No description available.

No / A computational fluid dynamics (CFD) model is used to investigate the droplet formation and deformation under the influence of different parameters. Droplet breakup phenomenon depends on several factors such as viscosity, velocity, pressure difference, and geometry. The most important parameter for droplet breakup is the Weber number (We) which is the ratio of disrupting aerodynamics forces to the surface tension forces. Volume of fluid (VOF) model is used in present work to simulate the droplet breakup. This work presents the effect of liquid velocity, viscosity, and orifice diameters on droplet formation and breakup.

Effective design of liquid fuel injection systems is a function of good understanding of liquid breakup mechanisms. A transient liquid breakup model is developed on the classical interfacial breakup theory by modifying the classical linear perturbation process to include time-dependent base and perturbed flow parameters. The non-isothermal condition on liquid jet instability and breakup is theoretically modelled; with the particular consideration of a spatially variation of surface tension along the liquid-gas interface. The model combines the classical interface hydrodynamic instability and breakup theory and heat-transfer through semi-infinite medium. Analytical liquid breakup model, which combines transient and non-isothermal effects on liquid jet breakup, is suggested. The suggested model could be simplified to the transient breakup model and the non-isothermal breakup model equivalents. A novel mechanistic model, which is based on a simple momentum balance between the injected jet and the aerodynamic drag force, is suggested for breakup length. A new model, which combines energy criterion and dual-timescale for turbulent shear in droplet dispersion, is suggested for droplet breakup criteria on the basis of critical Webber number. All developed models showed good predictions of available experimental data, and established empirical correlation, within the operational conditions of contemporary ICEs, specifically diesel engines. Continued research in these areas could benefit the development of the next generation of liquid fuel injectors and combustors – by accounting for transient effects and non-isothermal conditions in liquid jet breakup, and turbulent shear in droplet breakup.

Effective design of liquid fuel injection systems is a function of good understanding of liquid breakup mechanisms. A transient liquid breakup model is developed on the classical interfacial breakup theory by modifying the classical linear perturbation process to include time-dependent base and perturbed flow parameters. The non-isothermal condition on liquid jet instability and breakup is theoretically modelled; with the particular consideration of a spatially variation of surface tension along the liquid-gas interface. The model combines the classical interface hydrodynamic instability and breakup theory and heat-transfer through semi-infinite medium. Analytical liquid breakup model, which combines transient and non-isothermal effects on liquid jet breakup, is suggested. The suggested model could be simplified to the transient breakup model and the non-isothermal breakup model equivalents. A novel mechanistic model, which is based on a simple momentum balance between the injected jet and the aerodynamic drag force, is suggested for breakup length. A new model, which combines energy criterion and dual-timescale for turbulent shear in droplet dispersion, is suggested for droplet breakup criteria on the basis of critical Webber number. All developed models showed good predictions of available experimental data, and established empirical correlation, within the operational conditions of contemporary ICEs, specifically diesel engines. Continued research in these areas could benefit the development of the next generation of liquid fuel injectors and combustors – by accounting for transient effects and non-isothermal conditions in liquid jet breakup, and turbulent shear in droplet breakup.

No description available.

