Bubble rise velocity and trajectory in xanthan gum crystal suspension

An experimental set-up was used to visually observe the characteristics of bubbles as they moved up a column holding xanthan gum crystal suspensions. The bubble rise characteristics in xanthan gum solutions with crystal suspension are presented in this paper. The suspensions were made by using different concentrations of xanthan gum solutions with 0.23 mm mean diameter polystyrene crystal particles. The influence of the dimensionless quantities; namely the Reynolds number, Re, the Weber number, We, and the drag co-efficient, cd, are identified for the determination of the bubble rise velocity. The effect of these dimensionless groups together with the Eötvös number, Eo, the Froude number, Fr, and the bubble deformation parameter, D, on the bubble rise velocity and bubble trajectory are analysed. The experimental results show that the average bubble velocity increases with the increase in bubble volume for xanthan gum crystal suspensions. At high We, Eo and Re, bubbles are spherical-capped and their velocities are found to be very high. At low We and Eo, the surface tension force is significant compared to the inertia force. The viscous forces were shown to have no substantial effect on the bubble rise velocity for 45 < Re < 299. The results show that the drag co-efficient decreases with the increase in bubble velocity and Re. The trajectory analysis showed that small bubbles followed a zigzag motion while larger bubbles followed a spiral motion. The smaller bubbles experienced less horizontal motion in crystal suspended xanthan gum solutions while larger bubbles exhibited a greater degree of spiral motion than those seen in the previous studies on the bubble rise in xanthan gum solutions without crystal.

Modeling of Ascending/Descending Velocity of Metal Droplet Emulsified in Pb-Salt System

Metal-slag emulsion is an important process to enhance the reaction rate between the two phases; thus, it improves the heat and mass transfer of the process significantly. Various experimental studies have been carried out, and some system specific relations have been proposed by various investigators. A unified, theoretical study is lacking to model this complex phenomenon. Therefore, two simple models based on fundamental laws for metal droplet velocity (both ascending and descending) and bubble velocity, as well as its position at any instant of time, have been proposed. Analytical solutions have been obtained for the developed equations. Analytical solutions have been verified for the droplet velocity, traveling time, and size distribution in slag phase by performing high-temperature experiments in a Pb-salt system and comparing the obtained data with theory. The proposed model has also been verified with published experimental data for various liquid systems with a wide range of physical properties. A good agreement has been found between the analytical solution and the experimental and published data in all cases.

Dynamics of collapsing fluidized beds and its application in the simulation of pulsed fluidized beds

A new method to study collapsing process of fluidized bed was proposed. The method is based on the analysis of the pressure variation during collapse. A model is proposed to describe the pressure variation on any location of the bed during collapse. Three kind of particles were fluidized by air and the pressure variation after shutting down the gas supply was measured by pressure transducers and simulated by the proposed model. The simulated results were in good agreement with the experimental data. The parameters of the fluidized bed, such as bubble fraction alpha(b), particle fraction in dense phase alpha(p), bubble velocity u(b) and slip velocity of particle u(i), can be estimated from the measured pressure data by using the proposed model. The model was also used to calculate the pressure variation in pulsed fluidized beds with low frequency.

Simulations of Two-Dimensional Foam under Couette Shear

null Sponsorship: Financial support is acknowledged from the University of Wales Aberystwyth Senate Fund, the Ulysses France-Ireland Exchange Scheme and EPSRC (EP/D014956/1, EP/D048397/1, EP/D071127/1).

Pressure drop of gas–liquid Taylor flow in round micro-capillaries for low to intermediate Reynolds numbers

In this paper, a model is presented that describes the pressure drop of gas-liquid Taylor flow in round capillaries with a channel diameter typically less than 1 mm. The analysis of Bretherton (J Fluid Mech 10:166-188, 1961) for the pressure drop over a single gas bubble for vanishing liquid film thickness is extended to include a non-negligible liquid film thickness using the analysis of Aussillous and Qu,r, (Phys Fluids 12(10):2367-2371, 2000). This result is combined with the Hagen-Poiseuille equation for liquid flow using a mass balance-based Taylor flow model previously developed by the authors (Warnier et al. in Chem Eng J 135S:S153-S158, 2007). The model presented in this paper includes the effect of the liquid slug length on the pressure drop similar to the model of Kreutzer et al. (AIChE J 51(9):2428-2440, 2005). Additionally, the gas bubble velocity is taken into account, thereby increasing the accuracy of the pressure drop predictions compared to those of the model of Kreutzer et al. Experimental data were obtained for nitrogen-water Taylor flow in a round glass channel with an inner diameter of 250 mu m. The capillary number Ca (gl) varied between 2.3 x 10(-3) and 8.8 x 10(-3) and the Reynolds number Re (gl) varied between 41 and 159. The presented model describes the experimental results with an accuracy of +/- 4% of the measured values.

