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Comparison of spinning angular momentum, L s1 and L s2 , and orbital angular momentum, L o , at time instants of T = 0.0 and T = 1.0 with varying the azimuthal angle ϕ. (a) L x , (b) L y , and (c) L z are the angular momentum in x, y, and z directions, respectively.
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The effects of spinning motion on the bouncing and coalescence between a spinning droplet and a nonspinning droplet undergoing head-on collision were numerically studied by using a volume-of-fluid method. A prominent discovery is that the spinning droplet can induce significant nonaxisymmetric flow features for the head-on collision of equal-size d...
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... studied to reveal the angular momentum interchange between two droplets. It is seen that L t in each direction is conserved at time instants of T = 0.0 and The most significant nonaxisymmetric flow due to the spinning effects occurs in the direction parallel to the x-z plane, as indicated by the prominent L o after the droplet collision, shown in Fig. 8(b). Specifically, for L y shown in Fig. 8(b), the initial L s1 increases with increasing ϕ; regardless of the negligible L s2 , the L o after the droplet collision reaches a maximum value at ϕ = π/2, whereas for L x and L z shown in Figs. 8(a) and 8(c), a very small L o is observed at T = 1.0, implying that the interaction between D1 and ...
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... between two droplets. It is seen that L t in each direction is conserved at time instants of T = 0.0 and The most significant nonaxisymmetric flow due to the spinning effects occurs in the direction parallel to the x-z plane, as indicated by the prominent L o after the droplet collision, shown in Fig. 8(b). Specifically, for L y shown in Fig. 8(b), the initial L s1 increases with increasing ϕ; regardless of the negligible L s2 , the L o after the droplet collision reaches a maximum value at ϕ = π/2, whereas for L x and L z shown in Figs. 8(a) and 8(c), a very small L o is observed at T = 1.0, implying that the interaction between D1 and D2 is too weak (on the y-z plane and x-y ...
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... the separated TE 1 and TE 2 show that the energy is transferred from D2 to D1 with ϕ smaller than π/4 while being transferred from D1 to D2 with ϕ larger than π/4. The energy 113601-10 FIG. 9. Energy budget of head-on collisions between (a) a spinning droplet 1 and (b) a nonspinning droplet 2 with varying the azimuthal angle ϕ shown in Fig. 8. The total energy (TE), the surface energy (SE), the translational kinetic energy (TKE), the rotational kinetic energy (RKE), the total viscous dissipation energy (TVDE), and the total viscous dissipation rate (TVDR) are nondimensionalized for each liquid droplet separately. The reference TKE is for the collision between two ...
Citations
... Researches on dynamic droplet merging primarily focus on understanding the collision and coalescence dynamics of droplets. The process of collision-coalescence behavior between two droplets can be roughly divided into the following distinct stages: [45][46][47]75 (i) Approach: initially, two liquid droplets draw closer to each other; (ii) Contact and Deformation: as they approach, the droplets make contact and undergo deformation; (iii) Interfacial Liquid Film Discharge: the interfacial liquid film between the droplets undergoes a discharge process; (iv) Post-Collision Process: subsequently, the two droplets may either coalesce, adhere without coalescence, or rebound. The post-collision merging process can be further dissected into three stages: (a) Boundary Layer Interface Rupture and Reconnection Phase: this phase involves the rupture and reconnection of the boundary layer interface; (b) Convergence and Integration Stage: the droplets enter a stage of convergence and integration; (c) Damped Oscillation of Merged Droplet: following the merger, a new droplet undergoes a damped oscillation process. ...
The thermodynamic non-equilibrium (TNE) effects and the relationships between various TNE effects and entropy production rate, morphology, kinematics, and dynamics during two initially static droplet coalescences are studied in detail via the discrete Boltzmann method. Temporal evolutions of the total TNE strength D¯* and the total entropy production rate can both provide concise, effective, and consistent physical criteria to distinguish different stages of droplet coalescence. Specifically, when the total TNE strength D¯* and the total entropy production rate reach their maxima, it corresponds to the time when the liquid–vapor interface length changes the fastest; when the total TNE strength D¯* and the total entropy production rate reach their valleys, it corresponds to the moment of the droplet being the longest elliptical shape. Throughout the merging process, the force contributed by surface tension in the coalescence direction acts as the primary driving force for droplet coalescence and reaches its maximum simultaneously with coalescent acceleration. In contrast, the force arising from non-organized momentum fluxes (NOMFs) in the coalescing direction inhibits the merging process and reaches its maximum at the same time as the total TNE strength D¯*. In the coalescence of two unequal-sized droplets, contrary to the larger droplet, the smaller droplet exhibits higher values for total TNE strength D¯*, merging velocity, driving force contributed by surface tension, and resistance contributed by the NOMFs. Moreover, these values gradually increase with the initial radius ratio of the large and small droplets due to the stronger non-equilibrium driving forces stemming from larger curvature. However, non-equilibrium components and forces related to shear velocity in the small droplet are consistently smaller than those in the larger droplet and diminish with the radius ratio. This study offers kinetic insights into the complexity of thermodynamic non-equilibrium effects during the process of droplet coalescence, advancing our comprehension of the underlying physical processes in both engineering applications and the natural world.
