Harmonic holes with surface tension in an elastic plane under uniform remote loading

2016 ◽  
Vol 22 (9) ◽  
pp. 1806-1812 ◽  
Author(s):  
Ming Dai ◽  
Peter Schiavone ◽  
Cun-Fa Gao
Keyword(s):  
Surface Tension ◽  
Conformal Mapping ◽  
Linear Equations ◽  
Elastic Plane ◽  
Mean Stress ◽  
Remote Loading ◽  
The Mean ◽  
Non Linear Equations ◽  
Effect Of Surface

Harmonic holes are designed to leave undisturbed the mean stress in an uncut body subjected to a system of prescribed remote loadings. The role of residual surface tension in the design of harmonic holes is an important consideration, which is usually neglected at the macroscale but remains a significant factor in the design of such holes at the nanoscale. We consider the identification of the geometry of a single harmonic hole in an elastic plane subjected to uniform remote loading when residual surface tension is incorporated into the model of deformation. The geometry of the hole is defined by a conformal mapping with certain unknown coefficients determined from a system of non-linear equations. We illustrate our results with several examples. In particular, we show that for a given remote loading and surface tension, the shapes obtained exhibit strong size-dependency. Moreover, we find that the incorporation of the effect of surface tension greatly extends the range of admissible uniform remote loadings that guarantee the existence of harmonic holes.

Effect of surface tension of mucosal lining liquid on upper airway mechanics in anesthetized humans

2003 ◽  
Vol 95 (1) ◽  
pp. 357-363 ◽  
Author(s):  
Jason P. Kirkness ◽  
Peter R. Eastwood ◽  
Irene Szollosi ◽  
Peter R. Platt ◽  
John R. Wheatley ◽  
...  
Keyword(s):  
Surface Tension ◽  
Human Subjects ◽  
Upper Airway ◽  
Exogenous Surfactant ◽  
Airway Mechanics ◽  
Before And After ◽  
Airway Opening ◽  
Mucosal Lining ◽  
Effect Of Surface

Upper airway (UA) patency may be influenced by surface tension (γ) operating within the (UAL). We examined the role of γ of UAL in the maintenance of UA patency in eight isoflurane-anesthetized supine human subjects breathing via a nasal mask connected to a pneumotachograph attached to a pressure delivery system. We evaluated 1) mask pressure at which the UA closed (Pcrit), 2) UA resistance upstream from the site of UA collapse (RUS), and 3) mask pressure at which the UA reopened (Po). A multiple pressure-transducer catheter was used to identify the site of airway closure (velopharyngeal in all subjects). UAL samples (0.2 μl) were collected, and the γ of UAL was determined by using the “pull-off force” technique. Studies were performed before and after the intrapharyngeal instillation of 5 ml of exogenous surfactant (Exosurf, Glaxo Smith Kline). The γ of UAL decreased from 61.9 ± 4.1 (control) to 50.3 ± 5.0 mN/m (surfactant; P < 0.02). Changes in Po, RUS, and Po - Pcrit (change = control - surfactant) were positively correlated with changes in γ ( r2 > 0.6; P < 0.02) but not with changes in Pcrit ( r2 = 0.4; P > 0.9). In addition, mean peak inspiratory airflow (no flow limitation) significantly increased ( P < 0.04) from 0.31 ± 0.06 (control) to 0.36 ± 0.06 l/s (surfactant). These findings suggest that γ of UAL exerts a force on the UA wall that hinders airway opening. Instillation of exogenous surfactant into the UA lowers the γ of UAL, thus increasing UA patency and augmenting reopening of the collapsed airway.

scholarly journals A simplified treatment of surfactant effects on cloud drop activation

2011 ◽  
Vol 4 (1) ◽  
pp. 107-116 ◽  
Author(s):  
T. Raatikainen ◽  
A. Laaksonen
Keyword(s):  
Surface Tension ◽  
Analytical Solutions ◽  
Linear Equations ◽  
Computing Time ◽  
Cloud Droplets ◽  
Cloud Models ◽  
Non Linear ◽  
Solution Surface ◽  
Surfactant Effects ◽  
Non Linear Equations

