R. E. Kelly

Thermal convection with spatially periodic boundary conditions: resonant wavelength excitation

Thermal convection in a fluid contained between two rigid walls with different mean temperatures is considered when either spatially periodic temperatures are prescribed at the walls or surface corrugations exist. The amplitudes of the spatial non-uniformities are assumed to be small, and the wavelength is set equal to the critical wavelength for the onset of Rayleigh-Benard convection. For values of the mean Rayleigh number below the classical critical value, the mean Nusselt number and the mean flow are found as functions of Rayleigh number, Prandtl number, and modulation amplitude. For values of the Rayleigh number close to the classical critical value, the effects of the non-uniformities are greatly amplified, and the amplitude of convection is then governed by a cubic equation. This equation yields three supercritical states, but only the state linked to a subcritical state is found to be stable.

Instabilities of a liquid film flowing down a slightly inclined plane

Falling films on inclined planes display surface and shear instability modes, the latter being important at small angles β of inclination of the plane. These modes are analyzed with particular attention paid to the effects of surface tension. The results show that the critical Reynolds number of the shear mode is nonmonotonic in either the angle β or the surface‐tension parameter ζ but displays a local minimum at nonzero values of β and ζ. For large Reynolds number, an analysis shows that the shear mode is inviscidly stable, but that the surface mode is unstable.

The flow and stability of thin liquid films on a rotating disk

Measurements of the thickness and the stability of thin films of liquid (1–150 μmthick) formed on a rotating horizontal disk are presented and correlated in terms of an asymptotic-expansion solution of the thin-film equations. Water, various alcohols and water with wetting activities were used to cover a range of viscosity (1-2.5cP) and surface tension (20-72 dynes/cm). Smooth flow was found to occur in a region defined by the flow rate, rotational speed and physical properties of the liquid. Outside this region various wave patterns were observed (concentric, spiral and irregular waves). A linear theory of the stability of the film based on an extension of classical stability theories for plane films on inclined planes is given and contrasted with the experimental results. Surface phenomena associated with the use of wetting agents were found to have a strong effect on the stability of the film.

The mechanism for surface wave instability in film flow down an inclined plane

The equation governing the average rate of change of disturbance kinetic energy is evaluated for various wavenumbers at fixed values of Reynolds number, Weber number, and angle of inclination. The dominant energy production term is associated with the work done by the perturbation shear stress at the free surface. The mechanism of instability, however, is associated with a shift of perturbation vorticity relative to the surface displacement resulting from advection.

Pulmonary edema and fluid mobilization as determinants of the duration of ECMO support

The physiological variables that govern recovery of pulmonary function during neonatal extracorporeal membrane oxygenation (ECMO) remain poorly understood. We hypothesized that pulmonary hypertension (PHN) resolves soon after starting ECMO and that neonatal weight gain, pulmonary edema, and fluid mobilization are major determinants of recovery of pulmonary function and the ability to decrease ECMO support. To evaluate this, 17 consecutive neonates requiring ECMO for severe respiratory failure were reviewed. PHN was studied by daily echocardiography to assess the direction of ductal shunting. To evaluate fluid flux, pulmonary function, and edema during ECMO, we measured body weight, urine output, and ECMO flow every 12 hours. To evaluate pulmonary edema, serial chest radiographs obtained every 12 hours were randomly reviewed and scored by two radiologists with a semiquantitative chest radiograph index score (CRIS). By 25% of bypass time, PHN had resolved in all patients. However, at that time, weight had increased to 9.16% +/- 1.78% above birth weight, and the CRIS was 44% worse than the value just prior to ECMO. From 25% time on bypass, as urine output increased, patient weight and CRIS progressively decreased, allowing ECMO support to be weaned. At the time of discontinuation of ECMO support, weight had decreased to 2.0% +/- 1.3% above birth weight, and urine output remained steady at 3.0 +/- 0.3 mL/kg/h. Within 24 hours of stopping ECMO, the CRIS showed a 58% improvement compared to maximal scores during ECMO. We conclude that PHN decreases early in ECMO and that edema and its mobilization are important determinants of the improvement in pulmonary function and duration of ECMO.(ABSTRACT TRUNCATED AT 250 WORDS)

SURFACE WAVE AND THERMOCAPILLARY INSTABILITIES IN A LIQUID FILM FLOW

A liquid film flowing down an inclined heated plane subject to surface wave and thermocapillary instabilities is studied. Three mechanisms exist by which energy can be transferred to the disturbance. Two of these mechanisms are associated with the thermocapillary forces and one with the shear stress of the basic flow at the deformed free surface. Depending on which mechanism is dominant, the instability can assume the form of either long transverse waves or short longitudinal rolls.

