A note on the damping and oscillations of a fluid drop moving in another fluid

1969 ◽  
Vol 37 (4) ◽  
pp. 715-725 ◽  
Author(s):  
S. V. Subramanyam
Keyword(s):  
Weber Number ◽  
Critical Size ◽  
Correction Term ◽  
Frequency Mode ◽  
Viscous Effects ◽  
Fluid Medium ◽  
Two Fluids ◽  
Fluid Drop ◽  
Two Phases ◽  
Lower Frequency Mode

The oscillations of a drop moving in another fluid medium have been studied at low values of Reynolds number and Weber number by taking into consideration the shape of the drop and the viscosities of the two phases in addition to the interfacial tension. The deformation of the drop modifies the Lamb's expression for frequency by including a correction term while the viscous effects split the frequency into a pair of frequencies—one lower and the other higher than Lamb's. The lower frequency mode has ample experimental support while the higher frequency mode has also been observed. The two modes almost merge with Lamb's frequency for the asymptotic cases of a drop in free space or a bubble in a dense viscous fluid but the splitting becomes large when the two fluids have similar properties. Instead of oscillations, aperiodic damping modes are found to occur in drops with sizes smaller than a critical size ($\sim\hat{\rho}\hat{\nu}^2/T $). With the help of these calculations, many of the available experimental results are analyzed and discussed.

scholarly journals Encapsulation of Droplets Using Cusp Formation behind a Drop Rising in a Non-Newtonian Fluid

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 54 ◽  
Author(s):  
Raphaël Poryles ◽  
Roberto Zenit
Keyword(s):  
Critical Velocity ◽  
Newtonian Fluid ◽  
Formation Process ◽  
Critical Size ◽  
Long Tail ◽  
Capillary Effects ◽  
Velocity Discontinuity ◽  
Two Fluids ◽  
Viscous Solution ◽  
Surrounding Liquid

The rising of a Newtonian oil drop in a non-Newtonian viscous solution is studied experimentally. In this case, the shape of the ascending drop is strongly affected by the viscoelastic and shear-thinning properties of the surrounding liquid. We found that the so-called velocity discontinuity phenomena is observed for drops larger than a certain critical size. Beyond the critical velocity, the formation of a long tail is observed, from which small droplets are continuously emitted. We determined that the fragmentation of the tail results mainly from the effect of capillary effects. We explore the idea of using this configuration as a new encapsulation technique, where the size and frequency of droplets are directly related to the volume of the main rising drop, for the particular pair of fluids used. These experimental results could lead to other investigations, which could help to predict the droplet formation process by tuning the two fluids’ properties, and adjusting only the volume of the main drop.

scholarly journals Inertial settling of a sphere through an interface. Part 2. Sphere and tail dynamics

2017 ◽  
Vol 835 ◽  
pp. 808-851 ◽  
Author(s):  
Jean-Lou Pierson ◽  
Jacques Magnaudet
Keyword(s):  
Interfacial Instability ◽  
Linear Stability Theory ◽  
Rigid Sphere ◽  
Fluid Viscosity ◽  
Viscous Effects ◽  
Layer System ◽  
Two Fluids ◽  
Low Viscosity ◽  
Satellite Drops ◽  
Lower Fluid

Selected situations in which a rigid sphere settles through a two-layer system obtained by superimposing two immiscible Newtonian fluids are studied using a combination of experiments and direct numerical simulations. By varying the viscosity of the two fluids and the sphere size and inertia, the flow conditions cover situations driven by capillary and viscous effects, in which case the sphere detaches slowly from the interface and may even rise for a period of time, as well as highly inertial cases where its motion is barely affected by the interface and essentially reacts to the change in the fluid viscosity and density. The evolutions of the sphere velocity, effective drag force and entrained volume of upper fluid are analysed. In most cases considered here, this entrained volume first takes the form of an axisymmetric tail which elongates as time proceeds until it pinches off at some point. We examine the post-pinch-off dynamics of this tail under various conditions. When the viscosity of the lower fluid is comparable or larger than that of the upper one, an end-pinching process initiated near the initial pinch-off position develops and propagates along the tail, gradually transforming it into a series of primary and satellite drops; the size of the former is correctly predicted by the linear stability theory. In contrast, when the lower fluid is much less viscous than the upper one, the tail recedes without pinching off again. During a certain stage of the process, the tip velocity keeps a constant value which is significantly underpredicted by the classical Taylor–Culick model. An improved theoretical prediction, shown to agree well with observations, is obtained by incorporating buoyancy effects resulting from the density difference between the two fluids. Spheres with large enough inertia settling in a low-viscosity lower fluid are found to exhibit specific tail dynamics prefiguring wake fragmentation. Indeed, an interfacial instability quickly develops near the top of the sphere, resulting in the formation of thin axisymmetric corollas surrounding the central part of the tail and propagating upwards. A simplified inviscid model considering the role of the boundary layer around the tail and including surface tension effects is found to predict correctly the characteristics of the observed instability which turns out to be governed by the Kelvin–Helmholtz mechanism.