Estudo experimental do funcionamento de um sistema gas-lif

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mathematical models of bubble evolution in a Hele-Shaw Cell

This thesis concerns the mathematical model of moving fluid interfaces in a Hele-Shaw cell: an experimental device in which fluid flow is studied by sandwiching the fluid between two closely separated plates. Analytic and numerical methods are developed to gain new insights into interfacial stability and bubble evolution, and the influence of different boundary effects is examined. In particular, the properties of the velocity-dependent kinetic undercooling boundary condition are analysed, with regard to the selection of only discrete possible shapes of travelling fingers of fluid, the formation of corners on the interface, and the interaction of kinetic undercooling with the better known effect of surface tension. Explicit solutions to the problem of an expanding or contracting ring of fluid are also developed.

On the origin of the inflectional instability of a laminar separation bubble

This is an experimental and theoretical Study of a laminar separation bubble and the associated linear stability mechanisms. Experiments were performed over a flat plate kept in a wind tunnel, with an imposed pressure gradient typical of an aerofoil that would involve a laminar separation bubble. The separation bubble was characterized by measurement of surface-pressure distribution and streamwise velocity using hot-wire anemometry. Single component hot-wire anemometry was also used for a detailed study of the transition dynamics. It was foundthat the so-called dead-air region in the front portion of the bubble corresponded to a region of small disturbance amplitudes, with the amplitude reaching a maximum value close to the reattachment point. An exponential growth rate of the disturbance was seen in the region upstream of the mean maximum height of the bubble, and this was indicative of a linear instability mechanism at work. An infinitesimal disturbance was impulsively introduced into the boundary layer upstream of separation location, and the wave packet was tracked (in an ensemble-averaged sense) while it was getting advected downstream. The disturbance was found to be convective in nature. Linear stability analyses (both the Orr-Sommerfeld and Rayleigh calculations) were performed for mean velocity profiles, starting from an attached adverse-pressure-gradient boundary layer all the way up to the front portion of the separation-bubble region (i.e. up to the end of the dead-air region in which linear evolution of the disturbance could be expected). The conclusion from the present work is that the primary instability mechanism in a separation bubble is inflectional in nature, and its origin can be traced back to upstream of the separation location. In other words, the inviscid inflectional instability of the separated shear layer should be logically seen as an extension of the instability of the upstream attached adverse-pressure-gradient boundary layer. This modifies the traditional view that pegs the origin of the instability in a separation bubble to the detached shear layer Outside the bubble, with its associated Kelvin-Helmholtz mechanism. We contendthat only when the separated shear layer has moved considerably away from the wall (and this happens near the maximum-height location of the mean bubble), a description by the Kelvin-Helmholtz instability paradigm, with its associated scaling principles, Could become relevant. We also propose a new scaling for the most amplified frequency for a wall-bounded shear layer in terms of the inflection-point height and the vorticity thickness and show it to be universal.

Observations on transition in plane bubble plumes

Flow visualization studies of plane laminar bubble plumes have been conducted to yield quantitative data on transition height, wavelength and wave velocity of the most unstable disturbance leading to transition. These are believed to be the first results of this kind. Most earlier studies are restricted to turbulent bubble plumes. In the present study, the bubble plumes were generated by electrolysis of water and hence very fine control over bubble size distribution and gas flow rate was possible to enable studies with laminar bubble plumes. Present observations show that (a) the dominant mode of instability in plane bubble plumes is the sinuous mode, (b) transition height and wavelength are related linearly with the proportionality constant being about 4, (c) wave velocity is about 40 % of the mean plume velocity, and (d) normalized transition height data correlate very well with a source Grashof number. Some agreement and some differences in transition characteristics of bubble plumes have been observed compared to those for similar single-phase flows.

