Shattering of a liquid drop due to impact

1991 ◽  
Vol 435 (1895) ◽  
pp. 483-503 ◽  
Keyword(s):  
Surface Energy ◽  
Statistical Model ◽  
Surface Area ◽  
Liquid Drop ◽  
Drop Impact ◽  
Drop Breakup ◽  
Viscous Effects ◽  
Consistent Manner

Based on energy and entropy principles, a statistical model describing the shattered state of a single spherical liquid drop after being subjected to a relatively sudden but uniform (over the whole surface area of the drop) impact is developed. The problem is addressed from a fundamental standpoint, with the intention of providing a predictive framework for the various modes of breakup and the size and number of droplets produced. Upon neglecting viscous effects, several results in terms of the energy of impact, non-dimensionalized with respect to the surface energy of the drop before impact, are derived. The model is quite simple and straightforward, yet it appears to predict in a fairly consistent manner certain experimental observations that have been made repeatedly in relation to drop breakup in stirred dispersions, by collision, and exposure to shocks.

scholarly journals Use of discriminant analysis based on echocardiography for classification of congestive heart failure in dogs with myxomatous mitral valve disease

2014 ◽  
Vol 66 (6) ◽  
pp. 1727-1734
Author(s):  
A.C. Silva ◽  
R.A.L. Muzzi ◽  
L.A.L. Muzzi ◽  
D.F. Ferreira ◽  
G. Oberlender ◽  
...  
Keyword(s):  
Heart Failure ◽  
Mitral Valve ◽  
Statistical Model ◽  
Surface Area ◽  
Mitral Valve Disease ◽  
Clinical Signs ◽  
Valve Disease ◽  
Aortic Diameter ◽  
Mathematical Tool

Mixomatous mitral valve disease (MMVD) is one of the most common cardiac abnormalities in dogs and humans that can lead to cardiac heart failure (CHF). Its diagnosis remains based on echocardiography and clinical signs. However, the early diagnose of MMVD can contribute to a better prognosis and avoid CHF. The aim of this study was to evaluate the clinical, radiographic and echocardiographic presence of CHF in dogs with MMVD in combination with a statistical model as a mathematical tool. For this purpose, dogs were divided into three groups (healthy; MMVD without CHF; and MMVD with CHF), according the clinical, radiographic and echocardiographic evaluation findings. Thus, linear discriminant functions were obtained by analyzing the variables weight, body surface area, aortic diameter, the ratio of the left atrium/aortic diameter, the ratio between the mitral regurgitation jet area and the left atrial area, vena contracta diameter and mitral valve proximal isovelocity surface area. Then, mathematical equations were established for each group of dogs. Statistical functions obtained in this study enabled to classify the dogs, regarding the presence of CHF with a probability of correct classification of 90.4%. Thus the statistical model demonstrated that it could be used as an auxiliary method for identifying CHF in dogs with MMVD.

scholarly journals An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc

1986 ◽  
Vol 406 (1830) ◽  
pp. 93-106 ◽  
Keyword(s):  
Boundary Layer ◽  
Nonlinear Problems ◽  
Wave Number ◽  
Viscous Effects ◽  
Rotating Disc ◽  
Expansion Procedure ◽  
Asymptotic Investigation ◽  
Starting Point ◽  
Consistent Manner ◽  
High Reynolds

The paper investigates high-Reynolds-number stationary instabilities in the boundary layer on a rotating disc. The investigation demonstrates that, in addition to the inviscid mode found by Gregory, Stuart & Walker ( Phil. Trans. R. Soc. Lond. A 248, 155 (1955)) at high Reynolds numbers, there is a stationary short-wavelength mode. This mode has its structure fixed by a balance between viscous and Coriolis forces and cannot be described by an inviscid theory. The asymptotic structure of the wave-number and orientation of this mode is obtained, and a similar analysis is given for the inviscid mode. The expansion procedure provides the capacity of taking non-parallel effects into account in a self-consistent manner. The inviscid solution of Gregory et al . is modified to take account of viscous effects. The expansion procedure used is again capable of taking non-parallel effects into account. The results obtained suggest why the inviscid approach of Gregory et al . should give a good approximation to the experimentally measured orientation of the vortices. The results also explain partly why the inviscid analysis should not give such a good approximation to the wavenumber of the vortices. The asymptotic analysis of both modes provides a starting point for the corresponding nonlinear problems.

scholarly journals Decoupling the Contribution of Surface Energy and Surface Area on the Cohesion of Pharmaceutical Powders

2014 ◽  
Vol 32 (1) ◽  
pp. 248-259 ◽  
Author(s):  
Umang V. Shah ◽  
Dolapo Olusanmi ◽  
Ajit S. Narang ◽  
Munir A. Hussain ◽  
Michael J. Tobyn ◽  
...  
Keyword(s):  
Surface Energy ◽  
Surface Area ◽  
Pharmaceutical Powders

The Study of Statistical Model of Mass Liquid Drop during Metal Spray Forming Process

2005 ◽  
Vol 475-479 ◽  
pp. 2819-2822 ◽  
Author(s):  
Yin Zhang ◽  
Jun Fei Fan ◽  
You Duo He ◽  
San Bing Ren ◽  
Jing Guo Zhang ◽  
...  
Keyword(s):  
Statistical Model ◽  
Initial Velocity ◽  
Liquid Drop ◽  
Simulation Method ◽  
Deposition Process ◽  
Spray Forming ◽  
Liquid Droplets ◽  
Forming Process ◽  
Whole Space ◽  
Metal Spray

Through the probability simulation method, the statistical model of mass metal liquid droplets during metal spray forming process was developed and the ejecting process of molten steel was studied. The distribution of metal liquid droplets, their different initial velocity and the original appear location during spray forming were obtained based on the above computation. After made statistic and analyzed on large number of metal liquid droplets, the forming and motion of liquid drop in whole space were defined in detail, which provided the precondition and reference for further study of liquid droplets deposition process on substrate.

