Stability and collapse of holes in liquid layers

2018 ◽  
Vol 855 ◽  
pp. 1130-1155 ◽  
Author(s):  
Cunjing Lv ◽  
Michael Eigenbrod ◽  
Steffen Hardt
Keyword(s):  
Liquid Film ◽  
Power Laws ◽  
Theoretical Models ◽  
Liquid Volume ◽  
Capillary Length ◽  
Minimum Thickness ◽  
The Stability ◽  
Film Profile ◽  
Hole Closure ◽  
Good Agreement

We investigate experimentally and theoretically the stability and collapse of holes in liquid layers on bounded substrates with various wettabilities. It is shown that for a liquid layer with a thickness of the order of the capillary length, a stable hole exists when the hole diameter is bigger than a critical value $d_{c}$. Consequently, a further increase of the liquid volume causes the hole to collapse. It is found that$d_{c}$increases with the size of the container, but its dependence on the contact angle is very weak. The experimental results are compared with theory, and good agreement is obtained. Moreover, we present investigations of the dynamics of the hole and the evolution of the liquid film profile after the collapse. The diameter of the hole during collapse and the minimum thickness of the liquid film shortly after the collapse obey different power laws with time. Simple theoretical models are developed which indicate that the collapse of the hole is triggered by surface tension and the subsequent closure process results from inertia, whereas the growth of the liquid column after hole closure results from the balance between the capillary force and inertia. Corresponding scaling coefficients are determined.

An Exploration of the Effects of Dissolved Ionic Solids on Bubble Merging in Water and Its Impact on the Leidenfrost Transition

2010 ◽  
Author(s):  
Yu Gan ◽  
Van P. Carey
Keyword(s):  
Liquid Film ◽  
Theoretical Models ◽  
Md Simulations ◽  
Cast Aluminum ◽  
Film Stability ◽  
Instability Theory ◽  
Ionic Solids ◽  
Free Liquid Film ◽  
The Stability ◽  
Dissolved Salts

Theoretical models and MD simulation studies suggest that dissolved salts tend to alter the surface tension at liquid vapor interfaces and affect the stability of the free liquid film between adjacent bubbles. Recent modeling of the Leidenfrost phenomenon also indicates that bubble merging is a key mechanism affecting the Leidenfrost transition conditions. This investigation summarizes the results of an investigation of the effects of dissolved salts on liquid film stability and bubble merging in the aqueous solution. The interaction of pairs of bubbles injected into solution with different dissolved salt concentrations was studied experimentally to determine the probability of merging from statistics for ensembles of bubble pairs. The results of these experiments indicate that very low dissolved salt concentrations can strongly reduce the tendency of adjacent bubbles to merge, implying that the presence of the dissolved salt in such cases strongly enhances the stability of the free liquid film between adjacent bubbles. The trends are compared to predictions of free liquid film stability by wave instability theory and MD simulations. These trends are also compared to experimental data indicating the effects of dissolved salt on the Leidenfrost transition. These comparisons indicate that the suppression of merging due to the effects of some dissolved salts can significantly alter the Leidenfrost transition conditions. The implications of this in quenching of cast aluminum or steel parts using water of variable hardness are also discussed.

On large-amplitude pulsating fountains

1998 ◽  
Vol 366 ◽  
pp. 333-350 ◽  
Author(s):  
CHRISTOPHE CLANET
Keyword(s):  
Surface Tension ◽  
Large Amplitude ◽  
Characteristic Frequency ◽  
Oscillatory Regime ◽  
Hydrodynamic Properties ◽  
Capillary Length ◽  
Wide Range ◽  
The Stability ◽  
Existing Data ◽  
Good Agreement

We study the behaviour of an upward vertical water jet of density, ρ, and surface tension, σ, injected through a tube of diameter, D, with a momentum-averaged velocity, V. These fountains are shown to exhibit large-amplitude oscillations in the range 0.1[les ]D/a[les ]1.6, and 20[les ]V2/(gD)[les ]400, where g is the acceleration due to gravity and a is the capillary length, a≡(2σ/(ρg))1/2. The characteristic frequency of the oscillations, f, and their limits of existence are studied experimentally. A model is developed, leading to the expression for the frequency:formula hereThis expression is shown to be in good agreement with existing data and with new measurements, conducted over a wide range of Bond (Bo≡D/a) and Froude (Fr≡V2/gD) numbers. The stability of the model is considered and the limits of the oscillatory regime are related to the hydrodynamic properties of the flow.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

2011 ◽  
Vol 137 ◽  
pp. 72-76
Author(s):  
Wei Zhang ◽  
Xian Wen ◽  
Yan Qun Jiang
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Global Stability ◽  
Dimensional Model ◽  
Global Stability Analysis ◽  
The Stability ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Calculated Amount ◽  
Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

scholarly journals Asymptotic analysis for personalized Web search

2010 ◽  
Vol 42 (02) ◽  
pp. 577-604 ◽  
Author(s):  
Yana Volkovich ◽  
Nelly Litvak
Keyword(s):  
Web Search ◽  
Power Laws ◽  
User Preference ◽  
Importance Measure ◽  
Web Documents ◽  
Original Definition ◽  
Theoretical Predictions ◽  
Heavy Tailed ◽  
Definition Of ◽  
Good Agreement

PageRank with personalization is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution of a stochastic equationwhere theRis are distributed asR. This equation is inspired by the original definition of the PageRank. In particular,Nmodels the number of incoming links to a page, andBstays for the user preference. Assuming thatNorBare heavy tailed, we employ the theory of regular variation to obtain the asymptotic behavior ofRunder quite general assumptions on the involved random variables. Our theoretical predictions show good agreement with experimental data.

scholarly journals The Stability of the Liquid Film

1942 ◽  
Vol 63 (6) ◽  
pp. 691-696 ◽  
Author(s):  
Jitsusaburo SAMESHIMA ◽  
Masaji NAKAMUTA ◽  
Ryoiti TERADA
Keyword(s):  
Liquid Film ◽  
The Stability

STABILITY ANALYSIS OF THE THIN POWER LAW LIQUID FILM FLOWING DOWN ON A VERTICAL CYLINDER

2006 ◽  
Vol 30 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Po-Jen Cheng ◽  
Kuo-Chi Liu
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Flow Index ◽  
Free Film ◽  
Long Wave ◽  
Lateral Curvature ◽  
The Stability ◽  
Film Interface

The paper investigates the stability theory of a thin power law liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized linear kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The analysis results also indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

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