A simple analytical model for estimation of melt film variables in thermoplastic vibration welding

The strength of vibration welds of thermoplastics is governed by the weld zone microstructure, which in turn, is closely tied to the welding process variables, such as the thickness of the weld melt film and the temperature profiles therein. The mathematical model described in this report is aimed at describing the role of the rheology of the melt—specifically the magnitude and shear rate dependence of the melt viscosity—in governing the melt film variables during the steady state penetration phase (Phase III) of vibration welding. The steady state momentum balance and heat transfer within the melt film are solved by using the power law model for viscosity. Closed‐form analytical expressions are obtained for estimating the melt film thickness, the shear rates, and the temperature field within the film. This model has been used to estimate weld zone variables for four different polymers displaying a wide range of viscosities and shear thinning behaviors. POLYM. ENG. SCI., 54:499–511, 2014. © 2013 Society of Plastics Engineers     

Estimation of melt film variables during the steady‐state penetration phase of thermoplastic vibration welding using a generalized newtonian fluid model

The thickness of the melt film and the temperature profiles within the melt film in the weld zone are key process variables governing the development of weld‐zone microstructures and the resulting development of weld strengths, during vibration welding of thermoplastics. The mathematical model described in this report is aimed at investigating the role of the rheology of the melt—specifically the magnitude and shear‐rate as well as temperature dependence of the melt viscosity—in governing the process variables such as the molten film thickness and the viscosities, stresses, and the temperatures within the melt film during vibration welding. The analysis is focused on the steady‐state penetration phase (phase III) of vibration welding. The coupled steady‐state momentum balance and heat transfer within the melt film, formulated using the Cross‐WLF (Williams‐Landel‐Ferry) relationship for viscosity, are solved in an iterative finite element framework. The model has been implemented for two different polymers displaying significant differences in viscosities and shear thinning behaviors. An attempt has been made to correlate the trends in the estimated melt film variables with the experimentally measured weld quality. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Thickness uniformity of HDPE blown film: Relation to rheological properties and density

Previous work has elucidated that the wall slip velocity and viscosity of polymer melts influence the thickness uniformity of blown film. The present study investigates the effects of the stress dependence of wall slip, the shear thinning and the density on the uniformity. We have prepared high‐density polyethylenes with a variety of molecular weight distributions, which have different rheological properties. Examination of the thickness uniformity of their blown film has shown that the uniformity is correlated with wall slip velocity, the stress dependence of the velocity, melt viscosity, shear thinning and density; the coefficient of the correlation is determined to be 0.990. The reason why the stress dependence of wall slip and the shear thinning affect the uniformity is explained in terms of polymer melt flow behavior in a die, while the effect of density is interpreted considering bubble fluctuation in the blow‐up process. Polym. Eng. Sci. 44:965–972, 2004. © 2004 Society of Plastics Engineers.     

The effects of surface viscosity on the axisymmetric drainage of planar liquid films

The Reynolds equation is extended to allow for the effects of shear and dilational surface viscosities on the axisymmetric drainage of planar films. It is shown that the number of immobile surfaces, n, may be expected to decrease with increasing film radius and bulk viscosity and with decreasing film thickness and surface viscosity, as observed experimentally. The predicted rate of film thinning agrees well with available experimental results.     

Characterization of polymer-coated optical fibers using a torsion pendulum

A freely oscillating torsion pendulum has been used to characterize the dynamic mechanical behavior of single polymer-coated optical fibers. The dynamical mechanical spectra of the polymer coatings exhibit a glass transition temperature (T_g), a cryogenic glassy-state relaxation (T_sec), and another cryogenic relaxation that is attributed to water present in the coating (TH₂O). The shear modulus (G′) of the coating was computed from the shear moduli of the composite specimen and the core, assuming that the coating and core deform through the same angle on oscillation. The glassy-state modulus was the same for both thin and thick coatings, although the intensity of the damping peaks, as measured by the logarithmic decrement, increased with coating thickness. Comparison of the dynamic mechanical behavior of a coated optical fiber and of a free film cast from the same reactive components shows that the polymer itself can absorb water at ambient conditions and display a mechanical relaxation at cryogenic temperatures. The T., H₂O and T_sec relaxations are coupled with respect to their intensities. Latent chemical reactivity was found in one coating above its maximum temperature of cure. In this, the temperature of cure determines the glass transition temperature.     

Identification of Relaxation Functions in Glass by Mean of a Simple Experiment

This communication discusses the possibility of identifying the shear and structure relaxation functions in inorganic glass by means of a single, simple, and non-intrusive experiment. The latter consists of measuring the thickness variation over time of a glass plate cooled symmetrically from both sides from a temperature above the glass transition temperature down to room temperature. Results with "artificially" created experimental observations suggest that in spite of its simplicity, the thickness variation curve contains sufficient information to identify uniquely the relaxation function parameters using the Levenberg–Marquardt method.     

