The bubble breakup after collision with a vortex ring was validated as source of breakup paramete... more The bubble breakup after collision with a vortex ring was validated as source of breakup parameters for population balance modeling. This system was chosen as a deterministic alternative to the stochastic nature of bubble breakup studies under turbulent flow. The vortex ring was characterized by combining experimental visualization and numerical simulations. Breakup frequency, mean number of daughter bubbles, and its size distribution were obtained by high‐speed camera recording of the collision process. The dependence of breakup parameters on the size of the mother bubble and Weber number was determined.
Shape oscillations of bubbles in surfactant solutions are investigated by means of high-speed ima... more Shape oscillations of bubbles in surfactant solutions are investigated by means of high-speed imaging. Two cases are studied: bubbles attached to a capillary tip, and bubbles freely rising after detachment. The frequency f and the decay time τ of shape oscillations are evaluated, and their dependence on the surfactant concentration and on the bubble size is investigated. If the surfactant is present, τ shortens and a minimum is found for a certain concentration. This observation demonstrates that in the surfactant solutions, the energy dissipation linked to interfacial effects can be much more important than the dissipation due to liquid viscosity. The frequency f increases with increasing concentration of the surfactant first, and then it drops rapidly at concentration, at which τ is minimal. The initial increase of the oscillation frequency suggests that the interfacial elasticity can play an important role in surfactant solutions.
Multiphase contactors have broad application in chemical industry. This type of devices may be us... more Multiphase contactors have broad application in chemical industry. This type of devices may be used as reactors in chemical and biochemical processes, as well as in separations processes, e.g. absorption and distillation and its performance depends usually on the mass transfer rate. The present work focus on one of the less understood problems controlling the bubble size distribution in such devices and, as a result, the contact area between phases and the mass transfer rate: the coalescence. For the study of coalescence, a new coalescence cell was built allowing the control of the production of pairs of bubbles with the following parameters: bubble growth velocity, bubble size at contact moment and angle of the bubble production. This new coalescence cell was used for the study of the effect of the mentioned geometric parameters on coalescence of pairs of bubbles, contacted in liquids known to be either coalescent (pure water) or non-coalescent (surfactant solutions).
Shape oscillations of bubbles in surfactant solutions are investigated by means of high-speed ima... more Shape oscillations of bubbles in surfactant solutions are investigated by means of high-speed imaging. Two cases are studied: bubbles attached to a capillary tip, and bubbles freely rising after detachment. The frequency f and the decay time τ of shape oscillations are evaluated, and their dependence on the surfactant concentration and on the bubble size is investigated. If the surfactant is present, τ shortens and a minimum is found for a certain concentration. This observation demonstrates that in the surfactant solutions, the energy dissipation linked to interfacial effects can be much more important than the dissipation due to liquid viscosity. The frequency f increases with increasing concentration of the surfactant first, and then it drops rapidly at concentration, at which τ is minimal. The initial increase of the oscillation frequency suggests that the interfacial elasticity can play an important role in surfactant solutions.
ABSTRACT The goal of this study is to present new experimental data on the effect of the bubble a... more ABSTRACT The goal of this study is to present new experimental data on the effect of the bubble approach velocity and liquid viscosity on pairwise bubble coalescence. Measurements were performed to investigate the dynamics of bubble coalescence under well-defined laboratory conditions. Air and pure aqueous solutions of alginate (no surfactants) were the phases. The bubbles were formed from two vertical capillaries, under constant flow conditions. The coalescence process was recorded with a fast video and then image analysed, to evaluate the bubble growth, bubble expansion rate, the first bubble touch, bubble contact time T, bubble coalescence efficiency E. Three control parameters were tested. The bubble size D on contact was set by the spacing between the capillaries (D=1 and 1.5 mm). The bubble approach velocity V was controlled by the gas input (V=0.031-39 mm/s). The liquid viscosity μ was adjusted by the alginate content (μ=1.2-10.3 mPa.s). It was found that the bubble contact time T monotonously increases with the liquid viscosity, passing through three stages: initial rise (low μ, coalescence), then jump (intermediate μ, transient region), and finally forming a plateau (high μ, non-coalescence). In the coalescent regime, the bubble contact time monotonously decreases with the bubble approach velocity obeying a power law, which for a typical 1 mm bubble reads: T~V−0.85. The difference in the bubble size did not change the coalescence pattern qualitatively, but only quantitatively in a modest manner.
