The dynamics of head-on collision of unequal-size droplets were experimentally and theoretically investigated, with emphasis on identifying distinct collision outcomes and interpreting the size-ratio dependence. A unified regime diagram in terms of bouncing, permanent coalescence, and separation after coalescence was identified for hydrocarbon and water droplets in the parameter space of the size ratio and a collision Weber number. Experimental results show that the transition Weber number, We_b-c, that separates the bouncing and permanent coalescence regimes, weakly depends on the size ratio, while the transition Weber number, We_c-s, that separates permanent coalescence and separation regimes, significantly increases with the size ratio. A theoretical model based on energy balance and scaling analysis was developed to explain the size-ratio dependence of We_c-s. The theoretical results show good agreement with the experimental data for tetradecane and decane droplets, with a moderate discrepancy for water droplets.

A theoretical analysis was performed for the head-on collision of two identical droplets in a gaseous environment, with the attendant bouncing and coalescence outcomes, for situations in which the extent of droplet deformation upon collision is comparable to the original droplet radius, corresponding to O(1)–O(10) of the droplet Weber number. The model embodies the essential physics that describes the substantial amount of droplet deformation, the viscous loss through droplet internal motion induced by the deformation, the dynamics and rarefied nature of the gas film between the interfaces of the colliding droplets, and the potential destruction and thereby merging of these interfaces due to the van der Waals attraction force. The theoretical model was applied to investigate collisions involving hydrocarbon and water droplets at sub- and superatmospheric pressures. The results agree well with previous experimental observations in that as the Weber number increases in the range of O(1)–O(10), collision of hydrocarbon droplets at one atmospheric pressure results in the nonmonotonic coalescence-bouncing-coalescence transition, that while bouncing is absent for water droplets at atmospheric pressure, it occurs at higher pressures, and that while bouncing is observed for hydrocarbon droplets at atmospheric pressure, it is absent at lower pressures.

We present a theory on the coalescence of 2 spherical liquid droplets that are initially stationary. The evolution of the radius of a liquid neck formed upon coalescence was formulated as an initial value problem and then solved to yield an exact solution without free parameters, with its 2 asymptotic approximations reproducing the well-known scaling relations in the inertially limited viscous and inertial regimes. The viscous-to-inertial crossover observed in previous research is also recovered by the theory, rendering the collapse of data of different viscosities onto a single curve.

The flickering of buoyant diffusion flames is associated with the periodic shedding of toroidal vortices that are formed under gravity-induced shearing at the flame surface. Numerous experimental investigations have confirmed the scaling, $f\propto D^{-1/2}$ , where $f$ is the flickering frequency and $D$ is the diameter of the fuel inlet. However, the connection between the toroidal vortex dynamics and the scaling has not been clearly understood. By incorporating the finding of Gharibet al.(J. Fluid Mech., vol. 360, 1998, pp. 121–140) that the detachment of a continuously growing vortex ring is inevitable and can be dictated by a universal constant that is essentially a non-dimensional circulation of the vortex, we theoretically established the connection between the periodicity of the toroidal vortices and the flickering of a buoyant diffusion flame with small Froude number. The scaling theory for flickering frequency was validated by the existing experimental data of pool flames and jet diffusion flames.

To resolve the discrepancy between the numerical detonation cell size and experimental observations, simulations are conducted with a detailed thermochemical reaction model for a premixed argon-diluted hydrogen-oxygen mixture. Four different scenarios are considered: (i) The whole system is in thermodynamic equilibrium; (ii) the vibrational relaxation is considered and the translational-rotational temperature is used as the dominant temperature of the chemical reactions; (iii) the same non-equilibrium effect as in the second scenario is used along with Park’s two-temperature model to account for the effect of vibrational temperature on chemical reaction rates; and (iv) a more physically consistent vibration-chemistry-vibration coupling model is adopted. The simulated detonation cell widths for the first and second scenarios are significantly lower than the experimental measurements, whereas reasonable agreement is observed for the third and fourth scenarios. These results confirm that the involvement of vibrational relaxation in the chemical reactions is an important mechanism in gaseous detonation.