Abstract. Dissolved surface active species, or surfactants, have a tendency to partition to solution surface and thereby decrease solution surface tension. Activating cloud droplets have large surface-to-volume ratios, and the amount of surfactant molecules in them is limited. Therefore, unlike with macroscopic solutions, partitioning to the surface can effectively deplete the droplet interior of surfactant molecules. Surfactant partitioning equilibrium for activating cloud droplets has so far been solved numerically from a group of non-linear equations containing the Gibbs adsorption equation coupled with a surface tension model and an optional activity coefficient model. This can be a problem when surfactant effects are examined by using large-scale cloud models. Namely, computing time increases significantly due to the partitioning calculations done in the lowest levels of nested iterations. Our purpose is to reduce the group of non-linear equations to simple polynomial equations with well known analytical solutions. In order to do that, we describe surface tension lowering using the Szyskowski equation, and ignore all droplet solution non-idealities. It is assumed that there is only one surfactant exhibiting bulk-surface partitioning, but the number of non-surfactant solutes is unlimited. It is shown that the simplifications cause only minor errors to predicted bulk solution concentrations and cloud droplet activation. In addition, computing time is decreased at least by an order of magnitude when using the analytical solutions.

scholarly journals Estimation Leaf Area by Composite Leaves of Canavalia rosea Seedlings Through Linear Dimensions From Last Leaflet

2019 ◽  
Vol 11 (9) ◽  
pp. 299
Author(s):  
Ana Paula Braido Pinheiro ◽  
Vinicius de Souza Oliveira ◽  
Karina Tiemi Hassuda dos Santos ◽  
Jéssica Sayuri Hassuda Santos ◽  
Gleyce Pereira Santos ◽  
...  
Keyword(s):  
Leaf Area ◽  
Mean Absolute Error ◽  
Linear Equations ◽  
Absolute Error ◽  
Mean Values ◽  
Linear Dimensions ◽  
Power Models ◽  
Independent Variable ◽  
The Mean ◽  
Non Linear Equations

The objective of this work was to propose models of equations from measurements of the linear dimensions of the last leaflet for the estimation of the leaf area of the composite leaves of Canavalia rosea. For this purpose, 441 composite leaves of 198 seedlings were used, 45 days after sowing, produced in nursery and belonging to the Federal University of Esp&iacute;rito Santo, Campus S&atilde;o Mateus, located in the municipality of S&atilde;o Mateus, North of the State of Esp&iacute;rito Santo, Brazil. The length (L) along the main midrib and the maximum leaf width (W) of the last leaflet of each composite leaf, as well as the leaf area of all leaflets, were measured. Subsequently, it was determined the product of the multiplication of the length with the width (LW) and leaf area observed (OLA) from the sum of leaf area of leaflets in front of these measures were adjusted linear and non-linear equations of linear first degree, quadratic and power models, where, OLA was used as a dependent variable in function of L, W and LW as independent variable. Based on the models tested, we obtained equations for the estimated leaf area (ELA). The mean values of ELA and OLA were compared by Student&#39;s t test 5% probability. The mean absolute error (MAE), the root mean square error (RMSE) and the Willmott d index, were determined as criteria for validation. The best adjusted equation was chosen through the non-significant values in the comparison of the means of ELA and OLA, values of MAE and RMSE closer to zero, value of the index d near the unitary and higher values of R2. Thus, the leaf area of the composite leaf of C. rosea seedlings can be estimated by the power model represented by equation ELA = 2.2951 (LW)0.9474 quickly, easily and non-destructively.

Role of pulmonary surfactant in airway closure: a computational study

1993 ◽  
Vol 75 (3) ◽  
pp. 1323-1333 ◽  
Author(s):  
D. R. Otis ◽  
M. Johnson ◽  
T. J. Pedley ◽  
R. D. Kamm
Keyword(s):  
Surface Tension ◽  
Liquid Layer ◽  
Pulmonary Surfactant ◽  
Computational Study ◽  
Surface Shape ◽  
Airway Closure ◽  
Velocity Surface ◽  
The Mean ◽  
Layer Flow

A numerical model that simulates airway closure by liquid bridging during expiration has been developed. The effects of both surfactant and time-varying geometry have been included; the model determines the liquid layer flow resulting from a surface tension (Rayleigh) instability, and the computation traces the film's development to closure, yielding pressure, velocity, surface shape, and surfactant concentration distributions. It is found that surfactant is effective in retarding or eliminating liquid bridging through the reduction of the mean surface tension and the action of surface tension gradients. The former effect is also critical in minimizing the magnitude of the negative pressure in the liquid layer and thus presumably in reducing the tendency for airway compliant collapse.