ABSTRACT The high-speed imaging is used for studying oscillations of air bubble, which are excite... more ABSTRACT The high-speed imaging is used for studying oscillations of air bubble, which are excited by a motion of a tip of a capillary, to which the bubble is attached. The frequency, damping and shape of decaying oscillations are determined for the lowest three eigenmodes. In pure water, the experimental results agree well with an inviscid analysis of Bostwick and Steen (Phys Fluids 21, 2009), if the bubble size is small compared to the detachment size. For larger bubbles, the effect of neck formation on the oscillations is documented experimentally. The addition of a surfactant to the system modifies both the oscillation frequency and damping. The frequency initially increases with the increasing surfactant concentration due to Gibbs elasticity, and starts to decrease only after exceeding some surfactant concentration. The damping strongly increases, passes through a maximum and then slightly decreases. The maximum damping is observed for the concentration, at which the oscillation frequency starts to decrease. Concluding, bubble oscillations are strongly sensitive to presence of a surfactant.
ABSTRACT The shape oscillations of a bubble, which is attached to a tip of a capillary tube, are ... more ABSTRACT The shape oscillations of a bubble, which is attached to a tip of a capillary tube, are studied experimentally. It is observed that the attachment leads to an appearance of an additional low-frequency mode (denoted as mode 1), when compared to standard theories of oscillations of free bubbles or drops (e.g., Miller & Scriven, 1968). It is observed that the frequency of mode 1 scales with the bubble size as f ~ D-2. The oscillation dynamics of a bubble is strongly influenced if some surface active agent is present in the liquid. Due to interfacial elasticity, the surfactants presence in low concentration increases the oscillation frequency. The decay of oscillations is also faster, probably due to an increase of energy dissipation by Marangoni stresses.
An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted t... more An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted to simultaneously: (i) follow mass transfer to/from a single bubble a s it i nevitably gets contaminated; (ii) follow its s hape; and (iii) periodically measure its terminal velocity. This apparatus allows bubbles to be monitored for much longer periods of time than does the monitoring of rising bubbles. Thus, the effect of trace contaminants on bubbles of low solubility gases, like air, may be studied. Experiments were done with air bubbles 1 to 5 mm initial equivalent diameter in a water stream. Contamination results in a simultaneous increase in d rag coefficient, an increase in bubble sphericity and a decrease in gas-liquid mass transfer r ate. Initial values of gas-liquid mass transfer coefficients are consistent with theoretical prediction for a mobile surface, while final values are close to theoretical predictions for rigid bubbles. Normalized drag coefficient and mass transfer co...
Different modifications of the Rushton turbine were studied in a dual-impeller agitated tank (T= ... more Different modifications of the Rushton turbine were studied in a dual-impeller agitated tank (T= 0.4 m), to find the effect of blade form on power draw, turbulent dispersion, gas handling capacity, mixing, gas holdup, and mass-transfer rate performance under turbulent ...
... velocities. These distributions were sensitive to the additive content. Jamialahmadi and Mull... more ... velocities. These distributions were sensitive to the additive content. Jamialahmadi and Muller-Steinhagen(12) investigated the effect of several surfactants on the bubble size, bubble speed, and holdup in two bubble columns. The ...
ABSTRACT Experiments were carried out to investigate the effect a surface active agent on homogen... more ABSTRACT Experiments were carried out to investigate the effect a surface active agent on homogeneous–heterogeneous flow regime transition in a laboratory scale bubble column. Air and water with various amount of CaCl2 were the phases. The (voidage e) - (gas flow rate q) dependence was measured. The critical point where the homogeneous regime loses stability and the transition begins was evaluated by several methods. These methods are based on the slip speed concept and the drift flux model. The critical values of voidage and gas flow rate were taken as the quantitative measures of the homogeneous regime stability. They were plotted against the surfactant concentration. It was found that the surfactant has a dual effect on both the voidage and the regime transition: low concentration stabilizes and larger concentration destabilizes the homogeneous bubble bed. At present, we do not have an explanation to these observations. Possible physical mechanisms of the surfactant effect are expected to be revealed by further experiments, which are currently under way.
