Generalized Young Equation for Cylindrical Droplets within a Homogeneous and Smooth Regular Triangular Prism Filled with Gas in Three Convex Corners

2016 ◽  
Vol 6 (1) ◽  
pp. 14
Author(s):  
Long Zhou ◽  
Guang-Hua Sun ◽  
Ai-Jun Hu ◽  
Xiao-Song Wang
Keyword(s):  
Line Tension ◽  
Phase System ◽  
Triangular Prism ◽  
Gas Phases ◽  
Three Phase ◽  
Dividing Surface ◽  
Solid Liquid ◽  
Wetting Behaviors ◽  
Young Equation ◽  
Dividing Line

<p class="1Body">Based on the approaches of Gibbs’s dividing surface and Rusanov’s dividing line, the wetting behaviors of cylindrical droplets that at equilibrium are sitting inside a homogeneous and smooth regular triangular prism filled with gas in three convex corners are studied. For the three-phase system, which is composed of solid, liquid and gas phases, a generalized Young equation for cylindrical drops in a homogeneous and smooth regular triangular prism imbued with gas within three apex corners has been successfully derived including the effects of the line tension.</p>

scholarly journals Contact Angle for Spherical Nanodroplet in Cylindrical Cavity with Quadratic Curve Generatrix

2016 ◽  
Vol 6 (1) ◽  
pp. 96
Author(s):  
Ai-Jun Hu ◽  
Bao-Zhan Lv
Keyword(s):  
Contact Angle ◽  
Line Tension ◽  
Equilibrium Contact Angle ◽  
Cylinder Surface ◽  
Quadratic Curve ◽  
Dividing Surface ◽  
Solid Liquid ◽  
Young Equation ◽  
Homogeneous Cylinder ◽  
Young's Equation

<p class="1Body">Wetting of a spherical nanodroplet in smooth and homogeneous cylinder surface rotated by quadratic curve was studied by methods of thermodynamics. The solid-liquid-vapor system was separated into six parts using Gibbs method of dividing surface. The system free energy was calculated. A generalized Young equation for the equilibrium contact angle is proposed taking the line tension effects into consideration. On the basis of some assumptions, this generalized Young equation is the same as the classical Young’s equation.</p>

Generalized Young Equation of Cylindrical Droplets Between Two Parallel Cylinders

2016 ◽  
Vol 13 (10) ◽  
pp. 6944-6946
Author(s):  
Long Zhou ◽  
Guang-Hua Sun ◽  
Xiao-Song Wang ◽  
Ai-Jun Hu
Keyword(s):  
Line Tension ◽  
Industrial Applications ◽  
Critical Importance ◽  
Daily Lives ◽  
Dividing Surface ◽  
Young Equation ◽  
Dividing Line

Wetting phenomenon of a solid by a liquid is of critical importance for our daily lives and many industrial applications. In this study, we thermodynamically derive a generalized Young equation of cylindrical droplets between two homogeneous and smooth parallel cylinders including the influences of the line tension. The derivation is based on the concepts of Gibbs’s dividing surface and Rusanov’s dividing line in practice.

Numerical Modeling of Microporosity Formation in Aluminum-Rich Aluminum-Copper Alloys in Microgravity Conditions

2000 ◽  
Author(s):  
M. Xiong ◽  
A. V. Kuznetsov
Keyword(s):  
Copper Alloys ◽  
Heat Transfer Fluid ◽  
Gas Phases ◽  
Alloy Casting ◽  
Cu Alloy ◽  
Aluminum Copper Alloys ◽  
Three Phase ◽  
Microgravity Conditions ◽  
Parametric Analyses ◽  
Solid Liquid

Abstract The microporosity formation in a vertical unidirectionally solidifying Al-4.1%Cu alloy casting is modeled in both microgravity and standard gravity as well as in the conditions of decreased (Moon, Mars) and increased (Jupiter) gravity. Due to the unique opportunities offered by a low-gravity environment (absence of metallostatic pressure and of natural convection in the solidifying alloy) future microgravity experiments will significantly contribute to attaining a better physical understanding of the mechanisms of microporosity formation. One of the aims of the present theoretical investigation is to predict what microporosity patterns will look like in microgravity in order to help plan a future microgravity experiment. To perform these simulations, the authors suggest a novel three-phase model of solidification that accounts for the solid, liquid, and gas phases in the mushy zone. This model accounts for heat transfer, fluid flow, macrosegregation, and microporosity formation in the solidifying alloy. Special attention is given to the investigation of the influence of microporosity formation on the inverse segregation. Parametric analyses for different initial hydrogen concentrations and different gravity conditions are carried out.

