A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Freakel criterion and is obtained from the zeroth order approximation of the H-3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H-3 term in the evolution equation and is dependent on the film thinning velocity A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semiempirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams. (C) 2003 Elsevier Science B.V. All rights reserved.

Prediction of the growth of wear-type rail corrugation

The growth behaviour of the vibrational wear phenomenon known as rail corrugation is investigated analytically and numerically using mathematical models. A simplified feedback model for wear-type rail corrugation that includes a wheel pass time delay is developed with an aim to analytically distil the most critical interaction occurring between the wheel/rail structural dynamics, rolling contact mechanics and rail wear. To this end, a stability analysis on the complete system is performed to determine the growth of wear-type rail corrugations over multiple wheelset passages. This analysis indicates that although the dynamical behaviour of the system is stable for each wheel passage, over multiple wheelset passages, the growth of wear-type corrugations is shown to be the result of instability due to feedback interaction between the three primary components of the model. The corrugations are shown analytically to grow for all realistic railway parameters. From this analysis an analytical expression for the exponential growth rate of corrugations in terms of known parameters is developed. This convenient expression is used to perform a sensitivity analysis to identify critical parameters that most affect corrugation growth. The analytical predictions are shown to compare well with results from a benchmarked time-domain finite element model. (C) 2004 Elsevier B.V. All rights reserved.

Scaling laws for the critical rupture thickness or common thin films

Despite decades of experimental and theoretical investigation on thin films, considerable uncertainty exists in the prediction of their critical rupture thickness. According to the spontaneous rupture mechanism, common thin films become unstable when capillary waves. at the interfaces begin to grow. In a horizontal film with symmetry at the midplane. unstable waves from adjacent interfaces grow towards the center of the film. As the film drains and becomes thinner, unstable waves osculate and cause the film to rupture, Uncertainty sterns from a number of sources including the theories used to predict film drainage and corrugation growth dynamics. In the early studies, (lie linear stability of small amplitude waves was investigated in the Context of the quasi-static approximation in which the dynamics of wave growth and film thinning are separated. The zeroth order wave growth equation of Vrij predicts faster wave growth rates than the first order equation derived by Sharma and Ruckenstein. It has been demonstrated in an accompanying paper that film drainage rates and times measured by numerous investigations are bounded by the predictions of the Reynolds equation and the more recent theory of Manev, Tsekov, and Radoev. Solutions to combinations of these equations yield simple scaling laws which should bound the critical rupture thickness of foam and emulsion films, In this paper, critical thickness measurements reported in the literature are compared to predictions from the bounding scaling equations and it is shown that the retarded Hamaker constants derived from approximate Lifshitz theory underestimate the critical thickness of foam and emulsion films, The non-retarded Hamaker constant more adequately bounds the critical thickness measurements over the entire range of film radii reported in the literature. This result reinforces observations made by other independent researchers that interfacial interactions in flexible liquid films are not adequately represented by the retarded Hamaker constant obtained from Lifshitz theory and that the interactions become significant at much greater separations than previously thought. (c) 2005 Elsevier B.V. All rights reserved.

Effect of initial disturbance amplitude in gravity affected jet break-up

The initial disturbance amplitude has an effect on stretching jets that is not observed for capillary jet instability where gravitational acceleration is not significant. For inviscid and viscous fluids, gravity diminishes the effect that the initial amplitude has on jet length and its ability to prevent satellite formation. In stretching jets, not only the dimensionless frequency of the disturbance but also its initial amplitude must be known to properly study their satellite forming nature. Indirect methods of relating the applied disturbance energy to an initial velocity perturbation are not simple when the gravity parameter G is changing. When G A 0, the optimum disturbance frequency Omega(opt) and the initial disturbance amplitude are related, with Omega(opt) proportional to f (G) x In(1 /epsilon(nu)). Results from numerical simulations and experiments are presented here. (c) 2005 Elsevier Ltd. All rights reserved.

Systematic changes in the duration and precision of interception in response to variation of amplitude and effector size

The results of two experiments are reported that examined how performance in a simple interceptive action (hitting a moving target) was influenced by the speed of the target, the size of the intercepting effector and the distance moved to make the interception. In Experiment 1, target speed and the width of the intercepting manipulandum (bat) were varied. The hypothesis that people make briefer movements, when the temporal accuracy and precision demands of the task are high, predicts that bat width and target speed will divisively interact in their effect on movement time (MT) and that shorter MTs will be associated with a smaller temporal variable error (VE). An alternative hypothesis that people initiate movement when the rate of expansion (ROE) of the target's image reaches a specific, fixed criterion value predicts that bat width will have no effect on MT. The results supported the first hypothesis: a statistically reliable interaction of the predicted form was obtained and the temporal VE was smaller for briefer movements. In Experiment 2, distance to move and target speed were varied. MT increased in direct proportion to distance and there was a divisive interaction between distance and speed; as in Experiment 1, temporal VE was smaller for briefer movements. The pattern of results could not be explained by the strategy of initiating movement at a fixed value of the ROE or at a fixed value of any other perceptual variable potentially available for initiating movement. It is argued that the results support pre-programming of MT with movement initiated when the target's time to arrival at the interception location reaches a criterion value that is matched to the pre-programmed MT. The data supported completely open-loop control when MT was less than between 200 and 240 ms with corrective sub-movements increasingly frequent for movements of longer duration.

