The formation of a liquid bridge during the coalescence of drops

This paper examines a mathematical model for the coalescence of two viscous liquid volumes in an inviscid gas or in a vacuum which removes the pressure singularity at the instant of impact inherent in the classical formulation of the continuum model. The very early stages of coalescence are examined in order to study the formation of the liquid bridge in two cases: (i) for two infinitely long, coalescing liquid cylinders; and (ii) for two coalescing spheres. Numerical solutions are computed for the velocity and pressure fields in the flow in both cases, and they confirm the removal of the pressure singularity. Also, the free-surface position at small times is determined.     

Dilational rheology of an air–water interface functionalized by biomolecules: the role of surface diffusion

As an attempt to develop a sensitive device for biomolecule detection, a micromechanical methodology based on the rheological change of an air–water interface is put forward (Berthier and Davoust, CEA/CNRS patent, PCT International Application WO 2003/080209 A3, 2003). Capillary waves induced from the vertical electrodynamic vibration of a brimful cylindrical tank filled with water stand as a good way to identify dilational elasticity and viscosity of an aging interface. Before, we were interested of the fact that complex wave number and the frequency of waves are obtained through an optical technique, which allows us to accurately recognize the whole interface geometry. These two parameters, a modeling based on a dispersion relation (Lucassen-Reynders and Lucassen, Adv Colloid Interface Sci, 2:347, 1969) and the surface mass transport equation, are jointly used to identify the surface diffusivity and the dilational rheology of the interface for a nonsoluble biochemical surfactant. Preliminary results obtained from a water surface functionalized by DNA, thanks to a lipidic monolayer, demonstrate the capabilities of the proposed methodology. The sensitivity of dilational rheology and the surface diffusivity on DNA adsorption on lipids is made evident.This paper was presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.     

Evolution of material voids for highly anisotropic surface energy

In this paper we consider the evolution by surface diffusion of material voids in a linearly elastic solid, focusing on the evolution of voids with large surface energy anisotropy. It is well known that models for the time evolution of similar material surfaces can become mathematically ill-posed when the surface energy is highly anisotropic. In some cases, this ill-posedness has been associated with the formation of corners along the interface. Here the ill-posedness is removed through a regularization which incorporates higher order terms in the surface energy. Spectrally accurate numerical simulations are performed to calculate the steady-state solution branches and time-dependent evolution of voids, with a particular emphasis on inferring trends in the zero regularization (c→0) limit. For steady voids with large anisotropy we find that apparent corners form as c→0. In the presence of elastic stresses σ the limiting corner angles are most often found to differ from angles found on the (σ=0) Wulff shape. For large elastic stresses we find that steady solutions no longer exist; instead the void steadily lengthens via a filamenting instability referred to as tip streaming.     

Thermomechanics of the interface between a body and its environment

We formulate integral statements of force balance, energy balance, and entropy imbalance for an interface between a body and its environment. These statements account for interfacial energy, entropy, and stress but neglect the inertia of the interface. Our final results consist of boundary conditions describing thermomechanical interactions between the body and its environment. In their most general forms, these results are partial differential equations that account for dissipation and encompass as special cases Navier’s slip law, Newton’s law of cooling, and Kirchhoff’s law of radiation. When dissipation is neglected, our results reduce to the well-known zero-slip, free-surface, zero-shear, prescribed temperature, and flux-free conditions. Dedicated to James K. Knowles: teacher, colleague, friend     

Performance of hydrodynamic journal bearing under the combined influence of textured surface and journal misalignment: A numerical survey

A wisely chosen geometry of micro textures with the favorable relative motion of lubricated surfaces in contacts can enhance tribological characteristics. In this paper, a computational investigation related to the combined influence of bearing surface texturing and journal misalignment on the performances of hydrodynamic journal bearings is reported. To this end, a numerical analysis is performed to test three texture shapes: square “SQ”, cylindrical “CY”, and triangular “TR”, and shaft misalignment variation in angle and degree. The Reynolds equation of a thin viscous film is solved using a finite differences scheme and a mass conservation algorithm (JFO boundary conditions), taking into account the presence of textures on both full film and cavitation regions. Preliminary results are compared with benchmark data and are consistent with a positive enhancement in misaligned bearing performances (load carrying capacity and friction). The results suggest that the micro-step bearing mechanism is a key parameter, where the micro-pressure recovery action present in dimples located at the second angular part of the bearing (from 180° to 360°) can compensate for the loss on performances caused by shaft misalignment, while the micro-pressure drop effect at the full film region causes poor performances. Considering the right arrangement of textures on the contact surface, their contours geometries can have a significant impact on the performance of misaligned journal bearings, particularly at high eccentricity ratios, high misalignment degrees and when the misalignment angle α approaches to $0\mathrm{°}$ or $180\mathrm{°}$.     