An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted t... more An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted to simultaneously (i) follow mass transfer to/from a single bubble as it inevitably gets contaminated; (ii) follow its shape; and (iii) periodically measure its terminal velocity. This apparatus allows bubbles to be monitored for much longer periods of time than does the monitoring of rising bubbles. Thus, the effect of trace contaminants on bubbles of low solubility gases, like air, may be studied.
In this work, the e ects of surface-active contaminants on mass transfer coe cients kLa and kL we... more In this work, the e ects of surface-active contaminants on mass transfer coe cients kLa and kL were studied in two di erent bubble contactors. The oxygen transfer coe cient, kL, was obtained from the volumetric oxygen transfer coe cient, kLa, since the speciÿc interfacial area, a, could be determined from the fractional gas holdup, , and the average bubble diameter, d32. Water at di erent heights and antifoam solutions of 0.5 -100 ppm were used as working media, under varying gas sparging conditions, in small-scale bubble column and rectangular airlift contactors of 6.7 and 0:85 × 10 −3 m 3 capacity, respectively. Both the antifoam concentration and the bubble residence time were shown to control kLa and kL values over a span of almost 400%. A theoretical interpretation is proposed based on modelling the kinetics of single bubble contamination, followed by sudden surface transition from mobile to rigid condition, in accordance with the stagnant cap model. Model results match experimental kL data within ±30%. ?
Experimental gas-liquid mass transfer data from a system where single bubbles are kept stationary... more Experimental gas-liquid mass transfer data from a system where single bubbles are kept stationary by a low turbulence downward liquid flow are compared with predictions from theoretical models which take turbulence into account. The data clearly show that, for the turbulence intensities at play, turbulence does not affect mass transfer. Higbie's equation with contact time t e = d/u may be used for the calculation of the gas-liquid mass transfer coefficient of clean bubbles in systems with levels of turbulent kinetic energy dissipation of, at least, up to ∼0.04 m 2 s −3 .
ABSTRACT The dissolution of single bubbles of gases of low solubility kept stationary in a downwa... more ABSTRACT The dissolution of single bubbles of gases of low solubility kept stationary in a downward stream of water was studied. In “clean” water, two regimes are identified. Initially, the process is fast, consistent with the theory for circulating bubbles. Then, the mass-transfer rate falls sharply to that predicted for solid spheres. Transition times and transition diameters vary widely with experimental conditions. In untreated water, only the second regime is found. Results are explained in terms of the kinetics of trace surfactant accumulation at the interface. An adaptation of the stagnant-cap model is proposed, with surface immobilization expressed in terms of interface dynamics. The model yields good prediction of the transition point for a very large set of conditions, including different gases at various concentrations in the liquid stream and a wide range of initial bubble diameters.
The measurement accuracy of a mono-fiber optical probe is studied experimentally using isolated b... more The measurement accuracy of a mono-fiber optical probe is studied experimentally using isolated bubbles rising freely in a still liquid. The dwell time of the probe tip within the gas phase, which is obtained from both the optical probe signal and high-speed visualization, is compared with the value expected for a non-perturbed bubble. The difference originates mainly from the intrusive nature of the optical probe, which modifies the bubble behavior when it comes into contact with the probe tip. This interaction increases the dwell time if the bubble is pierced by the probe near its pole, and shortens it for piercing near the equator. The mean dwell time, obtained by averaging for various piercing locations, is shortened and the local void fraction indicated by the probe is thus underestimated. It is shown that the void fraction error can be correlated with a modified Weber number, and this correlation is helpful for sensor selection and for uncertainty estimate. In addition, the distribution of gas dwell time usually differs from the response expected for an ideal probe. This deviation results from the dependence of the dwell time error on the piercing location. The dwell time distribution can be used to infer the dependence of the dwell time on the piercing location. Finally, the deformation of long fibers during the bubble-probe interaction significantly increases the measurement error. Observed results are consistent with data of Andreotti (2009), which were measured in an airlift flow, suggesting that present results are applicable also to the case of moving liquid. Conclusions of this study could be applied also to conductivity probes or more generally to the interaction of a bubble with any kind of thin, intrusive sensor or fiber.
