scholarly journals Closed-form theoretical model of the secondary drop size in partial coalescence—Capturing pertinent timescales and viscous forces

2020 ◽  
Vol 32 (5) ◽  
pp. 052101
Author(s):  
Sammy Houssainy ◽  
Sofya Kabachek ◽  
H. P. Kavehpour
Keyword(s):  
Theoretical Model ◽  
Closed Form ◽  
Drop Size ◽  
Viscous Forces ◽  
Partial Coalescence ◽  
Secondary Drop

Jumping drops on the surface of the water

2020 ◽  
Vol 15 (3-4) ◽  
pp. 228-231
Author(s):  
A.G. Terentiev
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Theoretical Model ◽  
Drop Size ◽  
Initial Conditions ◽  
Water Drop ◽  
Numerical Calculations ◽  
Rise Height

The paper proposes a theoretical model for the bouncing of a water drop on a free surface. The motion of a drop in air is described by the usual equations connecting the forces of inertia, gravity, and Stokes (viscosity resistance). The drop is considered spherical with a given surface tension. Numerical calculations were carried out using the same algorithm, but with different initial conditions. Some conditions are set for the droplet disintegration, others for the droplet reflection from the free surface. It is shown that the disintegration of a drop occurs periodically with a decrease in the drop size and an increase in the drop rise height. In the interval between droplet decays, periodic reflection from the free surface occurs with a decrease in the rise height.

Generation of secondary droplets in coalescence of a drop at a liquid–liquid interface

2010 ◽  
Vol 655 ◽  
pp. 72-104 ◽  
Author(s):  
B. RAY ◽  
G. BISWAS ◽  
A. SHARMA
Keyword(s):  
Critical Value ◽  
Bond Number ◽  
Viscous Force ◽  
Time Range ◽  
Main Body ◽  
Ohnesorge Number ◽  
Partial Coalescence ◽  
Daughter Droplets ◽  
Secondary Droplets ◽  
Secondary Drop

When a droplet of liquid 1 falls through liquid 2 to eventually hit the liquid 2–liquid 1 interface, its initial impact on the interface can produce daughter droplets of liquid 1. In some cases, a partial coalescence cascade governed by self-similar capillary-inertial dynamics is observed, where the fall of the secondary droplets in turn continues to produce further daughter droplets. Results show that inertia and interfacial surface tension forces largely govern the process of partial coalescence. The partial coalescence is suppressed by the viscous force when Ohnesorge number is below a critical value and also by gravity force when Bond number exceeds a critical value. Generation of secondary drop is observed for systems of lower Ohnesorge number for liquid 1, lower and intermediate Ohnesorge number for liquid 2 and for low and intermediate values of Bond number. Whenever the horizontal momentum in the liquid column is more than the vertical momentum, secondary drop is formed. A transition regime from partial to complete coalescence is obtained when the neck radius oscillates twice. In this regime, the main body of the column can be fitted to power-law scaling model within a specific time range. We investigated the conditions and the outcome of these coalescence events based on numerical simulations using a coupled level set and volume of fluid method (CLSVOF).

scholarly journals The fluid trampoline: droplets bouncing on a soap film

2009 ◽  
Vol 625 ◽  
pp. 167-203 ◽  
Author(s):  
TRISTAN GILET ◽  
JOHN W. M. BUSH
Keyword(s):  
Theoretical Model ◽  
Contact Time ◽  
Soap Film ◽  
Quantitative Agreement ◽  
Coefficient Of Restitution ◽  
Static Case ◽  
Partial Coalescence ◽  
Simple Theoretical Model ◽  
Force Displacement ◽  
Insight Into

We present the results of a combined experimental and theoretical investigation of droplets falling onto a horizontal soap film. Both static and vertically vibrated soap films are considered. In the static case, a variety of behaviours were observed, including bouncing, crossing and partial coalescence. A quasi-static description of the soap film shape yields a force–displacement relation that provides excellent agreement with experiment, and allows us to model the film as a nonlinear spring. This approach yields an accurate criterion for the transition between droplet bouncing and crossing. Moreover, it allows us to rationalize the observed constancy of the contact time and scaling for the coefficient of restitution in the bouncing states. On the vibrating film, a variety of bouncing behaviours were observed, including simple and complex periodic states, multi-periodicity and chaos. A simple theoretical model is developed that captures the essential physics of the bouncing process, reproducing all observed bouncing states. The model enables us to rationalize the observed coexistence of multiple periodic bouncing states by considering the dependence of the energy transferred to the droplet on the phase of impact. Quantitative agreement between model and experiment is deduced for simple periodic modes, and qualitative agreement for more complex periodic and chaotic bouncing states. Analytical solutions are deduced in the limit of weak forcing and dissipation, yielding insight into the contact time and periodicity of the bouncing states.