The effect of temperature gradients on the sharkskin surface instability in polymer extrusion through a slit die

The sharkskin surface instability is commonly observed in the extrusion of polymer melts. We present a series of experiments in which a specifically designed rectangular slit die with insulated and independently heated sides and is used to induce precise temperature gradients across a flowing polyethylene melt. Our previous experiments demonstrated that the character of the surface distortions produced by the sharkskin instability was a function of the die wall temperature and therefore the extrudate had viscoelastic properties at the surface. In this paper, we explore the role of temperature and viscoelastic property gradients near the capillary wall. The amplitude of the sharkskin instability is quantified and plotted against apparent shear and extension rates. Analysis of the data demonstrates that the amplitude and frequency of the instability is independent of bulk temperature and temperature gradient and is dependent only on wall temperature. The data are normalized using a dimensionless Weissenberg number based on the extension rate to collapse the data collected over all temperatures and gradients onto a single master curve. We conclude with an example of a rectangular extrudate exhibiting varying surface roughness due to differential die heating and discuss the implications of our observations on the sharkskin surface instability mechanism and on commercial applications.     

Morphology development of a PS/PMMA polymer blend during flow in dies

The morphology development in dilute and semi-concentrated blends (2 and 15 wt% disperse phase) of viscoelastic polymers is studied during flow in dies. In the entrance region the droplets deform into fibrils. In the die itself some of the fibrils can break up depending on their shear history and hence on their radial position. The morphology at the exit of the die is investigated by quenching the extrudate and visualizing the structure via scanning electron microscopy (SEM). For fibrils moving along the die axis, the theory of Tomotika for break-up of a fibril in a quiescent matrix describes the observations satisfactorily. Fibrils flowing off center undergo a shearing flow in the die, which could have an effect on the growth of the Rayleigh disturbances that cause break-up. It is observed that during flow break-up still occurs via Rayleigh instabilities. As a first approximation the theory of Tomotika also predicts the break-up of fibrils flowing off center, if the viscosity at the relevant shear rate is used.     

L'approche variationnelle de la fatigue : des premiers résultats

By using a principle of least energy and a Dugdale surface energy with an irreversibility condition, we build a debonding model of thin films valid both for monotone and cyclic loading. We show that, if the internal length introduced in Dugdale model is small in comparison to the film length, then the growth of the debonding follows Griffith's law under monotone loading and a Paris-type law under cycling loading. To cite this article: A. Jaubert, J.-J. Marigo, C. R. Mecanique 333 (2005).     

抚顺石油一厂地表变形初步探讨

石油一厂地表变形的主要因素是西露天矿露天台阶开采, 引起厂南缘边坡失稳、变形和地面沉陷, 同时促使其它因素活化, 更加剧了地裂缝和变形发展。     

Crystallization kinetics and morphology of biodegradable poly(lactic acid) with a hydrazide nucleating agent

The effect of tetramethylenedicarboxylic dibenzoylhydrazide (designated here as TMC) on the nonisothermal and isothermal crystallization behavior of PLA was investigated by differential scanning calorimetry (DSC), polarized optical microscopy (POM) and wide angle X-ray diffraction (WAXD). TMC shows excellent nucleating effect on PLA. With the addition of 0.05 wt% TMC, the crystallization half-time of PLA decreases from 26.06 to 6.13 min at 130 °C. The isothermal crystallization data were further analyzed by the Avrami model. The values of the Avrami exponent of the blends are comparable to that of neat PLA, indicating that the presence of TMC does not change the crystallization mechanism of the matrix. The observation from POM and WAXD measurements showed that the presence of TMC increases significantly the nuclei density of PLA but has no discernible effect on its crystalline structure.