The bubble breakup after collision with a vortex ring was validated as source of breakup paramete... more The bubble breakup after collision with a vortex ring was validated as source of breakup parameters for population balance modeling. This system was chosen as a deterministic alternative to the stochastic nature of bubble breakup studies under turbulent flow. The vortex ring was characterized by combining experimental visualization and numerical simulations. Breakup frequency, mean number of daughter bubbles, and its size distribution were obtained by high‐speed camera recording of the collision process. The dependence of breakup parameters on the size of the mother bubble and Weber number was determined.
Shape oscillations of bubbles in surfactant solutions are investigated by means of high-speed ima... more Shape oscillations of bubbles in surfactant solutions are investigated by means of high-speed imaging. Two cases are studied: bubbles attached to a capillary tip, and bubbles freely rising after detachment. The frequency f and the decay time τ of shape oscillations are evaluated, and their dependence on the surfactant concentration and on the bubble size is investigated. If the surfactant is present, τ shortens and a minimum is found for a certain concentration. This observation demonstrates that in the surfactant solutions, the energy dissipation linked to interfacial effects can be much more important than the dissipation due to liquid viscosity. The frequency f increases with increasing concentration of the surfactant first, and then it drops rapidly at concentration, at which τ is minimal. The initial increase of the oscillation frequency suggests that the interfacial elasticity can play an important role in surfactant solutions.
Multiphase contactors have broad application in chemical industry. This type of devices may be us... more Multiphase contactors have broad application in chemical industry. This type of devices may be used as reactors in chemical and biochemical processes, as well as in separations processes, e.g. absorption and distillation and its performance depends usually on the mass transfer rate. The present work focus on one of the less understood problems controlling the bubble size distribution in such devices and, as a result, the contact area between phases and the mass transfer rate: the coalescence. For the study of coalescence, a new coalescence cell was built allowing the control of the production of pairs of bubbles with the following parameters: bubble growth velocity, bubble size at contact moment and angle of the bubble production. This new coalescence cell was used for the study of the effect of the mentioned geometric parameters on coalescence of pairs of bubbles, contacted in liquids known to be either coalescent (pure water) or non-coalescent (surfactant solutions).
Shape oscillations of bubbles in surfactant solutions are investigated by means of high-speed ima... more Shape oscillations of bubbles in surfactant solutions are investigated by means of high-speed imaging. Two cases are studied: bubbles attached to a capillary tip, and bubbles freely rising after detachment. The frequency f and the decay time τ of shape oscillations are evaluated, and their dependence on the surfactant concentration and on the bubble size is investigated. If the surfactant is present, τ shortens and a minimum is found for a certain concentration. This observation demonstrates that in the surfactant solutions, the energy dissipation linked to interfacial effects can be much more important than the dissipation due to liquid viscosity. The frequency f increases with increasing concentration of the surfactant first, and then it drops rapidly at concentration, at which τ is minimal. The initial increase of the oscillation frequency suggests that the interfacial elasticity can play an important role in surfactant solutions.
ABSTRACT The goal of this study is to present new experimental data on the effect of the bubble a... more ABSTRACT The goal of this study is to present new experimental data on the effect of the bubble approach velocity and liquid viscosity on pairwise bubble coalescence. Measurements were performed to investigate the dynamics of bubble coalescence under well-defined laboratory conditions. Air and pure aqueous solutions of alginate (no surfactants) were the phases. The bubbles were formed from two vertical capillaries, under constant flow conditions. The coalescence process was recorded with a fast video and then image analysed, to evaluate the bubble growth, bubble expansion rate, the first bubble touch, bubble contact time T, bubble coalescence efficiency E. Three control parameters were tested. The bubble size D on contact was set by the spacing between the capillaries (D=1 and 1.5 mm). The bubble approach velocity V was controlled by the gas input (V=0.031-39 mm/s). The liquid viscosity μ was adjusted by the alginate content (μ=1.2-10.3 mPa.s). It was found that the bubble contact time T monotonously increases with the liquid viscosity, passing through three stages: initial rise (low μ, coalescence), then jump (intermediate μ, transient region), and finally forming a plateau (high μ, non-coalescence). In the coalescent regime, the bubble contact time monotonously decreases with the bubble approach velocity obeying a power law, which for a typical 1 mm bubble reads: T~V−0.85. The difference in the bubble size did not change the coalescence pattern qualitatively, but only quantitatively in a modest manner.