Numerical Modeling of Unidirectional Stratified Flow Between Parallel Plates

2004 ◽  
Author(s):  
Y. F. Yap ◽  
J. C. Chai ◽  
K. C. Toh ◽  
T. N. Wong ◽  
Y. C. Lam
Keyword(s):  
Exact Solutions ◽  
Cross Section ◽  
Correction Term ◽  
Stratified Flow ◽  
Mass Conservation ◽  
Parallel Plates ◽  
Two Fluids ◽  
Mass Correction ◽  
Developing Region ◽  
Mass Flowrate

Unidirectional stratified flow of two fluids between two parallel plates is modeled using the Level-Set method. A localized mass correction term is used to ensure mass conservation at every axial cross section. The mass correction term is based on the mass flowrates. Results for various combinations of density, viscosity and mass flowrate ratios are presented. Available fully-developed exact solutions for unidirectional stratified flow are used to validate the numerical simulations. The evolutions of the interface in the developing region are also captured and compared well with “exact” solutions.

Structural Dynamics and Response of Roof Tiles Under Wind Loading: Effect of Vibration on Scattering

2007 ◽  
Author(s):  
S. Okamoto
Keyword(s):  
High Speed ◽  
Coherence Function ◽  
Slope Angle ◽  
Video Camera ◽  
Frequency Mode ◽  
Wind Loading ◽  
Camera System ◽  
High Speed Video ◽  
High Speed Video Camera ◽  
Lower Frequency Mode

This study has investigated the nature and source of the vibrating and scattering behavior of roof tiles with the aim of providing a better insight to the mechanism. The 100 roof tiles were set up on 10 lines and 10 lows on the pitched roof in the downstream of the flow from the wind tunnel. These experiments were followed by series of tests where the slope angle of the roof tiles was changed. The vibrations of the roof tiles were simultaneously measured by the two accelerometers, and the motions of the vibration and scattering were observed by the high-speed video camera. The frequency response function and coherence function of roof tile were measured by impact hammer test under no flow condition. Just before scattering of the roof tiles, both vibrations of higher frequency mode and vibrations of lower frequency mode appeared simultaneously in roof tiles. The values of the higher frequencies were corresponding to the values of resonant frequencies of the roof tiles. It was thought that the scattering of roof tiles was influenced by the vibration of the lower frequency mode. The frequencies of the vibration were measured by the high-speed video camera system. The values of the lower frequencies were 10 Hz ∼ 20 Hz. The mechanism of scattering of roof tiles could be understood by means of the information from the accelerations and the images of roof tiles.

scholarly journals Singularities in a two-fluid medium

1983 ◽  
Vol 6 (4) ◽  
pp. 737-754 ◽  
Author(s):  
Rathindra Nath Chakrabarti ◽  
Birendranath Mandal
Keyword(s):  
Horizontal Plane ◽  
Plane Surface ◽  
Finite Depth ◽  
Point Singularity ◽  
Fluid Medium ◽  
Two Fluids ◽  
Line Singularity ◽  
Lower Fluid ◽  
Irrotational Motion ◽  
Two Fluid

We compute the irrotational motion of two fluids with a horizontal plane surface of separation, under gravity. The fluids are nonviscous and incompressible, the upper one of finite depth with a free surface; they contain a line singularity or a point singularity. We obtain the velocity potentials for each singularity located in the upper or the lower fluid; if the upper depth tends to infinity, known results are recovered.

scholarly journals Ring source potentials in two superposed fluids separeted by an inertial surface

1988 ◽  
Vol 11 (3) ◽  
pp. 535-541
Author(s):  
B. N. Mandal ◽  
Krishna Kundu
Keyword(s):  
Time Dependent ◽  
Body Of Revolution ◽  
Fluid Medium ◽  
Two Fluids ◽  
Inertial Surface ◽  
Superposed Fluids ◽  
Two Fluid ◽  
Ring Source

The study of waves at the interface of two superposed fluids due to the presence of a vertical body of revolution requires the consideration of potentials due to horizontal ring sources submerged in one of the fluids. In this paper, the velocity potentials in the two fluids are computed due to a horizontal ring of sources of time-dependent strength submerged in either of the fluids of a two-fluid medium that are separated by an inertial surface.

scholarly journals Falling styles of disks

2013 ◽  
Vol 719 ◽  
pp. 388-405 ◽  
Author(s):  
Franck Auguste ◽  
Jacques Magnaudet ◽  
David Fabre
Keyword(s):  
Complex Dynamics ◽  
Three Dimensional ◽  
Relative Magnitude ◽  
The Body ◽  
Fluid Inertia ◽  
Viscous Effects ◽  
Fluid Medium ◽  
Body Experiences ◽  
Set Up ◽  
Thin Disks

AbstractWe numerically investigate the dynamics of thin disks falling under gravity in a viscous fluid medium at rest at infinity. Varying independently the density and thickness of the disk reveals the influence of the disk aspect ratio which, contrary to previous belief, is found to be highly significant as it may completely change the route to non-vertical paths as well as the boundaries between the various path regimes. The transition from the straight vertical path to the planar fluttering regime is found to exhibit complex dynamics: a bistable behaviour of the system is detected within some parameter range and several intermediate regimes are observed in which, although the wake is unstable, the path barely deviates from vertical. By varying independently the body-to-fluid inertia ratio and the relative magnitude of inertial and viscous effects over a significant range, we set up a comprehensive map of the corresponding styles of path followed by an infinitely thin disk. We observe the four types of planar regimes already reported in experiments but also identify two additional fully three-dimensional regimes in which the body experiences a slow horizontal precession superimposed onto zigzagging or tumbling motions.

