# Latest papers in fluid mechanics

### Analysis of sheet cavitation with bubble/bubble interaction models

A new cavitation model based on bubble/bubble interactions has been recently proposed by the authors Adama Maiga, Coutier-Delgosha, and Buisine [“A new Cavitation model based on bubble-bubble interactions,” Phys. Fluids 30, 123301 (2018)]. It includes all nonlinear interaction terms between two bubbles, and the only input is the local velocity divergence, while the classical Rayleigh-Plesset or Gilmore models only take into account the linear interaction terms and require the local pressure evolution. In this previous publication, the model has been validated against cases of single bubbles growths and collapses. In the present paper, the same model is applied to configurations of high-speed cavitating flow on a Venturi profile and a two-dimensional foil section, where experiments based on X-ray imaging have been recently conducted. Based on the flow velocity fields available in the two cases, the local velocity divergence is calculated, and a one-dimensional mean divergence evolution from the leading edge to the wake of the cavity is extracted and used as an input for the model validation. The evolutions of the biggest bubble and the volume of vapor are both found in good agreement with the experiments. A typical velocity divergence evolution is then defined, and our model is compared to the modified Rayleigh-Plesset equation that includes the interactions between multiple bubbles. It confirms that the radius evolution of the biggest bubble is systematically better estimated by the new model due to its capability to continuously take into account the interactions of big bubbles with smaller bubbles. Eventually, the model is used to investigate the scale effect, by applying 6 different time scales of cavitation development covering more than 5 orders of magnitude. It is shown that the bubble size does not vary proportionally to the scale, but according to a law that is empirically determined.

### Analysis of sheet cavitation with bubble/bubble interaction models

A new cavitation model based on bubble/bubble interactions has been recently proposed by the authors Adama Maiga, Coutier-Delgosha, and Buisine [“A new Cavitation model based on bubble-bubble interactions,” Phys. Fluids 30, 123301 (2018)]. It includes all nonlinear interaction terms between two bubbles, and the only input is the local velocity divergence, while the classical Rayleigh-Plesset or Gilmore models only take into account the linear interaction terms and require the local pressure evolution. In this previous publication, the model has been validated against cases of single bubbles growths and collapses. In the present paper, the same model is applied to configurations of high-speed cavitating flow on a Venturi profile and a two-dimensional foil section, where experiments based on X-ray imaging have been recently conducted. Based on the flow velocity fields available in the two cases, the local velocity divergence is calculated, and a one-dimensional mean divergence evolution from the leading edge to the wake of the cavity is extracted and used as an input for the model validation. The evolutions of the biggest bubble and the volume of vapor are both found in good agreement with the experiments. A typical velocity divergence evolution is then defined, and our model is compared to the modified Rayleigh-Plesset equation that includes the interactions between multiple bubbles. It confirms that the radius evolution of the biggest bubble is systematically better estimated by the new model due to its capability to continuously take into account the interactions of big bubbles with smaller bubbles. Eventually, the model is used to investigate the scale effect, by applying 6 different time scales of cavitation development covering more than 5 orders of magnitude. It is shown that the bubble size does not vary proportionally to the scale, but according to a law that is empirically determined.

### A microchannel flow application of a linearized kinetic Bhatnagar-Gross-Krook-type model for inert gas mixtures with general intermolecular forces

The flow of binary gaseous mixtures in microchannels, driven by a gradient of pressure, is investigated using the linearized Boltzmann equation based on a Bhatnagar-Gross-Krook-type model, able to describe general collision kernels, and diffuse reflection boundary conditions. Semi-analytical solutions have been obtained through a transformation in integral equations and the results compared with those derived by the McCormack model, which have revealed a good consistency with the experimental data.

### A microchannel flow application of a linearized kinetic Bhatnagar-Gross-Krook-type model for inert gas mixtures with general intermolecular forces

The flow of binary gaseous mixtures in microchannels, driven by a gradient of pressure, is investigated using the linearized Boltzmann equation based on a Bhatnagar-Gross-Krook-type model, able to describe general collision kernels, and diffuse reflection boundary conditions. Semi-analytical solutions have been obtained through a transformation in integral equations and the results compared with those derived by the McCormack model, which have revealed a good consistency with the experimental data.