Dependence of the Contact Angle on Adsorption at the Solid-Liquid Interface

2010 ◽  
Author(s):  
C. A. Ward
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Pressure Range ◽  
Line Tension ◽  
Liquid Interface ◽  
Fluid Interfaces ◽  
Phase Line ◽  
Three Phase ◽  
Solid Liquid Interface ◽  
Solid Liquid

A method for determining the surface tension of solid-fluid interfaces has been proposed. For a given temperature and fluid-solid combination, these surface tensions are expressed in terms of material properties that can be determined by measuring the amount of vapor adsorbed on the solid surface as a function of xV, the ratio of the vapor-phase pressure to the saturation-vapor pressure. The thermodynamic concept of pressure is shown to be in conflict with that of continuum mechanics, but is supported experimentally. This approach leads to the prediction that the contact angle, θ, can only exist in a narrow pressure range and that in this pressure range, the solid-vapor surface tension is constant and equal to the surface tension of the liquid-vapor interface, γLV. The surface tension of the solid-liquid interface, γSL, may be expressed in terms of measurable properties, γLV and θ: γSL = γLV(1 − cosθ). The value of θ is predicted to depend on both the pressure in the liquid at the three-phase, line x3L, and the three-phase line curvature, Ccl. We examine these predictions using sessile water droplets on a polished Cu surface, maintained in a closed, constant volume, isothermal container. The value of θ is found to depend on the adsorption at the solid-liquid interface, nSL = nSL(x3L,Ccl). The predicted value of θ is compared with that measured, and found to be in close agreement, but no effect of line tension is found.

The contact angle for a droplet on homogeneous and spherical concave surfaces

2016 ◽  
Vol 30 (07) ◽  
pp. 1650078
Author(s):  
Ai-Jun Hu ◽  
Bao-Zhan Lv ◽  
Xiao-Song Wang ◽  
Long Zhou
Keyword(s):  
Contact Angle ◽  
Chemical Potential ◽  
Rough Surfaces ◽  
Line Tension ◽  
Equilibrium Contact Angle ◽  
Precursor Film ◽  
Phase System ◽  
Spherical Droplet ◽  
Dividing Surface ◽  
Young's Equation

Wetting of droplets on homogeneous and spherical concave rough surfaces is investigated based on thermodynamics. In this study, neglecting the droplet gravity and the thickness of the precursor film of the liquid–vapor interface, the three-phase system is divided into six parts using Gibbs concept of dividing surface. The system Helmholtz free energy is established based on thermodynamics. Supposing the temperature and chemical potential to be constant, a new generalized Young’s equation of the equilibrium contact angle for a spherical droplet on a spherical concave rough surfaces is obtained including the line tension effects. Under certain conditions, this generalized Young’s equation is the same as the Rusanov’s equation.

Experimental analysis of the hydrodynamics of a three-phase system in a vessel with two impellers

2012 ◽  
Vol 66 (6) ◽  
Author(s):  
Anna Kiełbus-Rąpała ◽  
Joanna Karcz
Keyword(s):  
Experimental Analysis ◽  
Gas Flow ◽  
Gas Bubbles ◽  
Liquid System ◽  
Internal Diameter ◽  
Phase System ◽  
Gas Dispersion ◽  
Rushton Turbine ◽  
Three Phase ◽  
Solid Liquid

AbstractResults of experimental analysis concerning gas hold-up and average residence time of gas bubbles in a three-phase gas-solid-liquid system produced in a baffled, double-impeller vessel are presented. Measurements were carried out in a vessel with the internal diameter of 0.288 m. Two different double-impeller configurations were used for agitation: Rushton turbine (lower) — A 315 (upper) and Rushton turbine (lower) — HE 3 (upper). Upper impellers differed in the fluid pumping mode. Coalescing and non-coalescing systems were tested. Liquid phases were distilled water (coalescing system) and aqueous solutions of NaCl (non-coalescing systems). The ability of gas bubbles to coalesce in the liquid was described using parameter Y. Dispersed phases were air and particles of sea sand. The experiments were conducted at seven different gas flow rates and two particle loadings. Effects of the ability of gas bubbles to coalesce (liquid phase properties), operating parameters (superficial gas velocity, impeller speed, solids loadings), and of the type of the impeller configuration on the investigated parameters were determined. The results were approximated mathematically. For both impeller configurations tested, significantly higher gas hold-up values were obtained in the non-coalescing gas-solid-liquid systems compared to the coalescing one. Out of the tested impeller systems, the RT-A 315 configuration proved to have better performance ensuring good gas dispersion in the liquid in the three-phase systems.

