Sharp acceleration of a macroscopic contact line induced by a particle

2017 ◽  
Vol 830 ◽  
Author(s):  
Lizhong Mu ◽  
Daichi Kondo ◽  
Motochika Inoue ◽  
Toshihiro Kaneko ◽  
Harunori N. Yoshikawa ◽  
...  

Wetting of a planar solid substrate is investigated in the presence of a macroscopic particle in the complete wetting regime. A drop of silicone oil spreads on the substrate and its macroscopic edge is incident on the particle at the late stage of spreading. The drop–particle interaction is observed in detail by shadowgraph and interferometry. Although the spreading drop edge is pinned by the particle for a short time, a sharp acceleration occurs when the liquid starts wetting the extra surface area offered by the particle and forming a meniscus. This process yields a net gain in spreading speed. A theoretical model based on the classical wetting dynamics dictated by Cox’s law is developed. It predicts that the capillary energy of the meniscus gives rise to a rapid motion of the liquid edge, showing good agreement with the dynamics observed in the experiments.

Soft Matter ◽  
2019 ◽  
Vol 15 (17) ◽  
pp. 3580-3587 ◽  
Author(s):  
Anna Zigelman ◽  
Mohammad Abo Jabal ◽  
Ofer Manor

We employ a theoretical model to explain the wetting–dewetting motion of the contact line by incorporating opposing evaporation and Marangoni induced flows in the deposition process.


2012 ◽  
Vol 697 ◽  
pp. 92-114 ◽  
Author(s):  
H. Ding ◽  
E. Q. Li ◽  
F. H. Zhang ◽  
Y. Sui ◽  
P. D. M. Spelt ◽  
...  

AbstractA new regime of droplet ejection following the slow deposition of drops onto a near-complete wetting solid substrate is identified in experiments and direct numerical simulations; a coalescence cascade subsequent to pinch-off is also observed for the first time. Results of numerical simulations indicate that the propagation of capillary waves that lead to pinch-off is closely related to the self-similar behaviour observed in the inviscid recoil of droplets, and that motions of the crests and troughs of capillary waves along the interface do not depend on the wettability and surface tension (or Ohnesorge number). The simulations also show that a self-similar theory for universal pinch-off can be used for the time evolution of the pinching neck. However, although good agreement is also found with the double-cone shape of the pinching neck for droplet ejection in drop deposition on a pool of the same liquid, substantial deviations are observed in such a comparison for droplet ejection in rapid drop spreading (including the newly identified regime). This deviation is shown to result from interference by the solid substrate, a rapid downwards acceleration of the top of the drop surface and the rapid spreading process. The experiments also confirm non-monotonic spreading behaviour observed previously only in numerical simulations, and suggest substantial inertial effects on the relation between an apparent contact angle and the dimensionless contact-line speed.


1953 ◽  
Vol 26 (3) ◽  
pp. 655-673 ◽  
Author(s):  
A. G. Veith

Abstract The nonrubber content of typical samples of all grades of technically classified rubber has been determined. It is found that the nonrubber content increases in the order: red, yellow, and blue. The chemical analyses performed to determine the nonrubber content were as follows: per cent ash, per cent nitrogen, per cent acetone extract, and per cent fatty acid. The pH of both a slurry of the ash and the aqueous digest indicates that blue rubber is more basic in these respects than are red and yellow rubbers. The measurement of the cure rate of these samples of technically classified rubber has been carried out by means of (1) conventional stress-strain testing, (2) the present ASTM method utilizing the Mooney viscometer, (3) the National Bureau of Standards strain test, (4) a new and more quantitative approach developed by Gee and coworkers, and (5) a utilization of the Mooney viscometer to determine two of the parameters of Gee's equation which gives the time dependence of modulus. All of these methods place the rubbers in the same relative order. The use of the viscometer to determine two of the parameters of Gee's equation was prompted by the degree of correlation between the rate parameter obtained with the present ASTM method and the rate constant k calculated by Gee's methods. As a result of a preliminary investigation as to the causes of viscosity increases at curing temperatures, it was found that, within limits of experimental error, all of the viscosity increase is due to the formation of a cross-linked network, with a linear relationship existing between viscosity increase ΔVc and modulus (at 100 per cent elongation) f. The results of a comparison of the rate constants obtained by the viscometer and by Gee's method indicate that for MBT mixes at 260° F there is good agreement between the methods. Statistical analysis shows that the samples employed for this study are significantly different in their rate of cure. The variance, range, and mean of some of the parameters obtained with the viscometer over a 10-week period are also given. It is suggested that the Mooney viscometer be employed to classify natural rubber according to its cure rate. If this is done, it will be necessary to define the degree of accuracy desired. To determine accurately the cure rate, it is necessary that the viscometer be used in conjunction with a press cure for the estimation of the parameter f∞. If it is not feasible to carry out press cures, an average value for f∞ can be assumed, and then only a short time test with the viscometer is required.