### Bird’s total collision energy model: 4 decades and going strong

The focus of this work is the total collision energy model of chemical reactions, derived through the application of the collision theory in pioneer work of Bird in 1977–1978. Several aspects of the model, such as the inclusion of the internal degrees of freedom, the detailed balance, and some numerical limitations, are considered. The use of the model for exchange and dissociation reactions, its connection to other chemistry models of the direct simulation Monte Carlo method, and the applicability to different problems of rarefied gas dynamics are discussed.

### Bird’s total collision energy model: 4 decades and going strong

The focus of this work is the total collision energy model of chemical reactions, derived through the application of the collision theory in pioneer work of Bird in 1977–1978. Several aspects of the model, such as the inclusion of the internal degrees of freedom, the detailed balance, and some numerical limitations, are considered. The use of the model for exchange and dissociation reactions, its connection to other chemistry models of the direct simulation Monte Carlo method, and the applicability to different problems of rarefied gas dynamics are discussed.

### Stability and bifurcation analysis of stagnation/equilibrium points for peristaltic transport in a curved channel

The stability of equilibrium points and their bifurcations for a peristaltic transport of an incompressible viscous fluid through a curved channel have been studied when the channel width is assumed to be very small as compared to the wavelength of peristaltic wave and inertial effects are negligible. An analytic solution for the stream function has been obtained in a moving coordinate system which is translating with the wave velocity. Equilibrium points in the flow field are located and categorized by developing a system of nonlinear autonomous differential equations, and the dynamical system methods are used to investigate the local bifurcations and corresponding topological changes. Different flow situations, encountered in the flow field, are classified as backward flow, trapping, and augmented flow. The transition of backward flow into a trapping phenomenon corresponds to the first bifurcation, where a nonsimple degenerate point bifurcates under the wave crest and forms a saddle-center pair with the homoclinic orbit. The second bifurcation appears when the saddle point further bifurcates to produce the heteroclinic connection between the saddle nodes that enclose the recirculating eddies. The third bifurcation point manifests in the flow field due to the transition of trapping into augmented flow, in which a degenerate saddle bifurcates into saddle nodes under the wave trough. The existence of second critical condition is exclusive for peristaltic flow in a curved channel. This bifurcation tends to coincide with the first one with a gradual reduction in the channel curvature. Global bifurcation diagrams are utilized to summarize these bifurcations.

### Stability and bifurcation analysis of stagnation/equilibrium points for peristaltic transport in a curved channel

The stability of equilibrium points and their bifurcations for a peristaltic transport of an incompressible viscous fluid through a curved channel have been studied when the channel width is assumed to be very small as compared to the wavelength of peristaltic wave and inertial effects are negligible. An analytic solution for the stream function has been obtained in a moving coordinate system which is translating with the wave velocity. Equilibrium points in the flow field are located and categorized by developing a system of nonlinear autonomous differential equations, and the dynamical system methods are used to investigate the local bifurcations and corresponding topological changes. Different flow situations, encountered in the flow field, are classified as backward flow, trapping, and augmented flow. The transition of backward flow into a trapping phenomenon corresponds to the first bifurcation, where a nonsimple degenerate point bifurcates under the wave crest and forms a saddle-center pair with the homoclinic orbit. The second bifurcation appears when the saddle point further bifurcates to produce the heteroclinic connection between the saddle nodes that enclose the recirculating eddies. The third bifurcation point manifests in the flow field due to the transition of trapping into augmented flow, in which a degenerate saddle bifurcates into saddle nodes under the wave trough. The existence of second critical condition is exclusive for peristaltic flow in a curved channel. This bifurcation tends to coincide with the first one with a gradual reduction in the channel curvature. Global bifurcation diagrams are utilized to summarize these bifurcations.