<div>For centuries, fluid flows (hydrodynamics) and electromagnetic phenomena have interested scientists and laypeople alike. The earliest recording of the intersection of these two ideas, electro-hydrodynamics, was reported four centuries ago by William Gilbert who observed that static electricity generated from rubbed amber could ``attract" water. Today electrohydrodynamic phenomena are the underlying mechanisms driving the production of nano-fibers through electro-spinning, printing circuitry, and electrospraying, which John Fenn used in his Nobel prize winning work on electrospray ionization mass spectrometry. In all of these applications, a strong electric field is used to deform a liquid-gas interface (free surface) into a sharp conical tip. Unable to sustain these large interfacial stresses, a thin jet of fluid emerges from the tip of the cone and may subsequently break into a stream of smaller droplets. This tip-streaming phenomenon demands fundamental understanding of three canonical problems in fluid mechanics: electrified cones (Taylor cones), jets, and droplets. </div><div>In this thesis, the electrohydrodynamics of free surface flows are examined through both analytical and numerical treatment of the Cauchy momentum equations augmented with Maxwell's equations. Linear oscillations and stability of (inviscid) conducting charged droplets are examined in the presence of a solid ring shaped constraint. Here the constraint gives rise to an additional mode of oscillation---absent in the analysis of a free (unconstrained) droplet. Interestingly, the amount of charge necessary for instability, the Rayleigh charge limit, is unaltered by the constraint, but the mode of oscillation associated with instability changes. While all of the aforementioned applications involve electrified liquid-gas interfaces, recent experiments reveal a previously unknown type of streaming can occur for droplets suspended in another fluid. In these experiments, the suspending fluid is more conductive and an external electric field drives the intially spherical drop to adopt an oblate shape. Based on the viscosity ratio between the drop and suspending fluid, two different types of instability were observed: (i) if the drop is more viscous, then the drop forms a dimple at its poles and ruptures though its center, a phenomenon that is now referred to as dimpling, and (ii) if the suspending fluid is more viscous, then the drop adopts a lens-like shape and emits a sheet from its equator that subsequently breaks into a stream of rings and then tiny droplets, a phenomenon that is now called equatorial streaming. The physics of these two instabilities are far beyond the applicability of linear theory, requiring careful numerical analysis. Here steady-state governing equations are solved using the Galerkin finite element method (GFEM) to reveal the exact nature of these two instabilities and their dependence on the viscosity ratio. The fate of these drops once they succumb to instability is then analyzed by fully transient simulations.</div><div> Lastly, in a growing number of applications, the working fluid is non-Newtonian, and may even contain suspended solid particles. When non-Newtonian rheology is attributable to the presence of polymer, the dynamics is analyzed by means of a DEVSS-TG/SUPGFEM algorithm that is developed for simulating viscoelastic free surface </div><div>flows. When complex fluid rheology is due to the presence of suspended solid spherical particles, both early-time (linear) and asymptotic dynamics are uncovered by coupling the motion of the particles and Newtonian fluid implicitly in a GFEM fluid-structure interaction (FSI) algorithm. These novel algorithms are used to analyze the pinch-off dynamics of liquid jets and drops.</div>