On-Board Experimental Study Of Bubble Thermocapillary Migration In A Recoverable Satellite

An on-board space experiment of bubble thermocapillary migration was performed in the Chinese 22nd recoverable satellite in 2005. Silicone oil of nominal viscosity 5cSt was used as the continuous phase in the experiment. Air bubbles were injected into the liquid in the same direction as the constant temperature gradient in the liquid. The velocities of bubbles were obtained by recording the paths of the bubbles. The results indicate that the scaled velocity of bubbles decreases with an increase of the Marangoni number extended to 9288, which agrees with the results of previous space experiments and numerical simulation. In addition, the interaction between two bubbles was also observed in the space experiment. The trajectories and the velocities of the bubbles were obtained. The two-bubble experiment results are also consistent with the theoretical analysis.

Horizontal Bloch line motion in magnetic bubble materials

The purpose of this work is to extend experimental and theoretical understanding of horizontal Bloch line (HBL) motion in magnetic bubble materials. The present theory of HBL motion is reviewed, and then extended to include transient effects in which the internal domain wall structure changes with time. This is accomplished by numerically solving the equations of motion for the internal azimuthal angle ɸ and the wall position q as functions of z, the coordinate perpendicular to the thin-film material, and time. The effects of HBL's on domain wall motion are investigated by comparing results from wall oscillation experiments with those from the theory. In these experiments, a bias field pulse is used to make a step change in equilibrium position of either bubble or stripe domain walls, and the wall response is measured by using transient photography. During the initial response, the dynamic wall structure closely resembles the initial static structure. The wall accelerates to a relatively high velocity (≈20 m/sec), resulting in a short (≈22 nsec ) section of initial rapid motion. An HBL gradually forms near one of the film surfaces as a result of local dynamic properties, and moves along the wall surface toward the film center. The presence of this structure produces low-frequency, triangular-shaped oscillations in which the experimental wall velocity is nearly constant, v_s≈ 5-8 m/sec. If the HBL reaches the opposite surface, i.e., if the average internal angle reaches an integer multiple of π, the momentum stored in the HBL is lost, and the wall chirality is reversed. This results in abrupt transitions to overdamped motion and changes in wall chirality, which are observed as a function of bias pulse amplitude. The pulse amplitude at which the n^th punch- through occurs just as the wall reaches equilibrium is given within 0.2 0e by H_n = (2v_sH'/γ)^1/2 • (nπ)^1/2 + H_sv), where H' is the effective field gradient from the surrounding domains, and H_sv is a small (less than 0.03 0e), effective drag field. Observations of wall oscillation in the presence of in-plane fields parallel to the wall show that HBL formation is suppressed by fields greater than about 40 0e (≈2πM_s), resulting in the high-frequency, sinusoidal oscillations associated with a simple internal wall structure.

Periodic bubble emission and appearance of an ordered bubble sequence (train) during condensation in a single microchannel

Condensation of steam in a single microchannel, silicon test section was investigated visually at low flow rates. The microchannel was rectangular in cross-section with a depth of 30 pm, a width of 800 mu m and a length of 5.0 mm, covered with a Pyrex glass to allow for visualization of the bubble formation process. By varying the cooling rate during condensation of the saturated water vapor, it was possible to control the shape, size and frequency of the bubbles formed. At low cooling rates using only natural air convection from the ambient environment, the flow pattern in the microchannel consisted of a nearly stable elongated bubble attached upstream (near the inlet) that pinched off into a train of elliptical bubbles downstream of the elongated bubble. It was observed that these elliptical bubbles were emitted periodically from the tip of the elongated bubble at a high frequency, with smaller size than the channel width. The shape of the emitted bubbles underwent modifications shortly after their generation until finally becoming a stable vertical ellipse, maintaining its shape and size as it flowed downstream at a constant speed. These periodically emitted elliptical bubbles thus formed an ordered bubble sequence (train). At higher cooling rates using chilled water in a copper heat sink attached to the test section, the bubble formation frequency increased significantly while the bubble size decreased, all the while forming a perfect bubble train flowing downstream of the microchannel. The emitted bubbles in this case immediately formed into a circular shape without any further modification after their separation from the elongated bubble upstream. The present study suggests that a method for controlling the size and generation frequency of microbubbles could be so developed, which may be of interest for microfluidic applications. The breakup of the elongated bubble is caused by the large Weber number at the tip of the elongated bubble induced by the maximum vapor velocity at the centerline of the microchannel inside the elongated bubble and the smaller surface tension force of water at the tip of the elongated bubble.