... These experimental errors can be easily avoided by the numerical simulation. However, the asymmetric droplet deformation and droplet separation are still observed in previous numerical simulations [13,40,41,44,49,59,68], which is probably attributed to the numerical perturbations that accumulated and amplified with the development of instabilities. Thus, the symmetry-preserving method [69,70] can be applied to the binary droplet collision to ensure the symmetric droplet deformation and internal flow upon the collision between two identical droplets. ...
... He and Zhang [43,44,68] numerically simulated relevant canonical phenomena, s as coalescence, bouncing, and separation between spinning droplets, as shown in Fig 7a. The head-on collision between two spinning droplets shows the off-center effects w asymmetric droplet deformation because of the conversion of the spin ang ...
... He and Zhang [43,44,68] numerically simulated relevant canonical phenomena, such as coalescence, bouncing, and separation between spinning droplets, as shown in Figure 7a. The head-on collision between two spinning droplets shows the off-center effects with asymmetric droplet deformation because of the conversion of the spin angular momentum into the orbital angular momentum. ...
Binary droplet collision is a basic fluid phenomenon for many spray processes in nature and industry involving lots of discrete droplets. It exists an inherent mirror symmetry between two colliding droplets. For specific cases of the collision between two identical droplets, the head-on collision and the off-center collision, respectively, show the axisymmetric and rotational symmetry characteristics, which is useful for the simplification of droplet collision modeling. However, for more general cases of the collision between two droplets involving the disparities of size ratio, surface tension, viscosity, and self-spin motions, the axisymmetric and rotational symmetry droplet deformation and inner flow tend to be broken, leading to many distinct phenomena that cannot occur for the collision between two identical droplets owing to the mirror symmetry. This review focused on interpreting the asymmetric droplet deformation and the collision-induced internal mixing that was affected by those symmetry breaking factors, such as size ratio effects, Marangoni Effects, non-Newtonian effects, and droplet self-spin motion. It helps to understand the droplet internal mixing for hypergolic propellants in the rocket engineering and microscale droplet reactors in the biological engineering, and the modeling of droplet collision in real combustion spray processes.
... Recently, the collisions of a spinning droplet with a non-spinning droplet have been investigated by He and Zhang. 33 They found that for head-on collision of equally-sized droplets of the same liquid, the spinning droplet can generate significant non-axisymmetric flow patterns. Furthermore, He et al. 34 studied self-spin in a non-spinning droplet through its oblique impact on a non-slip boundary and corroborated that higher impact velocity or increased liquid viscosity leads to a higher angular speed of the spinning droplet. ...
There is a growing interest in the optimization of spray systems to minimize reflexive separation and enhance droplet coalescence, which has the potential to greatly benefit industrial and agricultural applications. In this investigation, the pinch-off dynamics in head-on impacts of unequal-size droplets on a hydrophobic surface are explored, employing both experimental and numerical approaches. The study focuses on size ratios ranging from 1.0 to 5.0 and impact Weber numbers up to 208. The captured images from the high-speed camera are meticulously processed and analyzed in a detailed manner. Two distinct scenarios are observed in the experimental findings: (1) reflexive separation occurring without the formation of satellite droplets and (2) reflexive separation characterized by the presence of satellite droplets. Direct numerical simulations are also conducted to probe the underlying dynamics during droplet impact. The direct numerical simulation results closely replicate the experimental results, demonstrating excellent agreement with the dynamics of the pinch-off process. The simulated velocity field demonstrates the liquid's movement away from the neck region, leading to progressive thinning and eventual pinch-off. Furthermore, the study examines the evolution of the neck radius over time (τ), revealing a linear variation in log–log plots. Remarkably, the neck radius scales with τ2/3, even for different size ratios. A regime diagram in We–Δ space is reported.
... The main challenges lie in the fact that it is difficult to generate a stable spinning droplet with the traditional droplet generator and quantitatively measure the spinning characteristics of collision-induced spinning droplets. The collision between spinning droplets is easy to set up in the numerical simulation and thereby some numerical studies (He and Zhang 2020;He et al. 2021He et al. , 2022 have demonstrated the significance of droplet spinning effects on the collision outcome. This can be understood as that the spin motion of droplets breaks the symmetry between two identical droplets collision, induces the local rotational flow, enhances viscous dissipation inner the droplet, and thereby affects the droplet coalescence, bouncing, reflexive separation, and stretching separation. ...