1969 ◽  
Vol 59 (1) ◽  
pp. 399-407
Author(s):  
Robert B. Herrmann

Abstract The propagation of Rayleigh waves with periods of 0.4 to 2.0 seconds across the Cincinnati arch is investigated. The region of investigation includes southern Indiana and Ohio and northern Kentucky. The experimental data for all paths are fitted by a three-layer model of varying layer thickness but of fixed velocity in each layer. The resulting inferred structural picture is in good agreement with the known basement trends of the region. The velocities of the best fitting theoretical model agree well with velocity-depth data from a well in southern Indiana.


1990 ◽  
Vol 209 ◽  
Author(s):  
P. Mulheran ◽  
J.H. Harding

A Monte Carlo procedure has been used to study the ordering of both two and three dimensional (2d and 3d) Potts Hamiltonians, further to the work of Anderson et al. For the 3d lattice, the short time growth rate is found to be much slower than previously reported, though the simulated microstructure is in agreement with the earlier studies. We propose a new stochastic model that gives good agreement with the simulations.


2012 ◽  
Vol 190 ◽  
pp. 39-42
Author(s):  
M. Medvedeva ◽  
Pavel V. Prudnikov

The dynamic critical behavior of the three-dimensional Heisenberg model with longrangecorrelated disorder was studied by using short-time Monte Carlo simulations at criticality.The static and dynamic critical exponents are determined. The simulation was performed fromordered initial state. The obtained values of the exponents are in a good agreement with resultsof the field-theoretic description of the critical behavior of this model in the two-loopapproximation.


1995 ◽  
Vol 377 ◽  
Author(s):  
M. Goerlitzer ◽  
P. Pipoz ◽  
H. Beck ◽  
N. Wyrsch ◽  
A. V. Shah

ABSTRACTTransient photoconductive response of undoped a-Si:H has been studied; the changes were analysed between two slightly different steady-state illumination conditions, at room temperature. A theoretical model is developed to describe transient photoconductivity; it yields good agreement with the measured curves for a whole range of light intensities. Numerical evaluations allows one to extract the recombination time of electrons. Comparison with steady-state photoconductivity yields a band mobility of free electrons between 0.1 and 6 cm2V−1s−1, depending upon sample quality.


1971 ◽  
Vol 93 (1) ◽  
pp. 77-84 ◽  
Author(s):  
Nam P. Suh ◽  
C. L. Tsai

The transient thermocouple response characteristics in deflagrating low-conductivity materials with high temperature gradients were investigated theoretically and experimentally. The theoretical model considers the thermocouple bead and lead wires separately, and the two resulting partial differential equations are solved simultaneously by a finite difference technique. The experimental results are obtained by embedding various size thermocouple wires in double-base solid propellants and consequently measuring the temperature profiles and the surface temperatures. The theoretical model is used to predict the experimentally measured temperatures. There is good agreement. The experimentally measured values are smaller than the correct surface temperature, corresponding to the model prediction for zero wire diameter, by at least 20 percent even when 1/2-mil thermocouple wire is used. Both the experimental and theoretical results show a plateau when the thermocouple bead emerges from the solid into the gas phase. The theoretical results also show that there is an optimum ratio of. the thermocouple bead diameter to the wire diameter, which is found to be close to three


2018 ◽  
Vol 839 ◽  
pp. 468-488 ◽  
Author(s):  
Yasufumi Yamamoto ◽  
Takahiro Ito ◽  
Tatsuro Wakimoto ◽  
Kenji Katoh

Droplet movement by electrowetting on dielectric (EWOD) in a Hele-Shaw cell is analysed theoretically and numerically. We propose a simple theoretical model for the motion, which describes well the voltage dependency of droplet speed below the saturation voltage as measured experimentally. The simulation method for numerical analyses is constructed by using the Young–Lippmann equation to represent EWOD and the generalised Navier boundary condition to represent the moving contact line in the context of the front-tracking method. With an adjusted slip parameter, the present full three-dimensional numerical simulation reproduces well the shape evolution and movement speed of droplets as observed experimentally. We verify the proposed theoretical model in numerical experiments with various shapes and voltages. Furthermore, we analyse theoretically the behaviour of the contact line at the onset of droplet motion as observed in the simulation and experiment, and we are able to estimate very well the time scale on which the contact angle changes.


2009 ◽  
Vol 53 (02) ◽  
pp. 59-67
Author(s):  
Mostafa Shakeri ◽  
Eric Maxeiner ◽  
Thomas Fu ◽  
James H. Duncan

Measurements of contact line height and longitudinal wave profiles from experiments with a three-dimensional naval ship model and experiments using a 2D+T wave maker with motions approximating the three-dimensional hull form are compared. The shape and maximum height of the contact line in the bow region are nearly the same in the two experiments, and the distance downstream along the hull over which the two measurements agree increases with increasing Froude number, Fn = Um/√gLm, where Um is the ship model speed, g is the acceleration of gravity, and Lm is the ship model waterline length. The comparison of the longitudinal wave profile (wave cut) data from the two experiments shows fairly good agreement for wavelengths and amplitudes at the highest Froude number and the measurement position closest to the hull.


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