Sessile-Water-Droplet Contact Angle: the Effect of Adsorption

2010 ◽  
Author(s):  
H. Ghasemi ◽  
C. A. Ward
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Closed System ◽  
Water Droplet ◽  
Line Tension ◽  
Water Droplets ◽  
Three Phase ◽  
To Come ◽  
Predicted Values ◽  
Solid Liquid

A method has been recently proposed for determining the surface tension of solid-vapor interfaces. The proposed method was used in conjunction with Gibbsian thermodynamics to investigate both analytically and experimentally the possible role of line tension in determining the contact angle of sessile-water-droplets. After forming a sessile-water-droplet in a closed system, its contact angle was determined by measuring the curvature of three-phase contact line and the height of the axisymmetric droplet on its centerline. The total number of the moles in the closed system was determined from the minimum in the Helmholtz function. The total number of moles in the system was then changed to a new value and the system allowed to come to equilibrium again. The contact angle in the new equilibrium condition could be measured and predicted by taking the adsorption at the solid-liquid and solid-vapor interfaces into account but with line tension completely neglected. The predicted values of contact angle are in closed agreement with those measured indicating line tension plays no role in determining the contact angle of mm-sized water droplets on a polished Cu surface. The surface tension of the solid-vapor interface was approximately constant and equal to the surface tension of adsorbing fluid; that is, the Young equation could be simplified.

Initial Study On Ultrasonic Tomography For Multiphase Flow Application

2012 ◽  
Author(s):  
Suzanna Ridzuan Aw ◽  
Hudabiyah Arshad Amari ◽  
Jaysuman Pusppanathan ◽  
Mohd Hafiz Fazalul Rahiman ◽  
Yasmin Abd Wahab
Keyword(s):  
Multiphase Flow ◽  
Pipe Wall ◽  
Initial Study ◽  
Phase System ◽  
Ultrasonic Tomography ◽  
Peak Voltage ◽  
Three Phase ◽  
Three Phase Flow ◽  
Projection Approach ◽  
Solid Liquid

Kertas kerja ini membentangkan kajian awal terhadap kaedah tomografi ultrasonik ke atas aplikasi pengaliran yang mempunyai lebih daripada satu fasa. Ianya bertujuan untuk mengkaji kemampuan tomografi ultrasonik untuk memantau aliran tiga fasa (pepejal/cecair/udara) berikutan kajian ini belum dilaksanakan oleh mana–mana penyelidik. Di dalam projek ini, lapan unit penderia ultrasonik berfrekuensi 40 kHz di pasang di sekeliling paip di mana empat daripadanya berfungsi sebagai pemancar dan empat lagi sebagai penerima. Setiap pemancar akan memancarkan dua kitar denyut berfrekuensi 40 kHz pada ujaan voltan 24Vp–p. Eksperimen ini adalah berdasarkan kaedah pancaran dan penerimaan gelombang ultrasonik di mana voltan puncak ke puncak gelombang ultrasonik di ambil dan di analisis. Maklumat yang diperoleh daripada projek ini menunjukkan bahawa kondisi dan komposisi aliran yang berbeza akan memberikan bacaan voltan keluaran yang berbeza. Ini disebabkan oleh galangan dan halaju setiap bahan adalah berbeza. Hasil dan analisis kajian boleh digunakan untuk kajian dan penyelidikan yang lebih mendalam ke atas sistem tiga fasa. Kata kunci: Tomografi ultrasonic; aliran pelbagai fasa; ultrasonik This paper presents the initial study on ultrasonic tomography for multiphase flow application to investigate ability of ultrasonic tomography for used in monitoring the three phase flow (solid/liquid/gas) at once since there are no research on this conducted yet. In this project, eight units of 40 kHz ultrasonic sensors were mounted non-invasively around the pipe wall where four of it acts as a transmitter and the other four as a receiver. Each transmitter will transmit two cycles of pulses of 40 kHz at an excitation voltage of 24Vp–p. By using transmission–mode and fan–shaped beam projection approach, the peak to peak voltage of the received ultrasonic wave are measured. The investigation was based on the transmission and reception of sensors that were mounted circularly on the surface of experiment vessel. The results obtained throughout this research project had shown that different flow condition and composition will gives different value of output voltage. And the information and analysis of the results can be used for further investigation on the three phase system. Key words: Ultrasonic tomography; multiphase flow; ultrasonic

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