### Driving mechanisms of ratchet flow in thin liquid films under tangential two-frequency forcing

In a recent paper, we demonstrated the emergence of ratchet flows in thin liquid films subjected to tangential two-frequency vibrations [E. Sterman-Cohen, M. Bestehorn, and A. Oron, “Ratchet flow of thin liquid films induced by a two-frequency tangential forcing,” Phys. Fluids 30, 022101 (2018)], and asymmetric forcing was found to be a sole driving mechanism for these ratchet flows. In this paper, we consider other two-frequency excitations and reveal an additional driving mechanism of an emerging ratchet flow when the acceleration imparted by forcing is symmetric with respect to a certain moment of time within the forcing period (this type of forcing referred to as “symmetric forcing”). This driving mechanism exhibits an intricate interaction between forcing, capillarity, and gravity. We find that in contradistinction with the case of asymmetric forcing where the flow intensity reaches a constant value in the large-time limit, in the case of symmetric forcing the flow intensity exhibits oscillatory variation in time. We also discuss the flow intensity variation of the emerging ratchet flows with the fundamental wavenumber of the disturbance.

### Driving mechanisms of ratchet flow in thin liquid films under tangential two-frequency forcing

In a recent paper, we demonstrated the emergence of ratchet flows in thin liquid films subjected to tangential two-frequency vibrations [E. Sterman-Cohen, M. Bestehorn, and A. Oron, “Ratchet flow of thin liquid films induced by a two-frequency tangential forcing,” Phys. Fluids 30, 022101 (2018)], and asymmetric forcing was found to be a sole driving mechanism for these ratchet flows. In this paper, we consider other two-frequency excitations and reveal an additional driving mechanism of an emerging ratchet flow when the acceleration imparted by forcing is symmetric with respect to a certain moment of time within the forcing period (this type of forcing referred to as “symmetric forcing”). This driving mechanism exhibits an intricate interaction between forcing, capillarity, and gravity. We find that in contradistinction with the case of asymmetric forcing where the flow intensity reaches a constant value in the large-time limit, in the case of symmetric forcing the flow intensity exhibits oscillatory variation in time. We also discuss the flow intensity variation of the emerging ratchet flows with the fundamental wavenumber of the disturbance.

### Oscillations of small bubbles and medium yielding in elastoviscoplastic fluids

Author(s): Marco De Corato, Brice Saint-Michel, George Makrigiorgos, Yannis Dimakopoulos, John Tsamopoulos, and Valeria Garbin

Bubble removal from yield-stress fluids by ultrasound is studied theoretically by combining the governing equation of bubble dynamics with an elastoviscoplastic constitutive model. The radius of the yielded region oscillates at twice the frequency of the ultrasound-driven bubble oscillations.

[Phys. Rev. Fluids 4, 073301] Published Mon Jul 01, 2019

### Pore-scale study of dissolution-driven density instability with reaction $A+B→C$ in porous media

Author(s): Timan Lei and Kai H. Luo

A dissolution-driven density instability with reaction A+B→C is simulated in both homogeneous and heterogeneous media at pore scale. Six types of fingering scenarios are found in each medium, and it is shown that media with large pore size in the top layer can enhance the storage of solute A in the host fluid.

[Phys. Rev. Fluids 4, 063907] Published Fri Jun 28, 2019

### Explosive, oscillatory, and Leidenfrost boiling at the nanoscale

Author(s): Thomas Jollans and Michel Orrit

We investigate the different boiling regimes around a single continuously laser-heated 80 nm gold nanoparticle and draw parallels to the classical picture of boiling. Initially, nanoscale boiling takes the form of transient, inertia-driven, unsustainable boiling events characteristic of a nanoscale ...

[Phys. Rev. E 99, 063110] Published Thu Jun 27, 2019

### Numerical investigation of vibration-induced droplet shedding on microstructured superhydrophobic surfaces

Author(s): Mostafa Moradi, Mohammad Hassan Rahimian, and Seyed Farshid Chini

The vibration-induced droplet shedding mechanism on microstructured superhydrophobic surfaces was simulated using the lattice Boltzmann method. The numerical simulations of natural droplet oscillations for various surface structures show that the natural frequency of the droplet is strongly dependen...

[Phys. Rev. E 99, 063111] Published Thu Jun 27, 2019

### Incompressible models of magnetohydrodynamic Richtmyer-Meshkov instability in cylindrical geometry

Author(s): A. Bakhsh and R. Samtaney

With a cylindrical and incompressible model of an impulsively accelerated conducting fluid interface, effects of normal or azimuthal magnetic fields on interface growth rates are studied. In the normal case growth decays at late times and in the azimuthal one a growth perturbation oscillates.

