Mathematical Model of Gas Bubble Evolution in a Straight Tube

1999 ◽  
Vol 121 (5) ◽  
pp. 505-513 ◽  
Author(s):  
D. Halpern ◽  
Y. Jiang ◽  
J. F. Himm
Keyword(s):  
Decompression Sickness ◽  
Ambient Pressure ◽  
Fluid Motion ◽  
Gas Bubbles ◽  
Coupled System ◽  
Bubble Surface ◽  
Inert Gas ◽  
Straight Tube ◽  
Gas Bubble ◽  
Bubble Evolution

Deep sea divers suffer from decompression sickness (DCS) when their rate of ascent to the surface is too rapid. When the ambient pressure drops, inert gas bubbles may form in blood vessels and tissues. The evolution of a gas bubble in a rigid tube filled with slowly moving fluid, intended to simulate a bubble in a blood vessel, is studied by solving a coupled system of fluid-flow and gas transport equations. The governing equations for the fluid motion are solved using two techniques: an analytical method appropriate for small nondeformable spherical bubbles, and the boundary element method for deformable bubbles of arbitrary size, given an applied steady flow rate. A steady convection-diffusion equation is then solved numerically to determine the concentration of gas. The bubble volume, or equivalently the gas mass inside the bubble for a constant bubble pressure, is adjusted over time according to the mass flux at the bubble surface. Using a quasi-steady approximation, the evolution of a gas bubble in a tube is obtained. Results show that convection increases the gas pressure gradient at the bubble surface, hence increasing the rate of bubble evolution. Comparing with the result for a single gas bubble in an infinite tissue, the rate of evolution in a tube is approximately twice as fast. Surface tension is also shown to have a significant effect. These findings may have important implications for our understanding of the mechanisms of inert gas bubbles in the circulation underlying decompression sickness.

Behavior of Inert Gas Bubbles in Forced Convective Liquid Metal Circuits

1976 ◽  
Vol 98 (1) ◽  
pp. 5-11 ◽  
Author(s):  
W. J. Minkowycz ◽  
D. M. France ◽  
R. M. Singer
Keyword(s):  
Liquid Metal ◽  
Bubble Dynamics ◽  
Bubble Radius ◽  
Gas Bubbles ◽  
Inert Gas ◽  
Liquid Sodium ◽  
Gas Bubble ◽  
Flowing Liquid ◽  
Argon Gas ◽  
The Core

Conservation equations are derived for the motion of a small inert gas bubble in a large flowing liquid-gas solution subjected to large thermal gradients. Terms which are of the second order of magnitude under less severe and steady-state conditions are retained, thus resulting in an expanded form of the Rayleigh equation. The bubble dynamics is a function of opposing mechanisms tending to increase or decrease bubble volume while being transported with the solution. Diffusion of inert gas between the bubble and the solution is one of the most important of these mechanisms included in the analysis. The analytical model is applied to an argon gas bubble flowing in a weak solution of argon gas in liquid sodium. Calculations are performed for these fluids under conditions typical of normal and abnormal operation of a liquid metal fast breeder reactor (LMFBR) core and the resulting bubble radius, internal gas pressure, and mass of inert gas are presented in each case. An important result obtained indicates that inert gas bubbles reaching the core inlet of an LMFBR will always grow as they traverse the core under normal and extreme abnormal conditions and that the rate of growth is quite small in all cases.

scholarly journals Gas bubble evolution on microstructured silicon substrates

2018 ◽  
Vol 11 (12) ◽  
pp. 3452-3462 ◽  
Author(s):  
Peter van der Linde ◽  
Pablo Peñas-López ◽  
Álvaro Moreno Soto ◽  
Devaraj van der Meer ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Gas Bubbles ◽  
Chemical Processes ◽  
Silicon Substrates ◽  
Gas Bubble ◽  
Bubble Evolution

The formation, growth and detachment of gas bubbles on electrodes and gas-producing chemical processes can be controlled with novel microfabricated structures.

