A global stability approach to wake and path instabilities of nearly oblate spheroidal rising bubbles

A global Linear Stability Analysis (LSA) of the three-dimensional flow past a nearly oblate spheroidal gas bubble rising in still liquid is carried out, considering the actual bubble shape and terminal velocity obtained for various sets of Galilei (Ga) and Bond (Bo) numbers in axisymmetric numerical simulations. Hence, this study extends the stability analysis approach of Tchoufag et al. [“Linear stability and sensitivity of the flow past a fixed oblate spheroidal bubble,” Phys. Fluids 25, 054108 (2013) and “Linear instability of the path of a freely rising spheroidal bubble,” J. Fluid Mech. 751, R4 (2014)] (which considered perfectly spheroidal bubbles with an arbitrary aspect ratio) to the case of bubbles with a realistic fore-aft asymmetric shape (i.e., a flatter front and a more rounded rear). The critical curve separating stable and unstable regimes for the straight vertical path is obtained both in the (Ga,Bo) and the (Re,χ) planes, where Re is the bubble Reynolds number and χ its aspect ratio (i.e., the major-to-minor axes length ratio). This provides new insight into the effect of the shape asymmetry on the wake instability of bubbles held fixed in a uniform stream and on the path instability of freely rising bubbles, respectively. For the range of Ga and Bo explored here, we find that the flow past a bubble with a realistic shape is generally more stable than that past a perfectly spheroidal bubble with the same aspect ratio. This study also provides the first critical curve for the onset of path instability that can be compared with experimental observations. The tendencies revealed by this critical curve agree well with those displayed by available data. The quantitative agreement is excellent for O(1) Bond numbers. However, owing to two simplifying assumptions used in the LSA scheme, namely, the steadiness of the base state and the uncoupling between the bubble shape and the flow disturbances, quantitative discrepancies (up to 20%–30%) with experimental threshold values of the Galilei number remain for both small and large Bond numbers

A novel particle tracking and break-up detection algorithm: application to the turbulent break-up of bubbles

A new method has been developed to measure experimentally the break-up properties of bubbles. The technique is based on the application of a particle tracking velocimetry algorithm to high-speed video images not only to measure the velocity of the bubbles, but also to detect the break-up events. Thus the algorithm is able to associate every broken bubble with the daughter bubbles formed upon their corresponding break-up. Moreover, the lifetime, as well as the number and size of fragments resulting from the break-up process, can be measured for a large number of bubbles. Statistical processing of the information collected allows us to compute the break-up frequency and daughter size distribution of the bubbles as a function of the bubble size and the mean properties of the base flow. The method has been employed to study the break-up of a cloud of bubbles injected at the central axis of a turbulent water jet. Experimental results for the break-up frequency and daughter bubble size distribution are also presented to illustrate the performance of the technique

On the breakup of an air bubble injected into a fully developed turbulent flow. Part 2. Size PDF of the resulting daughter bubbles

Based on energy principles, we propose a statistical model to describe the bubble size probability density function of the daughter bubbles resulting from the shattering of a mother bubble of size D0 immersed in a fully developed turbulent water flow. The model shows that the bubble size p.d.f. depends not only on D0, but also on the value of the dissipation rate of turbulent kinetic energy of the underlying turbulence of the water, [epsilon]. The phenomenological model is simple, yet it predicts detailed experimental measurements of the transient bubble size p.d.f.s performed over a range of bubble sizes and dissipation rates [epsilon] in a very consistent manner. The agreement between the model and the experiments is particularly good for low and moderate bubble turbulent Weber numbers, Wet = [rho][Delta]u2(D0)D0/[sigma] where the assumption of the binary breakup is shown to be consistent with the experimental observations. At larger values of Wet, it was found that the most probable number of daughter bubbles increases and the assumption of tertiary breakup is shown to lead to a better fit of the experimental measurements

On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency

The transient evolution of the bubble-size probability density functions resulting from the breakup of an air bubble injected into a fully developed turbulent water ow has been measured experimentally using phase Doppler particle sizing (PDPA) and image processing techniques. These measurements were used to determine the breakup frequency of the bubbles as a function of their size and of the critical diameter Dc defined as Dc = 1.26 ([sigma]/[rho])3/5[epsilon][minus sign]2/5, where [epsilon] is the rate of dissipation per unit mass and per unit time of the underlying turbulence. A phenomenological model is proposed showing the existence of two distinct bubble size regimes. For bubbles of sizes comparable to Dc, the breakup frequency is shown to increase as ([sigma]/[rho])[minus sign]2/5[epsilon][minus sign]3/5 [surd radical]D/Dc[minus sign]1, while for large bubbles whose sizes are greater than 1.63Dc, it decreases with the bubble size as [epsilon]1/3D[minus sign]2/3. The model is shown to be in good agreement with measurements performed over a wide range of bubble sizes and turbulence intensitie