[Phys. Rev. Fluids 4, 063906] Published Thu Jun 27, 2019

### Rotation of a rebounding-coalescing droplet on a superhydrophobic surface

Droplet impact and droplet coalescence are two very common phenomena. When these two processes occur on a superhydrophobic surface in an appropriate sequence, an interesting but little-noticed phenomenon will occur with rotation of the rebounding-coalescing droplet. When a droplet impacts another stationary droplet on a superhydrophobic surface with an appropriate velocity and position, the reaction force produced by the impact and the moment arm formed by the liquid bridge produces a reversed torque. This reverse torque causes the droplet to rotate after rebounding. The liquid bridge in the early stage of the coalescence process is the key to the rotation, and the relative development speed of coalescence and rebound determines whether rotation can occur and its relative strength.

### Modified normalized Rortex/vortex identification method

In this paper, a modified normalized Rortex/vortex identification method named [math] is presented to improve the original ΩR method and resolve the bulging phenomenon on the isosurfaces, which is caused by the original ΩR method. Mathematical explanations and the relationship between the Q criterion and [math] are described in detail. In addition, the new developed formula does not require two original coordinate rotations, and the calculation of [math] is greatly simplified. The numerical results demonstrate the effectiveness of the new modified normalized Rortex/vortex identification method.

### A meniscus fingering instability in viscoelastic fluids

We report experiments where a viscoelastic fingering instability develops at the free interface between air and a model viscoelastic fluid confined in a Hele-Shaw cell. The fluid is symmetrically stretched with constant velocity along two opposite directions, leading to the inflation of a two-dimensional air bubble growing from a millimetric centered hole. The instability is observed when the circumferential stretch of the inflating bubble reaches a threshold that depends on the viscoelastic properties of the fluid through the ratio of the material relaxation time to the time elapsed before the fingers start to develop. The critical stretch of the bulk fingering instability of a stretchable elastic solid [B. Saintyves, O. Dauchot, and E. Bouchaud, “Bulk elastic fingering instability in Hele-Shaw cells,” Phys. Rev. Lett. 111, 047801 (2013)] is recovered for large values of this ratio.

### Interaction of wave with multiple wide polynyas

A method based on the wide spacing approximation is applied to the wave scattering problem in multiple polynyas. An ice sheet is modeled as an elastic plate, and fluid flow is described by the velocity potential theory. The solution procedure is constructed based on the assumption that the ice sheet length is much larger than the wavelength. For each polynya, of free surface with an ice sheet on each side, the problem is solved exactly within the framework of the linearized velocity potential theory. This is then matched with the solution from neighboring polynyas at their interfaces below the ice sheet on each side, and only the traveling waves are included in the matching. Numerical results are provided to show that the method is very accurate and highly efficient. Extensive simulations are then carried out to investigate the effects of the ice sheet number, ice sheet length, distribution of ice sheets, as well as polynya width. The features of wave reflection and transmission are analyzed, and the physical mechanism is discussed.

### Stability analysis of asymmetric wakes

The shear layer thickness asymmetry effects on the incompressible inviscid asymmetric wakes are examined by means of both temporal and spatiotemporal stability analyses. To allow for the variation of the shear layer thicknesses on either side of the wake, a family of piecewise linear velocity profiles is introduced. The temporal stability analysis shows that the maximum growth rate of the sinuous mode is dominated by the shear layer thickness of the thinner side and the maximum growth rate of the varicose mode is dominated by the thicker side. The sinuous mode is more unstable than the varicose mode, and increasing the degree of asymmetry would increase the growth rate difference between the sinuous instability and the varicose instability. The spatiotemporal analysis shows that increasing the degree of asymmetry generally has a stabilizing effect. In particular, the influences of shear layer thickness on the absolute growth rate can be classified into three different regions: In region I, increasing shear layer thickness at either side would destabilize the flow. In region II, increasing the degree of symmetry has a destabilizing effect. In region III, decreasing shear layer thickness at either side would destabilize the flow. These findings provide us some information on how to control asymmetric wakes. Furthermore, we find that the frequency of the most absolutely unstable mode is mainly determined by the total shear layer thickness and has a slight dependence on the asymmetry ratio.