Fission Gas Bubbles in Fractured UO2

1968 ◽  
Vol 26 ◽  
pp. 286-287
Author(s):  
O. M. Katz
Keyword(s):  
Electron Microscopy ◽  
Thermal Gradient ◽  
Gas Bubbles ◽  
Inert Gas ◽  
Thermal Gradients ◽  
Fission Gas ◽  
Beam Heating ◽  
Limited Application ◽  
Bubble Characteristics ◽  
Electron Beam Heating

The swelling of irradiated UO2 has been attributed to the migration and agglomeration of fission gas bubbles in a thermal gradient. High temperatures and thermal gradients obtained by electron beam heating simulate reactor behavior and lead to the postulation of swelling mechanisms. Although electron microscopy studies have been reported on UO2, two experimental procedures have limited application of the results: irradiation was achieved either with a stream of inert gas ions without fission or at depletions less than 2 x 1020 fissions/cm3 (∼3/4 at % burnup). This study was not limited either of these conditions and reports on the bubble characteristics observed by transmission and fractographic electron microscopy in high density (96% theoretical) UO2 irradiated between 3.5 and 31.3 x 1020 fissions/cm3 at temperatures below l600°F. Preliminary results from replicas of the as-polished and etched surfaces of these samples were published.

EXTRACTION OF MINUTE GAS BUBBLES FROM LIQUIDS FLOWING IN A SIMULATED CARDIOPULMONARY BYPASS SYSTEM BY A VENTURI-ASPIRATOR UNIT

2002 ◽  
Vol 02 (03n04) ◽  
pp. 297-312
Author(s):  
WEN-JEI YANG ◽  
AMR EID ◽  
R. ECHIGO
Keyword(s):  
Cardiopulmonary Bypass ◽  
Flow Rate ◽  
Whole Blood ◽  
Pressure Difference ◽  
Gas Bubbles ◽  
Blood Oxygenation ◽  
Straight Tube ◽  
Suction Pressure ◽  
Total Flow ◽  
Total Flow Rate

An experimental study is performed to extract minute gas bubbles from liquids flowing in a simulated cardiopulmonary bypass system using a Venturi-aspirator unit. In other words, oxygen bubbles in oxygenated blood are simulated by air bubbles in water with AP30 (about same viscosity as whole blood). This study is intended to determine the feasibility of using a Venturi aspirator unit to extract minute gas bubbles from a simulated cardiopulmonary bypass system. Testing of the Venturi-type bubble extraction is carried out using three different test sections. Two Venturis are used, and a straight tube configuration is used as a control. The two Venturis are similar, with the exception that one has a longer inlet cone which causes the entering liquid to accelerate at a slower rate. Results are obtained for effectiveness of the aspirator unit as functions of total flow rate, extraction suction, suction pressure difference, and hydraulic head. It is concluded from the study that:(i) The effectiveness of the Venturis is typically between 90 and 100 percent. It increases with an increase in suction or suction pressure difference but decreases with an increase in total flow rate.(ii) The Venturi is most suitable for extraction of minute gas bubbles, especially for use with AP30 (whole blood), which yields substantially higher effectiveness than water.(iii) It is anticipated that a Venturi-aspirator unit can be superior to other bubble separation device as the cardiopulmonary bypass system for applications in extra corporeal blood oxygenation.

Gas bubble induced scalings in geothermal systems

2021 ◽  
Author(s):  
Lilly Zacherl ◽  
Thomas Baumann
Keyword(s):  
Ph Value ◽  
Saturation Index ◽  
Gas Bubbles ◽  
Gas Bubble ◽  
Geothermal Systems ◽  
Injection Wells ◽  
Term Operation ◽  
Maintenance Schedule ◽  
Local Experience ◽  
Maintenance Schedules

<p>Scalings in geothermal systems are affecting the efficiency and safety of geothermal systems. An operate-until-fail maintenance scheme might seem appropriate for subsurface installations where the replacement of pumps and production pipes is costly and regular maintenance comprises a complete overhaul of the installations. The situation is different for surface level installations and injection wells. Here, monitoring of the thickness of precipitates is the key to optimized maintenance schedules and long-term operation.</p><p>A questionnaire revealed that operators of geothermal facilities start with a standardized maintenance schedule which is adjusted based on local experience. Sensor networks, numerical modelling and predictive maintenance are not yet applied. In this project we are aiming to close this gap with the development of a non-invasive sensor system coupled to innovative data acquisition and evaluation and an expert system to quantitatively predict the development of precipitations in geothermal systems and open cooling towers.</p><p>Previous investigations of scalings in the lower part of production pipes of a geothermal facility suggest that the disruption of the carbonate equilibrium is triggered by the formation of gas bubbles in the pump and subsequent stripping of CO<sub>2</sub>. Although small in it's overall effect on pH-value and saturation index, significant amounts of precipitates are forming at high volumetric flow rates. To assess the kinetics of gas bubble induced precipitations laboratory experiments were run. The experiment addresses precipitations at surfaces and at the gas bubbles themselves.</p>