Effects of shear thinning on forward roll coating

This paper described the forward mode roll coating process of generalised non-Newtonian fluids characterised by the Ellis model. The fluid in the coating bead and the free surface formation are described by the lubrication approximation and the stability is also considered using a perturbation analysis of the downstream meniscus. Results highlight the complex behaviour of this coating process and volume flow rate and film thickness results are obtained for a range of operating conditions. The stability of the downstream meniscus is observed to improve with increasing level of shear thinning when τ_1/2 (the shear stress at which the viscosity is half that of the zero shear stress viscosity) is small, however as τ_1/2 increases the meniscus stability decreases with increasing levels of shear thinning.     

Pipe flow of a dense emulsion: Homogeneous shear‐thinning or shear‐induced migration?

The flow field of a 70% concentrated noncolloidal o/w emulsion in a pipe has been investigated by means of Particle Image Velocimetry in a matched refractive index medium. At steady state and in laminar regime, the shape of axial velocity profiles is not parabolic and exhibits a shear‐thinning behavior of the dense emulsion, with a flow index of 0.5 and a negligible yield stress (less than 1 Pa). However, instead of a square root law, the pressure drop increases linearly with U_m. To explain this apparent inconsistency, two mechanisms of different nature are considered. The first originates from a possible relation between the consistency factor and the drop mean diameter. The second mechanism is shear‐induced migration and leads to the development of a concentration gradient in the pipe cross section. Both mechanisms considered reconcile the experimental data, the apparent local shear‐thinning behavior and the linear evolution of the pressure drop with the flow rate. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Dielectric relaxations of lead zirconate titanate films up to millimeter-wave frequencies

Modern high-frequency applications critically depend on the availability of data on the dielectric properties of functional materials in the microwave and millimeter-wave range. This paper investigates the dielectric response of polycrystalline lead zirconate titanate (PZT) thin films prepared by solution deposition at frequencies between 10 MHz and 70 GHz and temperatures of 305–395 K by measuring the S-parameters of coplanar waveguides (CPW). The real and imaginary parts of the permittivity of the PZT film are de-coupled from the electrical properties of both the fused silica substrate and the copper electrodes. Two dielectric relaxations are identified: one around 850 MHz, with room-temperature permittivity dropping from 1080 to 560, and one around 36 GHz, with permittivity dropping below 100, respectively. The low-frequency relaxation shows a shift to lower frequencies with increasing temperature; it is explained by the conventional Arlt model of mechanical shear mode resonance across the film thickness. The high-frequency relaxation, which is practically independent of temperature, is attributed to the response of ferroelectric domain walls.     

Soft Matter in a Tight Spot: Nanorheology of Confined Liquids and Block Copolymers

The linear frequency-dependent shear rheology and force–distance profiles of molecularly-thin fluids of very different structure were contrasted: a globular molecule octamethylcyclotetrasiloxane (OMCTS), branched alkanes (3-methylundecane and squalane), and a polymer brush in near-theta solution (polystyrene-polyvinylpyridine). In each case the data suggest a prolongation of the longest relaxation time (τ₁) with increasing compression. At frequencies ω > 1/τ₁ the shear response was “solid-like”, but at ω < 1/τ₁ it was “liquid-like”. OMCTS under mild compression exhibited seeming power-law viscoelastic behavior with G′(ω) = G″(ω) over a wide frequency range. Of the branched-molecule fluids, 3-methylundecane exhibited oscillatory force–distance profiles; this confirms prior computer simulations. But squalane (6 pendant methyl groups in an alkane chain 24 carbons long) showed one sole broad attractive minimum. Polymer brushes in a near-theta solvent exhibited changes qualitatively similar to those OMCTS, in particular, a smooth progression of longest relaxation time, generating a transition from “liquid-like” to “solid-like” shear rheology with decreasing film thickness. The common trend of shear response in these systems, in spite of important differences in molecular structure and force–distance profiles, is emphasized.     

Is the structural relaxation of glasses controlled by equilibrium shear viscosity?

Knowledge of relaxation processes is fundamental in glass science and technology because relaxation is intrinsically related to vitrification, tempering as well as to annealing and several applications of glasses. However, there are conflicting reports—summarized here for different glasses—on whether the structural relaxation time of glass can be calculated using the Maxwell equation, which relates relaxation time with shear viscosity and shear modulus. Hence, this study aimed to verify whether these two relaxation times are comparable. The structural relaxation kinetics of a lead metasilicate glass were studied by measuring the refractive index variation over time at temperatures between 5 and 25 K below the fictive temperature, which was initially set 5 K below the glass-transition temperature. Equilibrium shear viscosity was measured above and below the glass-transition range, expanding the current knowledge by one order of magnitude. The Kohlrausch equation described very well the experimental structural relaxation kinetics throughout the investigated temperature range and the Kohlrausch exponent increased with temperature, in agreement with studies on other glasses. The experimental average structural relaxation times were much longer than the values computed from isostructural viscosity, as expected. Still, they were less than one order of magnitude higher than the average relaxation time computed through the Maxwell equation, which relies on equilibrium shear viscosity. Thus, these results demonstrate that the structural relaxation process is not controlled by isostructural viscosity and that equilibrium shear viscosity only provides a lower boundary for structural relaxation kinetics.     