Localised Single-Station Lightning Detection by Using TOA Method

2013 ◽  
Vol 64 (4) ◽  
Author(s):  
Behnam Salimi ◽  
Zulkurnain Abdul-Malek ◽  
Kamyar Mehranzamir ◽  
Saeed Vahabi Mashak ◽  
Hadi Nabipour Afrouzi
Keyword(s):  
Radiation Source ◽  
Detection System ◽  
Linear Equations ◽  
Lightning Strike ◽  
Time Of Arrival ◽  
Lightning Detection ◽  
Single Station ◽  
Mathematical Equations ◽  
Non Linear Equations

Lightning is an electrical discharge during storms that can be monitored continuously from certain distances. It can be either within clouds (intra cloud), or between clouds and the ground (cloud-ground). There are various techniques used nowadays to locate lightning, and to determine various parameters produced from lightning. Each technique provides its own claimed performances. This paper attempts to provide instantaneous detection of lightning strike lightning location using the Time of Arrival (TOA) method of a single detection station (comprises of four antennas). It also models the whole detection system using suitable mathematical equations so as to give some understanding on the differences between the measured and calculated (theoretical) results. The measurement system is based on the application of mathematical and geometrical formulas. Several parameters such as the distance from the radiation source to the station and the lightning path are significant in influencing the accuracy of the results (elevation and azimuth angles). The role of each parameter is examined in detail using Matlab. This study solved the resultant non-linear equations by Newton-Raphson techniques. Methods to determine the radiation source which include the exact coordinate of a given radiation source in 3-dimensions were also developed. Further clarifications on the cause of errors in the single-station TOA method and techniques to reduce the errors are given.

DECOUPLING THE EFFECT OF SURFACE TENSION AND VISCOSITY ON SPRAY CHARACTERISTICS UNDER DIFFERENT AMBIENT PRESSURES: NEAR-NOZZLE BEHAVIOR AND MACROSCOPIC CHARACTERISTICS

2019 ◽  
Vol 29 (7) ◽  
pp. 629-654
Author(s):  
Zehao Feng ◽  
Shangqing Tong ◽  
Chenglong Tang ◽  
Cheng Zhan ◽  
Keiya Nishida ◽  
...  
Keyword(s):  
Surface Tension ◽  
Spray Characteristics ◽  
Effect Of Surface

Surfactant Impurities Can Explain the Jones-Ray Effect

2018 ◽  
Author(s):  
Timothy Duignan ◽  
Marcel Baer ◽  
Christopher Mundy
Keyword(s):  
Surface Tension ◽  
Electrostatic Potential ◽  
Driving Forces ◽  
Salt Water ◽  
Fundamental Property ◽  
Apparent Contradiction ◽  
Low Salt ◽  
Air Water Interface ◽  
Added Salt ◽  
Effect Of Surface

<div> <p> </p><div> <div> <div> <p>The surface tension of dilute salt water is a fundamental property that is crucial to understanding the complexity of many aqueous phase processes. Small ions are known to be repelled from the air-water surface leading to an increase in the surface tension in accordance with the Gibbs adsorption isotherm. The Jones-Ray effect refers to the observation that at extremely low salt concentration the surface tension decreases in apparent contradiction with thermodynamics. Determining the mechanism that is responsible for this Jones-Ray effect is important for theoretically predicting the distribution of ions near surfaces. Here we show that this surface tension decrease can be explained by surfactant impurities in water that create a substantial negative electrostatic potential at the air-water interface. This potential strongly attracts positive cations in water to the interface lowering the surface tension and thus explaining the signature of the Jones-Ray effect. At higher salt concentrations, this electrostatic potential is screened by the added salt reducing the magnitude of this effect. The effect of surface curvature on this behavior is also examined and the implications for unexplained bubble phenomena is discussed. This work suggests that the purity standards for water may be inadequate and that the interactions between ions with background impurities are important to incorporate into our understanding of the driving forces that give rise to the speciation of ions at interfaces. </p> </div> </div> </div> </div>

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