ABSTRACT The high-speed imaging is used for studying oscillations of air bubble, which are excite... more ABSTRACT The high-speed imaging is used for studying oscillations of air bubble, which are excited by a motion of a tip of a capillary, to which the bubble is attached. The frequency, damping and shape of decaying oscillations are determined for the lowest three eigenmodes. In pure water, the experimental results agree well with an inviscid analysis of Bostwick and Steen (Phys Fluids 21, 2009), if the bubble size is small compared to the detachment size. For larger bubbles, the effect of neck formation on the oscillations is documented experimentally. The addition of a surfactant to the system modifies both the oscillation frequency and damping. The frequency initially increases with the increasing surfactant concentration due to Gibbs elasticity, and starts to decrease only after exceeding some surfactant concentration. The damping strongly increases, passes through a maximum and then slightly decreases. The maximum damping is observed for the concentration, at which the oscillation frequency starts to decrease. Concluding, bubble oscillations are strongly sensitive to presence of a surfactant.
ABSTRACT The shape oscillations of a bubble, which is attached to a tip of a capillary tube, are ... more ABSTRACT The shape oscillations of a bubble, which is attached to a tip of a capillary tube, are studied experimentally. It is observed that the attachment leads to an appearance of an additional low-frequency mode (denoted as mode 1), when compared to standard theories of oscillations of free bubbles or drops (e.g., Miller & Scriven, 1968). It is observed that the frequency of mode 1 scales with the bubble size as f ~ D-2. The oscillation dynamics of a bubble is strongly influenced if some surface active agent is present in the liquid. Due to interfacial elasticity, the surfactants presence in low concentration increases the oscillation frequency. The decay of oscillations is also faster, probably due to an increase of energy dissipation by Marangoni stresses.
An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted t... more An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted to simultaneously: (i) follow mass transfer to/from a single bubble a s it i nevitably gets contaminated; (ii) follow its s hape; and (iii) periodically measure its terminal velocity. This apparatus allows bubbles to be monitored for much longer periods of time than does the monitoring of rising bubbles. Thus, the effect of trace contaminants on bubbles of low solubility gases, like air, may be studied. Experiments were done with air bubbles 1 to 5 mm initial equivalent diameter in a water stream. Contamination results in a simultaneous increase in d rag coefficient, an increase in bubble sphericity and a decrease in gas-liquid mass transfer r ate. Initial values of gas-liquid mass transfer coefficients are consistent with theoretical prediction for a mobile surface, while final values are close to theoretical predictions for rigid bubbles. Normalized drag coefficient and mass transfer co...
Different modifications of the Rushton turbine were studied in a dual-impeller agitated tank (T= ... more Different modifications of the Rushton turbine were studied in a dual-impeller agitated tank (T= 0.4 m), to find the effect of blade form on power draw, turbulent dispersion, gas handling capacity, mixing, gas holdup, and mass-transfer rate performance under turbulent ...
... velocities. These distributions were sensitive to the additive content. Jamialahmadi and Mull... more ... velocities. These distributions were sensitive to the additive content. Jamialahmadi and Muller-Steinhagen(12) investigated the effect of several surfactants on the bubble size, bubble speed, and holdup in two bubble columns. The ...
ABSTRACT Experiments were carried out to investigate the effect a surface active agent on homogen... more ABSTRACT Experiments were carried out to investigate the effect a surface active agent on homogeneous–heterogeneous flow regime transition in a laboratory scale bubble column. Air and water with various amount of CaCl2 were the phases. The (voidage e) - (gas flow rate q) dependence was measured. The critical point where the homogeneous regime loses stability and the transition begins was evaluated by several methods. These methods are based on the slip speed concept and the drift flux model. The critical values of voidage and gas flow rate were taken as the quantitative measures of the homogeneous regime stability. They were plotted against the surfactant concentration. It was found that the surfactant has a dual effect on both the voidage and the regime transition: low concentration stabilizes and larger concentration destabilizes the homogeneous bubble bed. At present, we do not have an explanation to these observations. Possible physical mechanisms of the surfactant effect are expected to be revealed by further experiments, which are currently under way.