Three‐dimensional numerical simulation of coalescence and interactions of multiple horizontal bubbles rising in shear‐thinning fluids

The dynamics of multiple horizontal bubbles rising from different orifice arrangements in shear‐thinning fluids was simulated numerically by three‐dimensional Volume of Fluid method. The effects of bubble size, rheological properties of shear‐thinning fluids, and orifice structure arrangements on multiple bubbles interaction and coalescence were analyzed, and the mechanisms of bubble coalescence and breakup were fully discussed and elucidated. The variation of bubble rising velocity during coalescence process and freely rising processes for different orifice arrangements was also deeply investigated. The critical initial horizontal intervals for coalescence of multiple horizontal bubbles with various orifice arrangements were attained by simulation, which could serve as the critical criterion of bubble coalescence or noncoalescence. Furthermore, the critical bubble interval was predicted based on the film drainage model, the prediction accords well with the simulation result and is quite conducive for the design and optimization of perforated gas–liquid contact equipment. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3528–3546, 2015     

Electric-Field Induced Morphological Transitions in Elastic Contact Instability of Soft Solid Films

A soft elastic film, when placed in adhesive proximity with a contactor in a crack-like geometry, spontaneously undergoes a surface instability to form finger patterns with a characteristic wavelength of approximately 4h, where h is the film thickness. We study the morphological evolution and control of this elastic contact instability under the influence of an external electric field. The distinct electric field induced morphological changes, leading to the formation of two-dimensional hexagonally arranged pillars, large-amplitude fingers, and straightening of contact edge, which are studied comprehensively. The conditions for the evolution of morphologically distinct patterns are governed by the film parameters, such as its shear modulus and thickness. A theoretical model and its stability analysis provide an approximate estimate of the critical voltage required for the onset of changes and its scaling with the film parameters (thickness and shear modulus). Further, three-dimensional simulations based on energy minimization are presented to provide important clues regarding the physics of pattern evolution on soft elastic interfaces.     

Gas displacing liquids from non-circular tubes: high capillary number flow of a shear-thinning liquid

Transient, three-dimensional finite element analysis has been used to investigate the displacement of a shear thinning liquid from prismatic channels of square, rectangular and trapezoidal cross sections. Inertia, gravity and surface tension effects are neglected and the results therefore apply in the limits of low Reynolds and high capillary numbers. The analysis is carried out in a fixed frame of reference and gas penetration is modelled as the bubble moves down the tube, which is long relative to its transverse dimension. Results are provided for the thickness of the layers left on the channel walls under developed conditions, and the fraction of the cross section occupied by liquid, as a function of the channel cross-sectional geometry and the degree of shear thinning, modelled using the power law. Interface contours on the channel cross sections are displayed. It is found for the Newtonian liquid that the fingering instability arises in the rectangular channel when the aspect ratio reaches about five. Shear thinning delays the onset of the instability to higher aspect ratios. The results are systematized, and insights gained into the influence of channel geometry and shear thinning, by noting a qualitative, inverse relationship between the deposited layer thickness and the shear rate at the wall in the flow ahead of the bubble.     

切应力作用下层流降膜传热特性的数学分析

利用合流超几何函数求解了切应力作用下降膜过程的能量方程,其中液膜内速度分布由气液界面切应力决定,并解得努塞尔数的计算表达式,分析了液膜温度和努塞尔数的变化趋势,讨论了同向与反向切应力、贝克来数对层流降膜传热特性的影响。分析表明,同向切应力作用下液膜最大速度恒位于气液界面处,对液膜具有拉薄效应,因此换热效果优于反向切应力作用,且努塞尔数随着切应力的增大而增大,而反向切应力则相反;同时努塞尔数在发展段随贝克来数的增大而增大,在充分发展阶段趋于一致。     

Experimental investigations of non‐Newtonian/Newtonian liquid‐liquid flows in microchannels