Wear-type rail corrugation prediction: Field study

Rail corrugation consists of undesirable periodic fluctuations in wear on railway track and costs the railway industry substantially for it's removal by regrinding. Much research has been performed on this problem, particularly over the past two decades, however, a reliable cure remains elusive for wear-type corrugations. Recently the growth behaviour of wear-type rail corrugation-has been investigated using theoretical and experimental models as part of the RailCRC Project (#18). A critical part of this work is the tuning and validation of these models via an extensive field testing program. Rail corrugations have been monitored for 2 years on sites throughout Australia. Measured rail surface profiles are used to determine corrugation growth rates on each site. Growth rates and other characteristics are compared with theoretical predictions from a computer model for validation. The results from several pertinent sites are presented and discussed.

Distortion product otoacoustic emissions in schoolchildren: Effects of ear asymmetry, handedness and gender

The present study examined effects of ear asymmetry, handedness, and gender on distortion-product otoacoustic emissions (DPOAEs) obtained from schoolchildren. A total of 1003 children (528 boys and 475 girls), with a mean age of 6.2 years (SD = 0.4, range = 5.2-7.9 years), were tested in a quiet room at their schools using the GSI-60 DPOAE system. A distortion-product (DP)-gram was obtained for each ear, with f2 varying from 1.1 to 6.0 kHz and the ratio of f2/f1 at 1.21. The signal-to-noise ratios (SNRs) (DPOAE amplitude minus the mean noise floor) at the tested frequencies 1.1, 1.5, 1.9, 2.4, 3.0, 3.8, 4.8, and 6.0 kHz were measured. The results revealed a small but significant difference in SNR between ears, with right ears showing a higher mean SNR than left ears at 1.9, 3.0, 3.8, and 6.0 kHz. At these frequencies, the difference in mean SNR between ears was less than 1 dB. A significant gender effect was also found. Girls exhibited a higher SNR than boys at 3.8, 4.8, and 6.0 kHz. The difference in mean SNR, as a result of the gender effect, was about 1 to 2 dB at these frequencies. There was no significant difference in mean SNR between left-handed and right-handed children for all tested frequencies.

A Nonstationary Model of Newborn EEG

The detection of seizure in the newborn is a critical aspect of neurological research. Current automatic detection techniques are difficult to assess due to the problems associated with acquiring and labelling newborn electroencephalogram (EEG) data. A realistic model for newborn EEG would allow confident development, assessment and comparison of these detection techniques. This paper presents a model for newborn EEG that accounts for its self-similar and non-stationary nature. The model consists of background and seizure sub-models. The newborn EEG background model is based on the short-time power spectrum with a time-varying power law. The relationship between the fractal dimension and the power law of a power spectrum is utilized for accurate estimation of the short-time power law exponent. The newborn EEG seizure model is based on a well-known time-frequency signal model. This model addresses all significant time-frequency characteristics of newborn EEG seizure which include; multiple components or harmonics, piecewise linear instantaneous frequency laws and harmonic amplitude modulation. Estimates of the parameters of both models are shown to be random and are modelled using the data from a total of 500 background epochs and 204 seizure epochs. The newborn EEG background and seizure models are validated against real newborn EEG data using the correlation coefficient. The results show that the output of the proposed models has a higher correlation with real newborn EEG than currently accepted models (a 10% and 38% improvement for background and seizure models, respectively).

Bimanual aiming and overt attention: one law for two hands

Reaching to interact with an object requires a compromise between the speed of the limb movement and the required end-point accuracy. The time it takes one hand to move to a target in a simple aiming task can be predicted reliably from Fitts' law, which states that movement time is a function of a combined measure of amplitude and accuracy constraints (the index of difficulty, ID). It has been assumed previously that Fitts' law is violated in bimanual aiming movements to targets of unequal ID. We present data from two experiments to show that this assumption is incorrect: if the attention demands of a bimanual aiming task are constant then the movements are well described by a Fitts' law relationship. Movement time therefore depends not only on ID but on other task conditions, which is a basic feature of Fitts' law. In a third experiment we show that eye movements are an important determinant of the attention demands in a bimanual aiming task. The results from the third experiment extend the findings of the first two experiments and show that bimanual aiming often relies on the strategic co-ordination of separate actions into a seamless behaviour. A number of the task specific strategies employed by the adult human nervous system were elucidated in the third experiment. The general strategic pattern observed in the hand trajectories was reflected by the pattern of eye movements recorded during the experiment. The results from all three experiments demonstrate that eye movements must be considered as an important constraint in bimanual aiming tasks.