The local and the terminal velocities, the size and the degree of bubbles’ shape deformations were determined as a function of distance from the position of the bubble formation (capillary orifice) in solutions of n-octyltrimethylammonium bromide, n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside and n-octanoic acid.
These surface-active compounds have different polar groups but an identical hydrocarbon chain (C8) in the molecule. The motion of the bubbles was monitored and recorded using a stroboscopic illumination, a CCD camera, and a JVC professional video. The recorded bubble images were analyzed by the image analysis software. The bubbles accelerated rapidly and their shape was deformed immediately after detachment from the capillary. The extent of the bubbles’ shape deformation (ratio of horizontal and vertical diameters) was 1.5 in distilled water and dropped rapidly down to a level of ca. 1.05–1.03 with increasing surfactant concentration. After the acceleration period the bubbles either attained a constant value of the terminal velocity (distilled water and high concentrations of the solutions), or a maximum in the velocity profiles was observed (low concentrations). The values of the terminal velocity diminished drastically with increasing concentration, from the value of 35 cm/s in water down to about 15 cm/s, while the bubble diameter decreased by ca. 10% only. The surfactant adsorption at the surface of the bubbles was evaluated and the minimum adsorption coverages required to immobilize the bubbles’ surface were determined. It was found that this minimum adsorption coverage was ca. 4% for n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside, n-octanoic acid and 25% for n-octyltrimethylammonium bromide. The difference in the adsorption coverage together with the surfactants’ surface activities indicate that it is mainly the adsorption kinetics of the surfactants that governs the fluidity of interfaces of the rising bubbles. 相似文献
Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved. 相似文献
An analytic and numerical study of the behavior of the linear nonhomogeneous wave equation of the form ε2utt = Δu + tf with high wave speed (ε 1) is carried out. This study was initially motivated by meteorological observations which have indicated the presence of large spatial scale gravity waves in the neighborhood of a number of summer and winter storms, mainly from visible images of ripples in clouds in satellite photos. There is a question as to whether the presence of these waves is caused by the nearby storms. Since the linear wave equation is an approximation to the full system describing pressure waves in the atmosphere, yet is considerably more tractable, we have chosen to analyze the behavior of the linear nonhomogeneous wave equation with high wave speed. The analysis is shown to be valid in one, two, and three space dimensions. Partly because of the high wave speed, the solution is known to consist of behavior which changes on two different time scales, one rapid and one slow. Additionally, because of the presence of the nonhomogeneous forcing term tf, we show that there is a component of the solution which will vary only on a very large spatial scale. Since even the linearized wave equation can give rise to persistent large spatial scale waves under the right conditions, the implication is that certain storms could be responsible for the generation of large-scale waves. Numerical simulations in one and two dimensions confirm analytic results. 相似文献
The analysis of mechanical structures using the Finite Element Method in the framework of large elastoplastic strain, needs frequent remeshing of the deformed domain during computation. Indeed, the remeshing is due to the large geometrical distortion of finite elements and the adaptation to the physical behavior of the solution. This paper gives the necessary steps to remesh a mechanical structure during large elastoplastic deformations with damage. An important part of this process is constituted by geometrical and physical error estimates. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the BL2D-V2 adaptive mesher. To cite this article: H. Borouchaki et al., C. R. Mecanique 330 (2002) 709–716.相似文献
Tensile impact experiments of EC8.0−24×7 glass fiber bundles at different low temperaturesT(14°C, −40°C and −10°C) and strain rates ɛ were carried out, and complete stress-strain curves were obtained. Within the range
of the experiment temperatures and strain rates, it is found that the initial modulusE, the ultimate strength σmax and the unstable strain ɛb of the glass fiber bundles all increase with ɛ at an identicalT. At an identical ɛ, with the decrease ofT, E and σmax increase; but ɛb increases when 10°C>T>−40°C and decreases when −40°C>T>−100°C. The strain-rate- and temperature-dependent bimodal Weibull statistical constitutive theory was adopted for the statistical
analysis of the experimental results, and the Weibull parameters of single fiber were obtained. The results show that the
bimodal Weibull distribution function is suitable to represent the strength distribution of the glass fiber at low temperature
and different strain rates. The differences in the mechanical properties between EC8.0−24×7 and EC5.5−12 ×14 glass fiber bundles
were also discussed.
Project supported by the National Natural Science Foundation of China (No. 19772058). 相似文献