The plug flow of a non‐Newtonian and a Newtonian liquid was experimentally investigated in a quartz microchannel (200‐µm internal diameter). Two aqueous glycerol solutions containing xanthan gum at 1000 and 2000 ppm were the non‐Newtonian fluids and 0.0046 Pa s silicone oil was the Newtonian phase forming the dispersed plugs. Two‐color particle image velocimetry was used to obtain the hydrodynamic characteristics and the velocity profiles in both phases under different fluid flow rates. The experimental results revealed that the increase in xanthan gum concentration produced longer, bullet‐shaped plugs, and increased the thickness of the film surrounding them. From the shear rate and viscosity profiles, it was found that the polymer solution was in the shear‐thinning region while the viscosity was higher in the middle of the channel compared to the region close to the wall. Circulation times in the aqueous phase increased with the concentration of xanthan gum. © 2017 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 63: 3599–3609, 2017     

EFFECTS OF MASS TRANSFER ON THE THINNING AND RUPTURE OF A PLANE PARALLEL LIQUID FILM

The effects of mass transfer and physical properties upon the thinning and rupture of adraining plane parallel film are investigated.An equation is derived in which the thinning rate is afunction of bulk properties.surface properties(surface tension,surface viscosities,and the variationof surface tension with surface concentration),intermolecular forces(London-van der Waals forcesand electrostatic double layer forces),adsorption and surface diffusion coefficients,bubble size andfilm thickness.An estimation for the critical thickness at which a film rupture is carried out and thecoalescence time is obtained by integration to the critical thickness,The coalescence time is predictedas a function of bulk and surface properties,London-van der forces,adsorption and surfacediffusion coefficients,and bubble size.     

The growth kinetics and properties of potentiodynamically formed thin oxide films on aluminium in citric acid solutions

The growth kinetics and properties of potentiodynamically formed thin oxide films on Al were investigated in 0.05 M citric acid solutions of different pH (5, 6 and 7) by means of potentiodynamic polarization and a.c. electrochemical impedance spectroscopy (EIS) measurements. Al showed passive behaviour within the pH range that was examined. The potentiodynamic growth of the oxide film on Al takes place due to ionic conductivity under the influence of the high electric field. Characteristic kinetic oxide film growth parameters such as the high-field growth exponential law constants (A and B), ionic conductivity through the oxide film, field strength and half barrier width have been calculated. Impedance measurements were used to determine the parameters related to the characteristic sizes and properties of oxide film. The capacitive response of the impedance spectrum was related to the thickness and dielectric properties of the barrier oxide film. The oxide film resistance values were very high, indicating that the oxide films formed under potentiodynamic conditions are highly uniform in thickness and very resistant. The anodic behaviour of Al in the citric solutions under potentiodynamic conditions were characterized by the rapid growth of the oxide film which diminished the influence of relaxation processes on the growth kinetics and structural characteristics of the aluminium/anodic oxide film/electrolyte system.     

Viscosity properties of homogeneous polyelectrolyte complex solutions from sodium carboxymethyl cellulose and poly(acrylamide‐co‐dimethyldiallylammonium chloride)

The viscosity properties of homogeneous polyelectrolyte complex solutions of sodium carboxymethyl cellulose (CMC) and poly(acrylamide‐co‐dimethyldiallylammonium chloride) have been investigated by means of a rotation viscometer at different complexation ratios, shear rates and temperatures. Compared with aqueous solutions of the component polyelectrolytes, such complex solutions can afford substantially increased viscosities at the complexation ratios examined, together with enhanced shear‐thinning rheology and temperature stability. According to this study, it is possible to improve the viscosity properties of water‐soluble polymers by homogeneous interpolyelectrolyte complexation in aqueous solutions. © 2000 Society of Chemical Industry     

Assessment of development and relaxation of orientation in a sheared thermotropic liquid crystalline copolyester

Shear-induced chain orientation and relaxation of chain orientation in a thermotropic liquid-crystalline poly(4-hydroxybenzoic acid (73mol%)-co-2-hydroxy-6-naphthoic acid (27 mol%)) (Vectra A950) were studied by means of transmitted light intensity through crossed polarizers in a shear cell. Shear rates ranged between 4 and 1000 s^?1 and the level of chain orientation increased with increasing shear rate and increasing temperature. Overall, the times for relaxation were very short. The longest relaxation times (?21s) were obtained at the lowest shear temperatures and at intermediate shear rates. At high shear rates, the relaxation times were generally short (?2s) and independent of temperature. The rapid relaxation of orientation after high rate shearing (100–1000 s^?1) indicates that shear-induced crystallization is inhibited under these conditions. A certain degree of chain orientation was still present although the relaxation as judged by the transmitted light intensity was complete. Signs of recrystallization were observed if the samples were not preheated to 320°C prior to shearing. By simultanecous shearing and cooling, high degrees of orientation were achieved (f ? 0.7) as revealed by X-ray diffraction and infrared dichroism. Infrared spectroscopy showed that annealing of oriented samples at 250°C led to an increase in thermal stability of the orientation with annealing time.