Deformation of metallic liquid drop by electric field for contacts in molecular–organic electronics

2009 ◽  
Vol 465 (2106) ◽  
pp. 1799-1808 ◽  
Author(s):  
M. Bag ◽  
D. Gupta ◽  
N. Arun ◽  
K.S. Narayan
Keyword(s):  
Solid State ◽  
Surface Energy ◽  
Electric Field ◽  
Linear Response ◽  
Liquid Drop ◽  
Electrostatic Energy ◽  
Critical Voltage ◽  
Metallic Liquid ◽  
Linear Response Regime ◽  
Polymer Electronics

We study and use the behaviour of a metallic liquid drop in the presence of an external electric field (EF). The droplet profile is governed by the stabilizing surface energy and the destabilizing electrostatic energy, with a critical voltage beyond which the droplet becomes unstable. We explore the EF-induced behaviour of low melting temperature alloy in the liquid state and observe that the droplet modifications in the linear response regime can be retained upon cooling the drop to the solid state. We demonstrate that this procedure can be used as an electrode with precise dimensions for applications in molecular and polymer electronics.

scholarly journals Thermodynamics of manganese oxides: Sodium, potassium, and calcium birnessite and cryptomelane

2017 ◽  
Vol 114 (7) ◽  
pp. E1046-E1053 ◽  
Author(s):  
Nancy Birkner ◽  
Alexandra Navrotsky
Keyword(s):  
Surface Energy ◽  
Surface Area ◽  
Oxidation State ◽  
Manganese Oxides ◽  
Lower Surface ◽  
Surface Energies ◽  
Surface Areas ◽  
Bulk Thermodynamics ◽  
Lower Surface Energy

Manganese oxides with layer and tunnel structures occur widely in nature and inspire technological applications. Having variable compositions, these structures often are found as small particles (nanophases). This study explores, using experimental thermochemistry, the role of composition, oxidation state, structure, and surface energy in the their thermodynamic stability. The measured surface energies of cryptomelane, sodium birnessite, potassium birnessite and calcium birnessite are all significantly lower than those of binary manganese oxides (Mn3O4, Mn2O3, and MnO2), consistent with added stabilization of the layer and tunnel structures at the nanoscale. Surface energies generally decrease with decreasing average manganese oxidation state. A stabilizing enthalpy contribution arises from increasing counter-cation content. The formation of cryptomelane from birnessite in contact with aqueous solution is favored by the removal of ions from the layered phase. At large surface area, surface-energy differences make cryptomelane formation thermodynamically less favorable than birnessite formation. In contrast, at small to moderate surface areas, bulk thermodynamics and the energetics of the aqueous phase drive cryptomelane formation from birnessite, perhaps aided by oxidation-state differences. Transformation among birnessite phases of increasing surface area favors compositions with lower surface energy. These quantitative thermodynamic findings explain and support qualitative observations of phase-transformation patterns gathered from natural and synthetic manganese oxides.

Studies of two-dimensional liquid-wedge impact and their relevance to liquid-drop impact problems

1985 ◽  
Vol 401 (1821) ◽  
pp. 225-249 ◽  
Keyword(s):  
High Speed ◽  
Liquid Drop ◽  
Time History ◽  
Drop Impact ◽  
High Speed Photography ◽  
Two Dimensional ◽  
Surface Geometry ◽  
Repeated Impact ◽  
Liquid Impact ◽  
The Impact

In the initial stage of liquid-drop impact, the contact region expands faster than the wave speed in the liquid. This causes compressible behaviour in the liquid, and high transient pressures. High-velocity jetting results when the wave motion in the liquid overtakes the expanding contact edge and moves up the free surface of the drop. The detailed pressure fields in this early time history of impact have been calculated by Lesser ( Proc . R . Soc . Lond . 377, 289 (1981)) for both two and three-dimensional liquid masses and for targets of finite admittance. An important result is that the edge pressures exceed the central ‘water-hammer’ pressure 3ρ 0 CU i and at the time of shock-detachment approach ca . 3ρ 0 CU i . At this stage the edge pressures, for both spherical drops and two-dimensional liquid wedges, depend only on the impact velocity and the instantaneous angle between the liquid and solid surfaces. This suggests that the essential features of the early stage of liquid impact can be usefully studied by producing impacts with two-dimensional liquid wedges, and predicted data for pressures, shock angles and velocities are presented. Experiments are described for producing impacts with preformed shapes by using water-gelatine mixtures and observing the impact events with high-speed photography. The results confirm the main features of the model and give information on edge pressures, jetting, cavitation in the liquid and the effect of the admittance of the solid. The relevance of the results to the damage and erosion of materials subjected to liquid impact is discussed. In particular, it is possible to explain the apparently low damage-threshold of some materials, the form of damage and its development with repeated impact. The study highlights the importance of the detailed surface geometry in the region of contact.

Predictive Statistical Model for the Analysis of Drop Impact Damage on Peach

1999 ◽  
Vol 73 (3) ◽  
pp. 275-282 ◽  
Author(s):  
Paolo Menesatti ◽  
Claudio Beni ◽  
Graziella Paglia ◽  
Simona Marcelli ◽  
Stefano D'Andrea
Keyword(s):  
Statistical Model ◽  
Impact Damage ◽  
Drop Impact
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