scholarly journals Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor

2018 ◽  
Vol 45 (2) ◽  
pp. 253-278 ◽  
Author(s):  
Meraj Alam ◽  
Bibaswan Dey ◽  
Sekhar Raja
Keyword(s):  
Solid Tumor ◽  
Solid Phase ◽  
Fluid Motion ◽  
Extracellular Fluid ◽  
Mixture Theory ◽  
Coupled System ◽  
Weak Sense ◽  
Governing Equations ◽  
One Dimensional ◽  
2D And 3D

In this article, we present a biphasic mixture theory based mathematical model for the hydrodynamics of interstitial fluid motion and mechanical behavior of the solid phase inside a solid tumor. The tumor tissue considered here is an isolated deformable biological medium. The solid phase of the tumor is constituted by vasculature, tumor cells, and extracellular matrix, which are wet by a physiological extracellular fluid. Since the tumor is deformable in nature, the mass and momentum equations for both the phases are presented. The momentum equations are coupled due to the interaction (or drag) force term. These governing equations reduce to a one-way coupled system under the assumption of infinitesimal deformation of the solid phase. The well-posedness of this model is shown in the weak sense by using the inf-sup (Babuska?Brezzi) condition and Lax?Milgram theorem in 2D and 3D. Further, we discuss a one-dimensional spherical symmetry model and present some results on the stress fields and energy of the system based on ??2 and Sobolev norms. We discuss the so-called phenomena of ?necrosis? inside a solid tumor using the energy of the system.

scholarly journals The Influence of Impeller Geometry on the Gas Bubbles Dispersion in Uro-200 Reactor – RTD Curves / Wpływ Rodzaju Wirnika Na Dyspersję Pęcherzyków Gazowych W Reaktorze URO-200 – Krzywe Mieszania

2015 ◽  
Vol 60 (4) ◽  
pp. 2887-2894 ◽  
Author(s):  
M. Saternus ◽  
T. Merder ◽  
J. Pieprzyca
Keyword(s):  
Flow Rate ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Gas Bubbles ◽  
Refining Process ◽  
Inert Gas ◽  
Impeller Speed ◽  
Batch Reactors ◽  
Liquid Aluminium ◽  
Impeller Geometry

URO-200 reactor belongs to batch reactors used in refining process of aluminium and its alloys in polish foundries. The appropriate level of hydrogen removal from liquid aluminium can be obtained when the mixing of inert gas bubbles with liquid metal is uniform. Thus, the important role is played by the following parameters: flow rate of refining gas, geometry of the impeller, rotary impeller speed. The article presents the results of research conducted on physical model of URO-200 reactor. The NaCl tracer was introduced to water (modelling liquid aluminium) and then the conductivity was measured. Basing on the obtained results the Residence Time Distribution (RTD) curves were determined. The measurements were carried out for two different rotary impellers, flow rate equaled 5, 10, 15 and 20 dm3/min and rotary impeller speed from 250 to 400 rpm every 50 rpm.

Nuclei and Cavitation

1970 ◽  
Vol 92 (4) ◽  
pp. 681-688 ◽  
Author(s):  
J. William Holl
Keyword(s):  
Bubble Growth ◽  
Scale Effects ◽  
Gas Bubbles ◽  
Gas Content ◽  
Gas Bubble ◽  
Cavitation Nuclei ◽  
The Stability

This paper is a review of existing knowledge on cavitation nuclei. The lack of significant tensions in ordinary liquids is due to so-called weak spots or cavitation nuclei. The various forms which have been proposed for nuclei are gas bubbles, gas in a crevice, gas bubble with organic skin, and a hydrophobic solid. The stability argument leading to the postulation of the Harvey model is reviewed. Aspects of bubble growth are considered and it is shown that bubbles having different initial sizes will undergo vaporous cavitation at different liquid tensions. The three modes of growth, namely vaporous, pseudo, and gaseous are presented and implications concerning the interpretation of data are considered. The question of the source of nuclei and implications concerning scale effects are made. The measurement of nuclei is considered together with experiments on the effect of gas content on incipient cavitation.

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