Modeling and Simulation of High-Velocity Projectile Impact on Storage Tank

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Y. W. Kwon ◽  
K. Yang ◽  
C. Adams
Keyword(s):  
High Velocity ◽  
Storage Tank ◽  
Structural Response ◽  
Dynamic Responses ◽  
Second Phase ◽  
Fluid Medium ◽  
Parametric Studies ◽  
Two Phases ◽  
Improved Design ◽  
The Impact

A series of numerical modeling and simulations were conducted for dynamic responses of a fluid-filled storage tank subjected to impact loading resulting from a high-velocity projectile. The focus of the study was placed on two phases. The first phase examined the structural response during the impact period without penetration while the second phase investigated the period of a projectile traveling through a fluid medium inside the storage tank. Some parametric studies were conducted to understand the dynamic responses of the structure. The parameters considered were the fluid filling level in the storage tank, fluid density, tank material properties, and projectile mass and velocity. Understanding what parameters would result in most severe damage to the structure can lead to improved design of storage tanks and proper protection against any potential incident.

On the instability of small gas bubbles moving uniformly in various liquids

1957 ◽  
Vol 3 (1) ◽  
pp. 27-47 ◽  
Author(s):  
R. A. Hartunian ◽  
W. R. Sears
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Gas Bubbles ◽  
Hydrodynamic Pressure ◽  
Terminal Velocity ◽  
Approximate Methods ◽  
Stability Calculation ◽  
Fluid Medium ◽  
Critical Weber Number ◽  
The Stability

The instability of small gas bubbles moving uniformly in various liquids is investigated experimentally and theoretically.The experiments consist of the measurement of the size and terminal velocity of bubbles at the threshold of instability in various liquids, together with the physical properties of the liquids. The results of the experiments indicate the existence of a universal stability curve. The nature of this curve strongly suggests that there are two separate criteria for predicting the onset of instability, namely, a critical Reynolds number (202) and a critical Weber number (1.26). The former criterion appears to be valid for bubbles moving uniformly in liquids containing impurities and in the somewhat more viscous liquids, whereas the latter criterion is for bubbles moving in pure, relatively inviscid liquids.The theoretical analysis is directed towards an investigation of the possibility of the interaction of surface tension and hydrodynamic pressure leading to unstable motions of the bubble, i.e. the existence of a critical Weber number. Accordingly, the theoretical model assumes the form of a general perturbation in the shape of a deformable sphere moving with uniform velocity in an inviscid, incompressible fluid medium of infinite extent. The calculations lead to divergent solutions above a certain Weber number, indicating, at least qualitatively, that the interaction of surface tension and hydrodynamic pressure can result in instabilities of the bubble motion.A subsequent investigation of the time-independent equations, however, shows the presence of large deformations in shape of the bubble prior to the onset of unstable motion, which is not compatible with the approximation of perturbing an essentially spherical bubble. This deformation and its possible effects on the stability calculation are therefore determined by approximate methods. From this it is concluded that the deformation of the bubble serves to introduce quantitative, but not qualitative, changes in the stability calculation.

Effects of Ions on the Propagation of Langmuir Oscillations in Cold Quantum Electron-Ion Plasmas

2008 ◽  
Vol 63 (7-8) ◽  
pp. 400-404 ◽  
Author(s):  
Hyun-Jae Rhee ◽  
Young-Dae Jung
Keyword(s):  
Phase Velocity ◽  
Quantum Effect ◽  
Frequency Mode ◽  
Wave Number ◽  
Propagation Mode ◽  
Quantum Electron ◽  
Quantum Plasmas ◽  
Phase And Group Velocities ◽  
Lower Frequency Mode ◽  
Group Velocities

The effects of ions on the propagation of Langmuir oscillations are investigated in cold quantum electron-ion plasmas. It is shown that the higher and lower frequency modes of the Langmuir oscillations would propagate in cold quantum plasmas according to the effects of ions. It is also shown that these two propagation modes merge into one single propagation mode if the contribution of ions is neglected. It is found that the quantum effect enhances the phase and group velocities of the higher frequency mode of the propagation. In addition, it is shown that the phase velocity of the lower frequency mode is saturated with increasing the quantum wavelength and further that the group velocity of the lower frequency mode has a maximum position in the domains of the wave number and quantum wavelength.

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