C. Mehring

Review of theory of distortion and disintegration of liquid streams

Abstract Linear and nonlinear analyses of the instabilities and distortion of liquid streams injected into a gaseous media are discussed. The various fundamental mechanisms and the predictive capabilities for the distortions are emphasized. Round jets, planar sheets, annular sheets, and conical sheets are discussed in detail. The balance between capillary and inertial forces is primarily examined. The method for simplifying the analyses in the case of thin liquid sheets is discussed. The capabilities for representing the droplet size distribution that follows the stream disintegration are outlined.

Nonlinear capillary wave distortion and disintegration of thin planar liquid sheets

Linear and nonlinear dilational and sinuous capillary waves on thin inviscid infinite and semi-infinite planar liquid sheets in a void are analysed in a unified manner by means of a method that reduces the two-dimensional unsteady problem to a one-dimensional unsteady problem. For nonlinear dilational waves on infinite sheets, the accuracy of the numerical solutions is verified by comparing with an analytical solution. The nonlinear dilational wave maintains a reciprocal relationship between wavelength and wave speed modified from the linear theory prediction by a dependence of the product of wavelength and wave speed on the wave amplitude. For the general dilational case, nonlinear numerical simulations show that the sheet is unstable to superimposed subharmonic disturbances on the infinite sheet. Agreement for both sinuous and dilational waves is demonstrated for the infinite case between nonlinear simulations using the reduced one-dimensional approach, and nonlinear two-dimensional simulations using a discrete-vortex method. For semi-infinite dilational and sinuous distorting sheets that are periodically forced at the nozzle exit, linear and nonlinear analyses predict the appearance of two constant-amplitude waves of nearly equal wavelengths, resulting in a sheet disturbance characterized by a long-wavelength envelope of a short-wavelength oscillation. For semi-infinite sheets with sinuous waves, qualitative agreement between the dimensionally reduced analysis and experimental results is found. For example, a half-wave thinning and a sawtooth wave shape is found for the nonlinear sinuous mode. For the semi-infinite dilational case, a critical frequency-dependent Weber number is found below which one component of the disturbances decays with downstream distance. For the semi-infinite sinuous case, a critical Weber number equal to 2 is found; below this value, only one characteristic is emitted in the positive time direction from the nozzle exit.

Axisymmetric capillary waves on thin annular liquid sheets. I. Temporal stability

A reduced-dimension approach is employed to analyze the nonlinear distortion and disintegration of axisymmetric thin inviscid annular liquid sheets in a surrounding void with nonzero gas-core pressure at zero gravity. Linear and nonlinear solutions for the free motion of periodically disturbed infinite linearly stable and unstable sheets are obtained and compared in this first paper. (The forced motion of semi-infinite annular sheets exiting from a nozzle or atomizer is considered in the second paper.) Both sinuous and dilational modes are studied. Both modes are dispersive unlike the planar case where only the dilational mode is dispersive. These modes are coupled even in the linear representation although for sufficiently large annular radius, a pure dilational linear oscillation is found. The sinuous oscillation always excites the dilational mode. Nonlinear effects can modify the wave shapes substantially, causing an increase in breakup time for the dilational mode and a decrease in breakup time for th...

Axisymmetric capillary waves on thin annular liquid sheets. II. Spatial development

The forced motion of semi-infinite axisymmetric thin inviscid annular liquid sheets, exiting from a nozzle or atomizer into a surrounding void under zero gravity but with constant gas-core pressure is analyzed by means of the reduced-dimension approach described in C. Mehring and W. A. Sirignano [Phys. Fluids 12, 1417 (2000)]. Linear analytical time-dependent (“limit-cycle”) solutions to the pure boundary-value problem are presented as well as linear and nonlinear numerical (transient) solutions to the mixed boundary- and initial-value problem of initially undisturbed sheets harmonically forced at the orifice or nozzle exit. Group velocities for the six independent solutions to the linear boundary-value problem are used to determine the location of boundary conditions. Numerical simulations of the linear transient problem are employed to validate these predictions. Parameter studies on sheet breakup and collapse lengths as well as on breakup and collapse times are reported. The dependence on modulation fr...

Nonlinear capillary waves on swirling, axisymmetric free liquid films

Abstract The nonlinear distortion and breakup of a swirling axisymmetric thin inviscid liquid sheet in a void and at zero gravity is analyzed by means of a reduced dimension approach. Nonlinear steady-state solutions are presented for various boundary conditions imposed at the nozzle exit. Unsteady solutions describing the nonlinear breakup of the radially expanding film due to dilational or sinuous modulations at the nozzle exit are presented. Fluid rings with thin connecting shells are formed due to nonlinear effects and sheet thinning caused by sheet divergence is found to increase nonlinear breakup lengths and times for both sinuous and dilational modes. For the case of a swirling annular liquid sheet, comparisons are made with an annular sheet which is stabilized by a constant gas-core pressure. Here, swirl causes a reduction in breakup lengths and times.

Disintegration of planar liquid film impacted by two-dimensional gas jets

The distortion and break-up of a thin planar liquid film impacted by two gas jets while discharging from a twin-fluid atomizer is studied numerically. The gas momentum vector has components normal and parallel to the liquid stream. Viscosity and compressibility are neglected in both the liquid phase and the gas phase. The reduced-dimension (lubrication) approximation is employed to describe the nonlinear distortion and breakup of the thin film. The gas-phase dynamics are modelled by using a boundary-element-method formulation. For the considered parameter range and for a given energy expenditure, direct modulation of liquid-phase velocities at the nozzle exit is found to be more effective in causing film rupture than indirect modulation via adjacent impacting gas jets. In the former case, dilational film modulation results in shorter breakup lengths than sinuous modulation. On the other hand, for gas-jet modulated films, sinuous mode forcing is more effective than dilational forcing for the same energy in...

Dynamic stretching of a planar liquid bridge

A thin incompressible viscous planar free liquid film in a void and under zero gravity is analyzed by means of a reduced-dimension (lubrication) approach. Linear analysis focuses on films with harmonic modulations in the axial film velocity enforced at the ends of the planar bridge. Effects of changes in the problem parameters on the overall distortion characteristics of the film are discussed. Nonlinear film distortion and break-up are investigated for the case of temporally increasing velocity at the end of the film resulting in continuous film stretching eventually leading to film rupture. Implementation of the employed numerical model is validated for the linear limit by comparison with the analytical linear solutions and for harmonically modulated film-end velocities. Within the nonlinear analysis of the continuously stretched film bridge, several distinct film topologies are identified depending on liquid Weber number and Reynolds number, i.e., the magnitude of the stretching rate (end velocity) com...