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The review paper contains all known for today information on strength analysis, stability, and applications of drop shaped shells in construction and technics. The voluminous references containing 28 titles give an opportunity to ...
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The review paper contains all known for today information on strength analysis, stability, and applications of drop shaped shells in construction and technics. The voluminous references containing 28 titles give an opportunity to lay down subsequent investigations in this field.
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The time-averaged axis ratios, frequency and amplitude of oscillations of water drops of 2.67-6.6 mm diameter were determined by suspending them in a vertical wind tunnel in the absence and presence of horizontal electric fields u...
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The time-averaged axis ratios, frequency and amplitude of oscillations of water drops of 2.67-6.6 mm diameter were determined by suspending them in a vertical wind tunnel in the absence and presence of horizontal electric fields using a high speed camera at 1000 frames per second. A systematic decrease in the drop's axis-ratio is observed with increase in its diameter and/or horizontal electric field. The results revealed with high speed photography are in good agreement with earlier results. The drop distortion due to horizontal electric field is more pronounced for the drops in the size-range of 336-6 mm diameter showing that the electrical forces progressively enhance the horizontal elongation of the drop resulting in its instability at 6.6 mm. The drop oscillation frequency computed from temporal variation of axis ratio, decreases with increase in drop size but shows no significant change in oscillation frequency in the horizontal electric field of 收起
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The shaping of drops in a model system based on κ-carrageenan-emulsion drops in the millimetre range in silicon oil has been studied. The drops were shaped by exposing them to drag forces in a hyperbolic flow, while their shape w...
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The shaping of drops in a model system based on κ-carrageenan-emulsion drops in the millimetre range in silicon oil has been studied. The drops were shaped by exposing them to drag forces in a hyperbolic flow, while their shape was fixed simultaneously by introducing gel formation of the biopolymer in the drop. The shape and the shaping process were studied and evaluated with image analysis of macrograph sequences of the shaping. The effect of process conditions, flow speed and cooling temperature on the final shape and shape progress was investigated as well as the effect of different κ-carrageenan drop characteristics, such as drop viscosity and gel strength. Drop viscosity was altered by addition of locust bean gum, LBG, and the gel strength was altered by addition of ions. The κ-carrageenan solutions in the drop were characterised by rheological investigations. With the same type of flow, different shapes could be achieved with small process changes and with high reproducibility. The fixation of the characteristic drop features, perimeter, area, Feret's X and Y, does not occur at the same time and position. For the different process parameters investigated, a change in speed affected the process in a similar way to a change in the viscosity ratio. This applies if the viscosity ratio is changed at a constant temperature, but if the change in the viscosity ratio is temperature-induced, the effect is different. The final shape of the produced drops could be graded into three classes, correlated to the position in the flow field where the drops were fixed. A shape map of the different drop shapes obtained was presented.
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Evaporation of sessile drops deformed by gravity is quantified by an analytical-numerical approach. The shape of the drops is defined by minimizing the interfacial and potential drop energies, following a variational integral appr...
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Evaporation of sessile drops deformed by gravity is quantified by an analytical-numerical approach. The shape of the drops is defined by minimizing the interfacial and potential drop energies, following a variational integral approach, for a wide range of drop sizes (from 2.7 mu l to 1.4 ml for water drops) and contact angles for both hydrophilic and hydrophobic substrates. The extension of an analytical model for drop evaporation, which accounts for the effect of the Stefan flow and the temperature dependence of thermophysical properties, to the present conditions reduces the problem to the solution of a Laplace equation, which is then numerically calculated using COMSOL Multiphysics((R)). The vapor fluxes and evaporation rates are then quantified, and the systematic approach to the problem allows the derivation of two correlations, for hydrophilic and hydrophobic substrates, respectively, that can be used to correct the evaporation rate calculated for a drop of the same volume and contact angle in the absence of gravity effects.
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Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have bee...