Floquet stability analysis of a two-layer oscillatory flow near a flexible wall

We investigate the linear Floquet stability of two fluid layers undergoing oscillations in the direction parallel to the flexible wall that separates them. This canonical configuration is inspired by the cerebrospinal fluid flow in the spinal canal of subjects with hydro-/syringomyelia.The analysis focuses on the marginal conditions for the onset of instability, and how these depend on the spatial wavelength of the perturbation, and on the values of the control parameters, which are the two channel widths, the Reynolds number, and the wall stiffness. Unstable perturbations are found to oscillate synchronous with the base flow. The wavelength of the most unstable perturbation, of the order of the stroke length of the basic oscillatory motion, depends strongly on the wall stiffness, but is only weakly influenced by the channel widths and the Reynolds number. In general, around criticality, it was found that increasing the Reynolds number has a destabilizing effect, and that decreasing the canal widths stabilizes the instability. The wall stiffness on the other hand has a non-monotonic effect, exhibiting an intermediate value for which the instability is maximally amplified. The present analysis is a first step towards a better understanding of the physical mechanisms that govern many (bio)fluid mechanical problems that involve oscillatory flows near compliant walls

Cavity flow induced by a flexible membrane in an oscillatory channel flow: case study of syringomyelia.

In this work, we study the flow inside a Syringomyelia, modelled by a cavity separated from a channel with an elastic membrane. The oscillatory flow of the channel is transmitted to the cavity through the deformation of the membrane. We study the structure of the time-dependent and stationary flow induced inside the cavity and the deformation of the membrane under different problem conditions.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability

We report on a series of results provided by three-dimensional numerical simulations of nearly spheroidal bubbles freely rising and deforming in a still liquid in the regime close to the transition to path instability. These results improve upon those of recent computational studies [Cano-Lozano et al., Int. J. Multiphase Flow 51, 11 (2013); Phys. Fluids 28, 014102 (2016)] in which the neutral curve associated with this transition was obtained by considering realistic but frozen bubble shapes. Depending on the dimensionless parameters that characterize the system, various paths geometries are observed by letting an initially spherical bubble starting from rest rise under the effect of buoyancy and adjust its shape to the surrounding flow. These include the well-documented rectilinear axisymmetric, planar zigzagging, and spiraling (or helical) regimes. A flattened spiraling regime that most often eventually turns into either a planar zigzagging or a helical regime is also frequently observed. Finally, a chaotic regime in which the bubble experiences small horizontal displacements (typically one order of magnitude smaller than in the other regimes) is found to take place in a region of the parameter space where no standing eddy exists at the back of the bubble. The discovery of this regime provides evidence that path instability does not always result from a wake instability as previously believed. In each regime, we examine the characteristics of the path, bubble shape, and vortical structure in the wake, as well as their couplings. In particular, we observe that, depending on the fluctuations of the rise velocity, two different vortex shedding modes exist in the zigzagging regime, confirming earlier findings with falling spheres. The simulations also reveal that significant bubble deformations may take place along zigzagging or spiraling paths and that, under certain circumstances, they dramatically alter the wake structure. The instability thresholds that can be inferred from the computations compare favorably with experimental data provided by various sets of recent experiments guaranteeing that the bubble surface is free of surfactants

Analgesia preventiva con Diclofenaco en el dolor postoperatorio de colecistectomía videolaparoscópica

It was performed a prospective, quasi- experimental, controlled, double blind study in patients that were surgically assisted due to bladder stones by means of laparoscopic video surgery, at Celia Sanchez Manduley University Hospital in Manzanillo, during the period of January, 2010 to December, 2013; with the objective to evaluate the effectiveness of preventive analgesia with Diclofenac in the post- operative pain after the video laparoscopic cholecystectomy. The universe of study coincided with the sample and it was formed by 100 patients, who were distributed into two groups: group I (Experimental or study), created with the first 50 patients who came to the service and received preventive analgesia with Diclofenac, and the group II (Control), formed by the last 50 patients without preventive analgesia. It was applied the Chi- square test, from the statistical point of view to determine the existence of the association among the variables of the study. The preventive management of Diclofenac prevents the post – operative pain after the video laparoscopic cholecystectomy, proving its effectiveness in preventive analgesia. Female patients about 40-50 years prevailed. There were no adverse effects in the management of Diclofenac.Se realizó un estudio prospectivo, cuasi experimental, controlado, doble ciego en pacientes intervenidos quirúrgicamente por Litiasis Vesicular por cirugía video laparoscópica, en el Hospital Universitario “Celia Sánchez Manduley” de Manzanillo, en el período comprendido desde enero de 2010 hasta diciembre de 2013; con el objetivo de evaluar la efectividad de la analgesia preventiva con diclofenaco en el dolor postoperatorio de colecistectomía videolaparoscópica. El universo de estudio que coincidió con la muestra estuvo formado por 100 pacientes, los que fueron distribuidos en dos grupos: el grupo I (Experimental o estudio), formado por los primeros 50 pacientes que acudieron al servicio y que recibieron analgesia preventiva con diclofenaco, y el grupo II (Control), los últimos 50 pacientes en los que no se empleó analgesia preventiva. Se aplicó desde el punto de vista estadístico la prueba Chi-cuadrado de independencia para determinar la existencia de asociación entre las variables que participan en el estudio. La administración preventiva de diclofenaco previene la aparición de dolor postoperatorio de colecistectomía videolaparoscópica, demostrándose su efectividad en la analgesia preventiva. Prevalecieron los pacientes entre los 40 a 50 años de edad, del sexo femenino. No se presentaron efectos adversos con la administración del diclofenaco.