An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted t... more An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted to simultaneously (i) follow mass transfer to/from a single bubble as it inevitably gets contaminated; (ii) follow its shape; and (iii) periodically measure its terminal velocity. This apparatus allows bubbles to be monitored for much longer periods of time than does the monitoring of rising bubbles. Thus, the effect of trace contaminants on bubbles of low solubility gases, like air, may be studied.
In this work, the e ects of surface-active contaminants on mass transfer coe cients kLa and kL we... more In this work, the e ects of surface-active contaminants on mass transfer coe cients kLa and kL were studied in two di erent bubble contactors. The oxygen transfer coe cient, kL, was obtained from the volumetric oxygen transfer coe cient, kLa, since the speciÿc interfacial area, a, could be determined from the fractional gas holdup, , and the average bubble diameter, d32. Water at di erent heights and antifoam solutions of 0.5 -100 ppm were used as working media, under varying gas sparging conditions, in small-scale bubble column and rectangular airlift contactors of 6.7 and 0:85 × 10 −3 m 3 capacity, respectively. Both the antifoam concentration and the bubble residence time were shown to control kLa and kL values over a span of almost 400%. A theoretical interpretation is proposed based on modelling the kinetics of single bubble contamination, followed by sudden surface transition from mobile to rigid condition, in accordance with the stagnant cap model. Model results match experimental kL data within ±30%. ?
Experimental gas-liquid mass transfer data from a system where single bubbles are kept stationary... more Experimental gas-liquid mass transfer data from a system where single bubbles are kept stationary by a low turbulence downward liquid flow are compared with predictions from theoretical models which take turbulence into account. The data clearly show that, for the turbulence intensities at play, turbulence does not affect mass transfer. Higbie's equation with contact time t e = d/u may be used for the calculation of the gas-liquid mass transfer coefficient of clean bubbles in systems with levels of turbulent kinetic energy dissipation of, at least, up to ∼0.04 m 2 s −3 .
ABSTRACT The dissolution of single bubbles of gases of low solubility kept stationary in a downwa... more ABSTRACT The dissolution of single bubbles of gases of low solubility kept stationary in a downward stream of water was studied. In “clean” water, two regimes are identified. Initially, the process is fast, consistent with the theory for circulating bubbles. Then, the mass-transfer rate falls sharply to that predicted for solid spheres. Transition times and transition diameters vary widely with experimental conditions. In untreated water, only the second regime is found. Results are explained in terms of the kinetics of trace surfactant accumulation at the interface. An adaptation of the stagnant-cap model is proposed, with surface immobilization expressed in terms of interface dynamics. The model yields good prediction of the transition point for a very large set of conditions, including different gases at various concentrations in the liquid stream and a wide range of initial bubble diameters.
The measurement accuracy of a mono-fiber optical probe is studied experimentally using isolated b... more The measurement accuracy of a mono-fiber optical probe is studied experimentally using isolated bubbles rising freely in a still liquid. The dwell time of the probe tip within the gas phase, which is obtained from both the optical probe signal and high-speed visualization, is compared with the value expected for a non-perturbed bubble. The difference originates mainly from the intrusive nature of the optical probe, which modifies the bubble behavior when it comes into contact with the probe tip. This interaction increases the dwell time if the bubble is pierced by the probe near its pole, and shortens it for piercing near the equator. The mean dwell time, obtained by averaging for various piercing locations, is shortened and the local void fraction indicated by the probe is thus underestimated. It is shown that the void fraction error can be correlated with a modified Weber number, and this correlation is helpful for sensor selection and for uncertainty estimate. In addition, the distribution of gas dwell time usually differs from the response expected for an ideal probe. This deviation results from the dependence of the dwell time error on the piercing location. The dwell time distribution can be used to infer the dependence of the dwell time on the piercing location. Finally, the deformation of long fibers during the bubble-probe interaction significantly increases the measurement error. Observed results are consistent with data of Andreotti (2009), which were measured in an airlift flow, suggesting that present results are applicable also to the case of moving liquid. Conclusions of this study could be applied also to conductivity probes or more generally to the interaction of a bubble with any kind of thin, intrusive sensor or fiber.
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Papers by Sandra Orvalho