... To study the spinning characteristics of a single droplet and the subsequent collision between two spinning droplets, apart from the common approaches of the levitated droplet by acoustic waves (Foresti and Poulikakos 2014;Kitahata et al. 2015;Saha et al. 2012) or the ferrofluid microscopic droplet (Hill and Eaves 2008;Janiaud et al. 2000) under electromagnetic fields, the present paper proposes the ideal of computationally generating a spinning droplet upon the oblique collision of an initially non-spinning droplet on the solid surface by utilizing the shearing layer flow within the interaction region between the droplet and the solid surface. This idea was inspired by the observation of the off-center droplet collision (He et al. , 2020) that a prominent shearing layer flow occurring in the vicinity of the interaction region between two droplets accounts for the droplet rotation owing to the nonzero angular momentum. ...
... The volume fraction c satisfies the advection equation with c = 1 for the liquid phase, c = 0 for the gas phase, and 0 < c < 1 for the gas-liquid interface. The present VOF method has been implemented into an open source code, GERRIS (Popinet 2003(Popinet , 2009(Popinet , 2018, featuring the 3D octree adaptive mesh refinement, the geometrical VOF interface reconstruction, and continuum surface force with height function curvature estimation, which has been demonstrated to be competent for high-fidelity simulation of a wide range of multiphase flow problems (Chen et al. 2011;Chen et al. 2012;Chen and Yang 2014;He et al. 2019He et al. , 2020He et al. 2021He et al. , 2022He and Zhang 2020;Tang et al. 2016;Xia et al. 2017;Xia et al. 2019). ...
... The previous understanding of droplet collision would be modulated by considering the presence of droplet spin. For the head-on bouncing between spinning droplets [32], the spinning droplet can induce significant nonaxisymmetric droplet deformation because of the conversion of the spin angular momentum into the orbital angular momentum. The interchange between orbital and spin angular momentums during the collision process is of significance because it can influence the postcollision velocities of bouncing droplets. ...
... The interchange between orbital and spin angular momentums during the collision process is of significance because it can influence the postcollision velocities of bouncing droplets. For head-on coalescence between a spinning droplet and a nonspinning droplet of equal size [32], the spinning motion can promote the mass intermingling of droplets because the locally nonuniform mass exchange occurs at the early collision stage by nonaxisymmetric flow and is further stretched along the filament at later collision stages. Apart from the study of spinning effects on droplet bouncing and coalescence, the spin-affected droplet separation and subsequent satellite droplet formation are highly probable in practical dense sprays, but relevant studies have been rare in the literature. ...
... The present study adopts the volume-of-fluid (VOF) method, which has been implemented in the open source code, GERRIS [33,34], featuring the 3D octree adaptive mesh refinement, the geometrical VOF interface reconstruction, and continuum surface force with height function curvature estimation. GERRIS has been demonstrated to be competent for high-fidelity simulation of a wide range of multiphase flow problems [29][30][31][32][35][36][37][38][39][40]. A major challenge of VOF simulation of droplet collision lies in the absence of subgrid models describing the rarefied gas effects and the van der Waals force [41] within the gas film, thereby prohibiting the physically realistic prediction of droplet coalescence and separation. ...
Recent studies have demonstrated the significant roles of droplet self-spin motion in affecting the head-on collision of binary droplets. In this paper, we present a computational study by using the volume-of-fluid method to investigate the spin-affected droplet separation of off-center collisions, which are more probable in reality and phenomenologically richer than head-on collisions. Different separation modes are identified through a parametric study with varying spinning speed and impact parameter. A prominent finding is that increasing the droplet spinning speed tends to suppress the reflexive separation and to promote the stretching separation. Physically, the reflexive separation is suppressed because the increased rotational energy reduces the excessive reflexive kinetic energy within the droplet, which is the cause for the droplet reflexive separation. The stretching separation is promoted because the increased droplet angular momentum enhances the local stretching flow within the droplet, which tends to separate the droplet. The roles of orbital angular momentum and spin angular momentum in affecting the droplet separation are further substantiated by studying the collision between two spinning droplets with either the same or opposite chirality. In addition, a theoretical model based on conservation laws is proposed to qualitatively describe the boundaries of coalescence-separation transition influenced by droplet self-spin motion.
... The previous understanding of droplet collision would be modulated by considering the presence of droplet spin. For the head-on bouncing between spinning droplets [32], the spinning droplet can induce significant non-axisymmetric droplet deformation because of the conversion of the spin angular momentum into the orbital angular momentum. The interchange between orbital and spin angular momentums during the collision process is of significance because it can influence the post-collision velocities of bouncing droplets. ...