Helical Shift Mechanics of Rubber V-Belt Variators

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Francesco Sorge ◽  
Marco Cammalleri
Keyword(s):  
Theoretical Model ◽  
Numerical Solution ◽  
Closed Form ◽  
Operating Conditions ◽  
The Other ◽  
Experimental Comparison ◽  
Axial Thrust ◽  
Shooting Technique ◽  
Strongly Nonlinear ◽  
Tension Level

A very common configuration of V-belt variators for motorcycles considers the correction of the belt tensioning depending on the resistant torque by means of suitable helical-shaped tracks allowing the driven half-pulleys to close/open. The theoretical model for belt-pulley coupling is rather complex for this configuration, where one half-pulley may run in advance and the other one behind with respect to the belt, and requires the repeated numerical solution of a strongly nonlinear differential system by a sort of shooting technique, until all the operating conditions are fulfilled (angular contact extent, torque, and axial force). After solving the full equations, the present study develops closed-form approximations, which are characterized by an excellent correspondence with the numerical plots, and suggests a simple and practical formulary for the axial thrust as a function of the torque and of the tension level. Then, the results of a theoretical–experimental comparison are also reported, and they indicate a fine agreement between the model and the real operation.

Submicron Superhydrophobic Surface Treatment Suitable for High Performance Condensers: A Modeling

2009 ◽  
Author(s):  
Sunwoo Kim ◽  
Kwang J. Kim ◽  
John M. Kennedy ◽  
Jiong Liu ◽  
Ganesh Skandan
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Theoretical Model ◽  
Size Distribution ◽  
Drop Size ◽  
Drop Size Distribution ◽  
Condensation Heat Transfer ◽  
Dropwise Condensation ◽  
Superhydrophobic Coating ◽  
Single Droplet

The effect of the drop-contact angle on dropwise condensation heat transfer of saturated steam on a single horizontal copper tube with the superhydrophobic coating was investigated theoretically. The theoretical model is established by combining heat transfer through a single droplet with a well-known drop size distribution theory. The analysis of single droplet heat transfer incorporates resistances due to vapor-liquid interface, drop curvature, conduction through the drop, and conduction through the superhydrophobic coating layer. Each resistance is expressed as a function of the contact angle. The total resistance for a drop with a fixed radius increases as the contact angle increases. A population balance model is used to develop a drop distribution function for the small drops that grow by direct condensation. Drop size distribution for large drops that grow mainly by coalescence is obtained from the empirical equation proposed by Le Fevre and Rose (1966). The results indicate that the contact angle has a strong correlation with the maximum drop radius, which plays a pivotal role in determining drop size distribution. A high contact angle leads to a significant reduction in the radius of the largest drop that is about to fall down due to gravity and sweep away drops in its path. Thus, there are more areas on the condensing surface for small drops, allowing for greater heat transfer. Also, it is shown that surface wettability affects the performance of dropwise condensation heat transfer and our theoretical model successfully predicts this phenomenon.

On the Main Flow Pattern in Hydrocyclones

1993 ◽  
Vol 115 (1) ◽  
pp. 21-25 ◽  
Author(s):  
C. C. Hwang ◽  
H. Q. Shen ◽  
G. Zhu ◽  
M. M. Khonsari
Keyword(s):  
Theoretical Model ◽  
Flow Field ◽  
Closed Form ◽  
Flow Pattern ◽  
Main Flow ◽  
Experimental Measurements ◽  
Main Body ◽  
Governing Equations ◽  
Adequate Representation ◽  
Good Agreement

A theoretical model is developed for the prediction of the main flow pattern in hydrocyclones. The model regards the main body of the cyclone as inviscid and includes provisions for the fluid underflow in cyclones. The governing equations are solved analytically in closed form. To verify the results, a laboratory-scale conically-shaped hydrocyclone was designed, built, and tested. Experimental measurements for axial and tangential velocities are presented with a series of tests solely devoted to the effect of underflow. The theoretical and experimental results are shown to be in good agreement. It is concluded that such an inviscid model gives an adequate representation of the main flow field in a cyclone.

