High-fidelity numerical simulations have been performed to study the formation and fragmentation of liquid sheets formed by two impinging jets using an improved volume-of-fluid (VOF) method augmented with several adaptive mesh refinement (AMR) techniques. An efficient topology-oriented strategy was further established to optimize the performance and accuracy of the AMR algorithm. Two benchmark cases pertaining to low- and high-velocity impinging jets are simulated as part of a grid refinement study. Calculated jet dynamics show excellent agreement with experimental observations in terms of the rim shape, droplet size distribution and impact wave structures. Detailed flow physics associated with the temporal evolution and spatial development of the jets are explored over a wide range of Reynolds and Weber numbers. A realistic rendering post-processing using a ray-tracing technique is performed to obtain direct insight to the flow evolution. Special attention is paid to the dynamics of the impact wave which dominates the atomization of the injected liquid. The work appears to be the first systematic numerical study in which all the flow patterns formed by impingement of two liquid jets are obtained. Fine structures are captured based on their characteristic length scales. Various atomization modes, from stable to highly unstable, are resolved with high fidelity.

The microfluidic inertial effect is an effective way of focusing and sorting droplets suspended in a carrier fluid in microchannels. To understand the flow dynamics of microscale droplet migration, we conduct numerical simulations on the droplet motion and deformation in a straight microchannel. The results are compared with preliminary experiments and theoretical analysis. In contrast to most existing literature, the present simulations are three-dimensional and full length in the streamwise direction and consider the confinement effects for a rectangular cross section. To thoroughly examine the effect of the velocity distribution, the release positions of single droplets are varied in a quarter of the channel cross section based on the geometrical symmetries. The migration dynamics and equilibrium positions of the droplets are obtained for different fluid velocities and droplet sizes. Droplets with diameters larger than half of the channel height migrate to the centerline in the height direction and two equilibrium positions are observed between the centerline and the wall in the width direction. In addition to the well-known Segré-Silberberg equilibrium positions, new equilibrium positions closer to the centerline are observed. This finding is validated by preliminary experiments that are designed to introduce droplets at different initial lateral positions. Small droplets also migrate to two equilibrium positions in the quarter of the channel cross section, but the coordinates in the width direction are between the centerline and the wall. The equilibrium positions move toward the centerlines with increasing Reynolds number due to increasing deformations of the droplets. The distributions of the lift forces, angular velocities, and the deformation parameters of droplets along the two confinement direction are investigated in detail. Comparisons are made with theoretical predictions to determine the fundamentals of droplet migration in microchannels. In addition, existence of the inner equilibrium position is linked to the quartic velocity distribution in the width direction through a simple model for the slip angular velocities of droplets.

Direct numerical simulations are performed to investigate the multiscale flow physics of binary droplet collision over a wide range of Weber numbers and impact factors. All possible collision outcomes, including bouncing (both head-on and off-center), coalescence, reflexive separation, and stretching separation, are considered. The theoretical formulation is based on a complete set of conservation equations for both the liquid and gas phases. An improved volume-of-fluid technique, which is augmented by an adaptive mesh refinement algorithm, is used to track the liquid/gas interface. Several local refinement criteria are validated and employed to improve the computational accuracy and efficiency substantially. In particular, a thickness-based refinement technique is implemented for treating cases involving extremely thin gas films between droplets. The smallest numerical grid is ∼10 nm, which is on the order of 10⁻⁵ times the initial droplet diameter. A photorealistic visualization technique is employed to gain direct insights into the detailed collision dynamics, including both the shape evolution and mass relocation. The numerical framework allows us to systematically investigate the underlying mechanisms and processes, such as gas-film drainage and energy and mass transfer, at scales sufficient to resolve the near-field dynamics during droplet collision. The nonmonotonic transition of bouncing and merging outcomes for head-on collision is identified by varying the Weber number over two orders of magnitude. A geometric relation defining the droplet interactions is developed. Analytical models are also established to predict the mass transfer between colliding droplets.

In this paper, a combined theoretical and numerical analysis is performed to study the internal and external flowfields of a liquid swirl injector. The effect of ambient pressure on the injector dynamics is explored systematically over a range of 1-50 atm. An increase in the ambient pressure increases the liquid film thickness, but decreases the spreading angle. This phenomenon can be attributed to the modification of the velocity profiles within the liquid film near the gas-liquid interface due to the alteration of the gas-phase shear stresses with pressure. The friction force at the interface plays a minor role. The generation and existence of stationary waves in the injector nozzle is also considered. At a higher ambient pressure, the pressure drop across the liquid sheet downstream of the injector exit increases, thereby suppressing the spreading of the liquid sheet. This in turn increases the thickness of the liquid sheet, and subsequently increases the breakup length at higher pressure. A semi-empirical model is developed to relate the velocity and pressure distributions near the surface of the liquid sheet. Good agreement is achieved between the measured and predicted shape and spreading angle of the liquid sheet.

Inertial migration has emerged as an efficient tool for manipulating both biological and engineered particles that commonly exist with non-spherical shapes in microfluidic devices. There have been numerous studies on the inertial migration of spherical particles, whereas the non-spherical particles are still largely unexplored. Here, we conduct three-dimensional direct numerical simulations to study the inertial migration of rigid cylindrical particles in rectangular microchannels with different width/height ratios under the channel Reynolds numbers (Re) varying from 50 to 400. Cylindrical particles with different length/diameter ratios and blockage ratios are also concerned. Distributions of surface force with the change of rotation angle show that surface stresses acting on the particle end near the wall are the major contributors to the particle rotation. We obtain lift forces experienced by cylindrical particles at different lateral positions on cross sections of two types of microchannels at various Re. It is found that there are always four stable equilibrium positions on the cross section of a square channel, while the stable positions are two or four in a rectangular channel, depending on Re. By comparing the equilibrium positions of cylindrical particles and spherical particles, we demonstrate that the equivalent diameter of cylindrical particles monotonously increases with Re. Our work indicates the influence of a non-spherical shape on the inertial migration and can be useful for the precise manipulation of non-spherical particles.