<p>Free surface flows, characterized by a deformable interface between two immiscible fluids or between a liquid and a gas, play a pivotal role in numerous natural phenomena and industrial processes. The fluid-fluid interface dynamics, governed by the complex interplay of forces such as inertia, capillary force, viscous force, and possibly elastic force, significantly influence the behavior of the fluids involved. Examples of free surface flows can be observed in everyday situations, such as droplet formation from a faucet, propagation and breaking of ocean waves, and tear films that coat the eye. An in-depth understanding of free surface flows and fluid-fluid interface dynamics has extensive implications for optimizing applications like inkjet printing, coating, spraying, and droplet formation while providing insights into the intricate behavior of natural fluid systems. Most of these applications, except for coating, involve abrupt and catastrophic topological changes of interfaces present in processes such as drop breakup, sheet rupture, and drop impact, where small droplets form from liquid sheets or filaments.</p> <p>This thesis examines the dynamics of contracting liquid filaments through computational means. Previous computational simulations have assumed that initially the fluid within the filament is quiescent which, however, may not typically be the case in practical applications. Here, the effect of a realistic, non-zero initial velocity profile is considered with the hypothesis that the fact that the fluid is already in motion when it starts to contract may result in significant alterations in the filament’s final fate vis-a-vis whether it breaks up into multiple small droplets or contracts into a sphere as its ends retract toward each other. The transient system of governing equations, the three-dimensional but axisymmetric (3DA) Navier-Stokes and continuity equations subjected to interfacial boundary conditions, are solved using rigorous and robust numerical algorithms in both fully 3DA and one-dimensional (1D) settings using the Galerkin finite element (GFEM) method. The simulation results are then used to construct comprehensive phase diagrams to delineate regions where filaments break up into smaller droplets from those where filaments contract to spheres without breakup.</p> <p>Polymer additives are often present in practical applications involving filament contraction and breakup. The presence of polymer molecules in an otherwise Newtonian solvent gives rise to non-Newtonian rheology. In this thesis, the dynamics of filaments containing polymer additives are analyzed using a 1D algorithm that is developed specifically for simulating viscoelastic free surface flows where the fluid’s rheology is described by the oft-used Oldroyd-B model. In real-world applications, filaments produced from nozzles are expected to be prestressed at the instant when they are created and begin to contract. It is demonstrated that the retraction velocity of tips of highly viscous, prestressed filaments is significantly increased compared to filaments in which the polymer molecules are initially relaxed and Newtonian filaments. This enhancement is explained by examining the value of f σ: D (σ: Elastic stress; D: Rate-of-strain tensor), which can be positive or negative. This quantity is positive when the flow does work on the polymer molecules but negative when the molecules do work on the flow, i.e., when elastic recoiling or unloading takes place. In prestressed filaments, elastic unloading takes place because σ: D < 0. The elastic stresses work by pulling the fluid in axially and pushing it out radially, thereby drastically increasing the tip velocity.  However, this enhancement in contraction velocity is not observed in low to intermediate viscosity prestressed filaments and whose Newtonian counterparts typically experience end-pinching. It has been established by others that end-pinching can be precluded in either filaments of intermediate viscosity or surfactant-laden filaments of low viscosity through a process known as escape from end-pinching. In this study, we demonstrate that a similar escape can also occur in prestressed viscoelastic filaments of low-to-intermediate viscosity, as revealed by one-dimensional numerical simulations and rationalized by examining when and where the elastic recoil takes place.</p> <p>Beyond cylindrical filaments, thin liquid films or planar liquid sheets are also prevalent in atomization, curtain coating, and other processes where liquid sheet stability has been a subject of extensive research. Numerous authors have examined wave formation and growth leading to sheet breakup. Free liquid films or sheets without edges or caps at their two ends, which typically have two free surfaces and are surrounded by air or sometimes another liquid, can destabilize and rupture due to intermolecular van der Waals attractive forces, despite the stabilizing influence of surface tension. In this thesis, the dynamics of contracting free films or sheets with caps---two-dimensional (2D) drops---of Newtonian fluids is examined without considering van der Waals forces to confirm or refute the hypothesis that such systems can rupture due to finite-amplitude perturbations even in the absence of intermolecular forces. In particular, both two-dimensional and one-dimensional high-accuracy simulations are employed to demonstrate that unlike inviscid 2D drops that can rupture in the absence of van der Waals forces, 2D drops or sheets can escape from pinch-off due to the action of viscous forces which are present in real systems no matter how small their viscosity. The reopening of the interface and escape from pinch-off in 2D drops and sheets are explained by demonstrating the key role played by vorticity. New power-law relations or scaling laws are obtained as a function of Ohnesorge number (ratio of viscous to the square root of the product of inertial and capillary forces) for the value of the minimum film thickness for which 2D drops or sheets stop thinning and after which the interface begins to reopen. Simple yet powerful arguments are presented rationalizing these scaling laws. It is expected that these power-law relations should be of great interest to experimentalists who study such phenomena by high-speed visualization experiments.</p> <p>Some of the motivation for this thesis research comes from crop spraying applications in which achieving zero or negligible drift is highly desirable. To further the understanding of fluid mechanics underpinning current and future drift reduction technologies, a simplified experimental setup is adopted to generate liquid sheets and analyze their disintegration into droplets. This new setup is both simpler and more universal than commonly utilized experimental systems that use single or multiple nozzles to generate liquid sheets and spray droplets from the disintegration of free liquid films. In the current experiments, droplets of test fluids are made to collide with or impact the top planar surface of a solid cylinder or rod. A series of MATLAB codes are developed and employed to extract droplet size distributions from images that are obtained from high-speed visualization experiments. The experimental setup and the means of data analysis are then used to probe the effect of fluid properties on the dynamics of sheet disintegration and droplet size distributions. It is hoped that future researchers will be able to combine what has been done in this thesis by simulations and in this chapter via experimental observations to develop an improved mechanistic understanding of spray formation.</p>