A Theoretical Approach to Dropwise Condensation Using Population Balance Concept

2004 ◽  
Author(s):  
S. Vemuri ◽  
K. J. Kim ◽  
B. D. Wood ◽  
T. W. Bell
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Theoretical Model ◽  
Size Distribution ◽  
Drop Size ◽  
Population Balance ◽  
Theoretical Formula ◽  
Dropwise Condensation ◽  
Sweeping Effect ◽  
Direct Condensation

A model using the population balance concept is used to derive a theoretical formula to predict the drop-size distribution of small drops which grow mainly by direct condensation. All the important resistances to heat transfer such as the heat conduction through the drop, vapor-liquid interface are considered in developing this model. By knowing the contact angle of the drop made with the condensing surface and the maximum drop radius the sweeping effect of large falling drops could be calculated which is also incorporated into the model. This is combined with the well known size distribution for large drops proposed by Le Fevre and Rose (1966) which grow mainly by coalescence and with the growth rate of single drops to compute the heat flux during the process of dropwise condensation. The data obtained from this theoretical model is compared to that of the data obtained from our experimentation. There has been a satisfactory agreement between our experimental data and the present theoretical model.

DYNAMICAL DISPERSION IN THE FAST-PARTICLE EMISSION AFTER PERIPHERAL HEAVY-ION COLLISIONS

2007 ◽  
Vol 16 (01) ◽  
pp. 149-168
Author(s):  
A. ITALIANO ◽  
A. STRAZZERI
Keyword(s):  
Reaction Mechanism ◽  
Theoretical Model ◽  
Closed Form ◽  
Angular Correlation ◽  
Heavy Ion ◽  
Particle Emission ◽  
Inelastic Collisions ◽  
Heavy Ion Collision ◽  
Ion Collisions ◽  
Ion Collision

The closed-form theoretical model, already employed to successfully describe in a single picture, the nonequilibrium component and the evaporation component of the angular correlation between particles and reaction residues emitted in a peripheral heavy-ion collision, is here revisited. This revised approach, applied to the C-α differential multiplicities for the 16O+58Ni at 6 MeV/A and 16O+48Ti at 8.3 MeV/A deep inelastic collisions, allows to explain more in detail the reaction mechanism of such processes.

A Model for Analyzing Suicide Prevention

Crisis ◽  
2000 ◽  
Vol 21 (2) ◽  
pp. 80-89 ◽  
Author(s):  
Maila Upanne
Keyword(s):  
Risk Factors ◽  
Theoretical Model ◽  
Protective Factors ◽  
Suicide Prevention ◽  
Suicide Risk ◽  
Practical Work ◽  
Individual Risk ◽  
Self Assessment ◽  
Prevention Project ◽  
Individual Risk Factors

This study monitored the evolution of psychologists' (n = 31) conceptions of suicide prevention over the 9-year course of the National Suicide Prevention Project in Finland and assessed the feasibility of the theoretical model for analyzing suicide prevention developed in earlier studies [ Upanne, 1999a , b ]. The study was formulated as a retrospective self-assessment where participants compared their earlier descriptions of suicide prevention with their current views. The changes in conceptions were analyzed and interpreted using both the model and the explanations given by the subjects themselves. The analysis proved the model to be a useful framework for revealing the essential features of prevention. The results showed that the freely-formulated ideas on prevention were more comprehensive than those evolved in practical work. Compared to the earlier findings, the conceptions among the group had shifted toward emphasizing a curative approach and the significance of individual risk factors. In particular, greater priority was focused on the acute suicide risk phase as a preventive target. Nonetheless, the overall structure of prevention ideology remained comprehensive and multifactorial, stressing multistage influencing. Promotive aims (protective factors) also remained part of the prevention paradigm. Practical working experiences enhanced the psychologists' sense of the difficulties of suicide prevention as well as their criticism and feeling of powerlessness.

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