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Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have been efforts quantifying the range of applicability of drop techniques by studying the deviation of Laplacian drops from the spherical shape. A shape parameter was introduced in the literature and was modified several times to accommodate different drop constellations. However, new problems arise every time a new configuration is considered. Therefore, there is a need for a universal shape parameter applicable to pendant drops, sessile drops, liquid bridges as well as captive bubbles. In this work, the use of the total Gaussian curvature in a unified approach for the shape parameter is introduced for that purpose. The total Gaussian curvature is a dimensionless quantity that is commonly used in differential geometry and surface thermodynamics, and can be easily calculated for different Laplacian drop shapes. The newdefinition of the shape parameter using the total Gaussian curvature is applied here to both pendant and constrained sessile drops as an illustration. The analysis showed that the new definition is superior and reflects experimental results better than previous definitions, especially at extreme values of the Bond number.
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Axisymmetric drop shape analysis-diameter (ADSA-D) was developed to measure contact angles on non-ideal and/or hydrophilic surfaces (e.g. biological surfaces). ADSA-D determines the contact angle by solving the Laplace equation of...
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Axisymmetric drop shape analysis-diameter (ADSA-D) was developed to measure contact angles on non-ideal and/or hydrophilic surfaces (e.g. biological surfaces). ADSA-D determines the contact angle by solving the Laplace equation of capillarity numerically, the using as input the liquid surface tension, the drop volume and diameter of the drop as viewed from above. The diameter is the main experimental parameter to be determined as the liquid surface tension is known and the volume of the sessile drop can be obtained precisely by means of the micrometer syringe used to form the drop. The edge detection method to determine the diameter, which consisted of manually extracting coordinates from a digital image was found to be time consuming and somewhat subjective. Therefore, an automated image processing module was developed to replace the manual scheme. This automated module uses nonlinear filters to process the images and uses a region growing scheme to determine the total area of the drop as viewed from above. This area is then used to calculate the equivalent diameter of the idealized contact or equatorial circle for the drop. The robust design of the automated module enables it to process accurately many different types of drop images. Two very different examples of water drops on bacteria and carboxylic acid terminated self assembled surfaces are used to demonstrate the capabilities of the new image processing scheme. Also, using these two examples, it is shown through contact angle measurements that the results of this new ADSA-D version are more accurate than those obtained through the manual digitization scheme previously used.
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Experiments have been conducted to investigate the geometric parameters necessary to describe the shapes of liquid drops on vertical and inclined plane surfaces.Two liquids and eight surfaces have been used to study contact angles...
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Experiments have been conducted to investigate the geometric parameters necessary to describe the shapes of liquid drops on vertical and inclined plane surfaces.Two liquids and eight surfaces have been used to study contact angles,contact lines,profiles,and volumes of drops of different sizes for a range of surface conditions.The results show the contact-angle variation along the circumference of a drop to be best fit by a third-degree polynomial in the azimuthal angle.This contact-angle function is expressed in terms of the maximum and minimum contact angles of the drop,which are determined for various conditions.The maximum contact angle,theta_max,is approximately equal to the advancing contact angle,theta_A,of the liquid on the surface.As the Bond number,Bo,increases from 0 to a maximum,the minimum contact angle,theta_min decreases almost linearly from the advancing to the receding angle.A general relation is found between theta_min/theta_A and Bo for different liquid-surface combinations.The drop contour can be described by an ellipse,with the aspect ratio increasing with Bo.These experimental results are valuable in modeling drop shape,as presented in Part II of this work.
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Drop shape techniques are extensively used for surface tension measurement. The accuracy of surface tension measurements using a pendant drop setup depends mainly on the drop shape. As the pendant drop shape becomes close to spher...