... The interchange between orbital and spin angular momentums during the collision process is of significance because it can influence the post-collision velocities of bouncing droplets. For head-on coalescence between a spinning droplet and a non-spinning droplet of equal size [32], the spinning motion can promote the mass interminglement of droplets because the locally nonuniform mass exchange occurs at the early collision stage by non-axisymmetric flow and is further stretched along the filament at later collision stages. Apart from the study of spinning effects on droplet bouncing and coalescence, the spin-affected droplet separation and subsequent satellite droplet formation are highly probable in practical dense sprays, but relevant studies have not been reported in the literature. ...
... The present study adopts the Volume-of-Fluid (VOF) method, which has been implemented in the open source code, Gerris [33,34], featuring the 3D octree adaptive mesh refinement, the geometrical VOF interface reconstruction, and continuum surface force with height function curvature estimation. Gerris has been demonstrated to be competent for high-fidelity simulation of a wide range of multiphase flow problems [29][30][31][32][35][36][37][38][39][40]. ...
Recent studies have demonstrated the significant roles of droplet self-spin motion in affecting the head-on collision of binary droplets. In this paper, we present a computational study by using the Volume-of-Fluid (VOF) method to investigate the spin-affected droplet separation of off-center collisions, which are more probable in reality and phenomenologically richer than head-on collisions. Different separation modes are identified through a parametric study with varying spinning speed and impact parameter. A prominent finding is that increasing the droplet spinning speed tends to suppress the reflexive separation and to promote the stretching separation. Physically, the reflexive separation is suppressed because the increased rotational energy reduces the excessive reflexive kinetic energy within the droplet, which is the cause for the droplet reflexive separation. The stretching separation is promoted because the increased droplet angular momentum enhances the local stretching flow within the droplet, which tends to separate the droplet. The roles of orbital angular momentum and spin angular momentum in affecting the droplet separation are further substantiated by studying the collision between two spinning droplets with either the same or opposite chirality. In addition, a theoretical model based on conservation laws is proposed to qualitatively describe the boundaries of coalescence-separation transition influenced by droplet self-spin motion.
In the present mini‐review, droplet impacting on a liquid pool, jet impingement, and binary droplet collision of nonreacting liquids are first summarized in terms of basic phenomena and the corresponding nondimensional parameters. Then, two representative hypergolic bipropellant systems, a hypergolic fuel of N,N,N′,N′ ‐tetramethylethylenediamine (TMEDA) and an oxidizer of white fuming nitric acid (WFNA) and a monoethanolamine‐based fuel (MEA‐NaBH 4 ) and a high‐density hydrogen peroxide (H 2 O 2 ), are discussed in detail to unveil the rich underlying physics such as liquid‐phase reaction, heat transfer, phase change, and gas‐phase reaction. This review focuses on quantifying and interpreting the parametric dependence of the gas‐phase ignition induced by droplet collision of liquid hypergolic propellants. The advances in droplet collision of hypergolic propellants are important for modeling the real hypergolic impinging‐jet (spray) combustion and for the design optimization of orbit‐maneuver rocket engines.
The head-on collision of two droplets near the critical point is investigated based on the Boltzmann-BGK equation. Gauss-Hermite quadratures with different degree of precision are used to solve the kinetic equation, so that the solutions truncated at the Navier-Stokes order and non-continuum (i.e., rarefied fluid dynamics) solutions can be compared. When the kinetic equation is solved with adequate accuracy, prominent variations of the vertical velocity (the collision is in the horizontal direction), the viscous stress components, and droplet morphology are observed during the formation of liquid bridge, which demonstrates the importance of the rarefaction effects and the failure of the Navier-Stokes equation. The rarefaction effects change the topology of streamlines near the droplet surface, suppress the high-magnitude vorticity concentration inside the interdroplet region, and promote the vorticity diffusion around outer droplet surface. Two physical mechanisms responsible for the local energy conversion between the free and kinetic energies are identified, namely, the total pressure-dilatation coupling effect and the interaction between the density gradient and strain rate tensor. An energy conversion analysis is performed to show that the rarefaction effects can enhance the conversion from free energy to kinetic energy and facilitate the discharge of the gas interval along the vertical direction, thereby boosting droplet coalescence. Furthermore, the magnitude and the spatial oscillation frequency of the Lamb vector divergence inside the gas interval are shown to be suppressed by the rarefaction effects. It is found that the dynamic process in the gas interval is closely associated with the interaction between the adjacent positive and negative regions of the Lamb vector divergence.
