reynolds number range [[math]]. An analysis combining flow visualization and quantitative measurements reveals that spatially local values of high mixing efficiency occur after the occurrence of certain dissipative stirring events. These events, largely associated with vortical overturns, are commonly observed near the interface between the two fluids and are a precursor to locally efficient mixing.