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Drop shape techniques are extensively used for surface tension measurement. The accuracy of surface tension measurements using a pendant drop setup depends mainly on the drop shape. As the pendant drop shape becomes close to spherical, the performance of drop shape techniques deteriorates. It is important to consider how to optimize the pendant drop design and how to quantify the accuracy of the surface tension measurements. In this paper, the design and accuracy of pendant drop methods is considered in detail. Dimensional analysis is used to describe similarity in pendant drop shapes and to express the problem using appropriate dimensionless groups. A quantitative criterion called shape parameter is then used to express quantitatively the difference in shape between a given experimental drop and a spherical shape. The shape parameter is found to depend only on two dimensionless groups: the dimensionless volume and the Bond number. A critical shape parameter (minimum value of the shape parameter that guarantees a specified accuracy) is shown to depend only on Bond number. A set of experiments were performed with pure liquids to illustrate the change of the critical shape parameter with the Bond number. Results show that high accuracy is indeed reachable independent of the algorithms used.
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The performance of a new algorithm developed to measure contact angle and surface tension of sessile drops is examined. To calculate the contact angle and surface tension, the new algorithm (ADSA-TD) requires the radius (contact o...
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The performance of a new algorithm developed to measure contact angle and surface tension of sessile drops is examined. To calculate the contact angle and surface tension, the new algorithm (ADSA-TD) requires the radius (contact or equatorial) and volume of two sessile drops of different sizes that are placed on the same surface. Initially, the algorithm was tested using synthetic drops (synthetic or theoretical drops are produced by numerical integration of the Laplace equation). The radii and volumes of synthetic drops were used as ADSA-TD inputs. The calculated contact angle (theta) and surface tension (gamma) by ADSA-TD matched perfectly the assumed values of theta and gamma used to produce the synthetic drops, confirming theoretically the validity of the new algorithm. In the next step, the sensitivity of the algorithm to input errors was examined. It was shown experimentally that both calculated contact angle and surface tension are affected by the errors in volume and radius. Besides the error in input values, it was shown that the size difference between the paired drops and the differences in their contact angles would affect the output of ADSA-TD. As it turns out, the calculated surface tension is so sensitive to the above factors that ADSA-TD does not appear to be promising as a surface tension measurement technique. However, ADSA-TD produced acceptable contact angle values as compared to measurements made by other proven techniques such as axisymmetric drop shape analysis-profile. Thus, ADSA-TD may be of interest as a contact angle measurement technique which does not require the liquid surface tension as input. (C) 2000 Elsevier Science B.V. All rights reserved. [References: 14]
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The shape of liquid drops on solid surfaces deviates from the spherical as tension decreases and gravity effects start affecting the drop shape. This paper attempts to define this deviation and estimates the dimensionless Eotvos n...
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The shape of liquid drops on solid surfaces deviates from the spherical as tension decreases and gravity effects start affecting the drop shape. This paper attempts to define this deviation and estimates the dimensionless Eotvos number limits above which the deviation becomes "significant". The use of these limiting values can facilitate estimation of contact angle in the following manner. It is well known that the equilibrium contact angle made by a liquid drop on a solid surface can be estimated from measurements of two drop parameters. These parameters can be any two chosen from the drop volume, height, and watted radius. In case the effect of gravity on the drop shape is negligible, simple algebraic relations derived from the spherical section assumption exist, from which the contact angle can be estimated. In systems where the "spherical section" assumption is invalid, the Laplace equation for the drop shape has been solved numerically with any two of the above parameters as the constraints, to obtain the contact angle. In this paper, Eotvos numbers at which the deviation of the drop profile from the spherical is significant enough to result in contact angle deviation of 1 deg are estimated. The limiting values of Eotvos number, expressed as a function of the original contact angle made by the spherical profile, are obtained by solving the Laplace equation for the drop shape with the drop volume and wetted radius constraints for decreasing values of Interfacial tension. These limiting values are also estimated for different drop sizes and for cases where the drop phase is heavier (sessile) and lighter(buoyant) than the surrounding fluid. The independence of the Eotvos numbher estimates from the sign of the density difference as well as the drop size shown. These Eotvos number limits can be used to check if the spherical section assumption, with the resulting simple algebraic relations, can be used for contact angle estimation and other shape-related analysis for a system.
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