Film Drainage between Colliding Drops at Constant Approach Velocity: Experiments and Modeling

Experiments and modeling of the drainage of the thin liquid film between two deformable spherical drops approaching each other at constant velocity in another liquid are being presented. Two numerical models based on the lubrication theory have been developed considering the cases of immobile or mobile drop interfaces. The absolute film thickness and the thinning rate have been measured using laser interferometry for a wide range of capillary numbers. In all studied cases, the model with immobile interfaces was found to give the best predictions of the experimental time evolution of the film thickness and radial expansion. These results made it possible to derive a typical time scale of the drainage process. Copyright 2000 Academic Press.     

Effect of mass transfer on the film drainage between colliding drops

The influence of mass transfer on the drainage behaviour of the thin liquid film between two drops immersed in another liquid colliding at constant approach velocity has been studied experimentally. The liquid-liquid system used is glycerol in silicone oil. The transferred solute is acetone and the volume concentration difference across the interface ranges from 1 to 5%. The film thickness evolution has been measured using a laser interferometry technique. The direction of mass transfer (from the drops towards the film phase and inversely) has been investigated and the results compared to the case with no mass transfer. When the solute transfers from the drops towards the continuous phase, the drainage rate is significantly higher than in the case with no mass transfer. This result is interpreted as a consequence of the mass transfer induced surface mobility in the film region (the so-called Marangoni effect) due to localized surface tension differences. This effect has been demonstrated by the visualization of the flow patterns in the drops and in the film phase (using a particle tracer technique). In this case, the slope of the film height as a function of time seems to be independent of the approach velocity condition imposed on the drop and appears to be controlled by the interfacial tension gradient. In the opposite case, when the solute transfers from the continuous phase towards the drops, the film drainage rate is lowered with respect to the case of no mass transfer, goes to zero or even changes its sign depending on the mass transfer intensity. The results also show that in the range of solute concentration studied, the effect of mass transfer on the film drainage process takes place at large distances compared to the scales at which lubrication theory is valid.     

Study of structural and electronic transport properties of Ce-doped LaMnO3

The structural and electronic transport properties of La_1−x Ce _x MnO₃ (x=0.0–1.0) have been studied. All the samples exhibit orthorhombic crystal symmetry and the unit cell volume decreases with Ce doping. They also make a metal-insulator transition (MIT) and transition temperature increases with increase in Ce concentration up to 50% doping. The system La_0.5Ce_0.5MnO₃ also exhibits MIT instead of charge-ordered state as observed in the hole doped systems of the same composition.     

Forward Scattering Signature of a Spherical Particle Crossing a Laser Beam out of the Beam Waist

When a particle crosses a laser beam out of the focal plane, the light attenuation signal occuring on the beam axis contains some information regarding the particle size and trajectory. These attenuation signatures are analysed and predicted with a simplified model based on Fraunhofer diffraction. Numerical and experimental results are found to be in good agreement. A modified laser Doppler velocimeter using this sizing method is able to perform simulataneous measurement of size and velocity of spherical particle in the range 10 μm–500 μm.     

Two connected inverse spectral transforms

We establish a transformation which connects the potentials of the one-dimensional Dirac and Klein-Gordon operators. This transformation links the solutions of the nonlinear evolution equations solvable by means of the two inverse spectral transforms which use the Dirac and Klein-Gordon direct and inverse spectral problems.