An improved model of experimental gastroschisis in fetal rabbits

Previous animal models of gastroschisis have been associated with high mortality and variable degrees of intestinal evisceration. Using current fetal surgical techniques, an improved model of gastroschisis in fetal rabbits was developed. Twenty-eight time-mated New Zealand white rabbits underwent hysterotomies and fetal exposure on gestational day 25 (33-day gestation). Control fetuses (C) underwent fetal manipulation only. Gastroschisis fetuses (GS) had creation of right midabdominal wall defects. Twenty-five of 28 does (89%), 9 of 13 C fetuses (69%), and 18 of 22 GS fetuses (82%) survived. At the time of cesarean delivery 5 days later, GS fetuses had significantly lower body weights, intestinal lengths, and mucosa/submucosa height ratios (a measure of bowel wall edema), and significantly greater intestinal densities when compared with C fetuses (P less than .05, t test). This study demonstrates that (1) gastroschisis abdominal wall defects can be created in fetal rabbits with high survival rates; (2) experimental gastroschisis is associated with a profound decrease in fetal weight; and (3) eviscerated intestine is heavier, shorter, and thickened compared with normal control intestine, mimicking the clinical situation.

Instabilities of longitudinal convection rolls in couette flow

SummaryAn investigation has been made of the instabilities of longitudinal convection rolls in a Couette flow which is heated from below. The instabilities occur either as stationary waves or as waves which propagate along the convection rolls. Neutral stability curves are presented as a function of Rayleigh and Reynolds numbers for a Prandtl number of 0.7. The disturbance energy budget is given for selected values of the Rayleigh and Reynolds numbers.ZusammenfassungDie Instabilitäten von longitudinalen Konvektionsrollen in einer ebenen Couette-Strömung, die von unten erhitzt wird, sind untersucht worden. Die Instabilitäten nehmen entweder die Form von stehenden Wellen an oder von Wellen, die sich entlang der Konvektionsrollen fortpflanzen. Die Kurven für marginale Stabilität sind als Funktion der Rayleigh-und Reynoldszahl dargestellt worden im Fall der Prandtlzahl 0.7. Das Energiebudget der Störungen wird für ausgewählte Werte der Rayleigh-und Reynoldszahl angegeben.

Transverse-jet shear-layer instabilities. Part 2. Linear analysis for large jet-to-crossflow velocity ratio

The dominant non-dimensional parameter for isodensity transverse jet flow is the mean jet-to-crossflow velocity ratio, R . In Part 1 (Megerian et al ., J. Fluid Mech ., vol. 593, 2007, p. 93), experimental results are presented for the behaviour of transverse-jet near-field shear-layer instabilities for velocity ratios in the range 1 R ≤ 10. A local linear stability analysis is presented in this paper for the subrange R >4, using two different base flows for the transverse jet. The first analysis assumes the flow field to be described by a modified version of the potential flow solution of Coelho & Hunt ( J. Fluid Mech ., vol. 200, 1989, p. 95), in which the jet is enclosed by a vortex sheet. The second analysis assumes a continuous velocity model based on the same inviscid base flow; this analysis is valid for the larger values of Strouhal number expected to be typical of the most unstable disturbances, and allows prediction of a maximum spatial growth rate for the disturbances. In both approaches, results are obtained by expanding in inverse powers of R so that the free-jet results are obtained as R →∞. The results from both approaches agree in the moderately low-frequency regime. Maximum spatial growth rates and associated Strouhal numbers extracted from the second approach both increase with decreasing velocity ratio R , in agreement with the experimental results from Part 1 in the range 4 R ≤10. The nominally axisymmetric mode is found to be the most unstable mode in the transverse-jet shear-layer near-field region, upstream of the end of the potential core. The overall agreement of theoretical and experimental results suggests that convective instability occurs in the transverse-jet shear layer for jet-to-crossflow velocity ratios above 4, and that the instability is strengthened as R is decreased.

Effects of viscosity variation on the stability of film flow down heated or cooled inclined surfaces: Long‐wavelength analysis

The linear stability of liquid film flow, when the viscosity depends exponentially on temperature, is investigated here for the case of heating or cooling from below by means of an analysis valid for long waves. It is shown that cooling stabilizes the flow, while heating destabilizes it. For the case of cooling, a cutoff Prandtl number exists, above which the flow is stable with respect to long waves.