A theoretical study of bubble motion in surfactant solutions

We examine the effect of surfactants on a spherical gas bubble rising steadily in an infinite fluid at low and order one Reynolds number with order one and larger Peclet numbers. Our mathematical model is based on the Navier-Stokes equations coupled with a convection-diffusion equation together with appropriate interfacial conditions. The nonlinearity of the equations and boundary conditions, and the coupling between hydrodynamics and surfactant transport make the problem very challenging. When a bubble rises in a fluid containing surface-active agents, surfactant adsorbs onto the bubble surface at the leading edge, convects to the trailing edge by the surface flow and desorbs into the bulk along the interface. This adsorption develops a surface concentration gradient on the interface that makes the surface tension at the back end relatively lower than that at the front end, and thus retards the bubble velocity. Because of surfactant impurities unavoidably present in materials, this retardation can cause a problem in materials processing in space and glass processing when bubbles are created during chemical reactions. Thus the study of how to remobilize (remove the surfactant gradient on the surface) the bubble surface becomes necessary. Many studies have been done on this retarding effects of the surfactant on a moving bubble. However, most were focused on the retarding effect due to a trace amount of surfactant, in which case the bubble velocity monotonically decreases as the bulk concentration increases. The question of how to remobilize the bubble surface remains unanswered. In this work, we will show that the bubble velocity can be controlled by remobilizing the bubble interface using the surfactant concentration. This technique not only can be used to maximize the bubble velocity, but also can be used to maximize mass transfer on purifying materials and extracting materials from mixtures. In the first part of the work, we illustrate numerically that the bubble interface can be remobilized by increasing the bulk concentration of surfactant, for any fixed Peclet number, at low Reynolds number. For any fixed bulk concentration, the bubble velocity decreases with increasing Peclet number. The larger the Peclet number is the larger the required bulk concentration needed to bring the velocity back to the clean surface value. In the second part of the work, we will show that the remobilization still remains effective for order one Reynolds numbers. Moreover, when the rate of convection on the surface is much larger than the rate of diffusion at the back end, a stagnant cap develops near the back stagnation point that makes the bubble surface there act like a solid boundary. Wakes form at higher Reynolds numbers that drastically reduce the terminal velocity, and disappear as the bubble interface remobilizes. Finally, we consider the problem analytically for asymptotically large Peclet numbers. When the Peclet number is very large, a stagnant cap forms at the back end which makes one part of the bubble surface clean of surfactant, and the other part completely immobile. Also boundary layers develop along the bubble surface with different thicknesses on the clean part of the surface and on the stagnant cap. The asymptotic structures are obtained and the governing equations posed and partly addressed numerically and analytically

The Relationship between Leadership Styles and Labour Disputes in British Columbia\u27s Public Schools

For the last decade, adversarial relationships between teachers\u27 associations and district administrators in the British Columbia public school system have been commonplace, frequently resulting in formal grievances and arbitration. Since dealing with these issues imposes enormous costs on both teachers\u27 unions and school boards, this study used hierarchical regression analysis to explain why some schools have fewer grievances filed than other schools in the province. Specifically, this study used data gathered from 160 principals in the British Columbia public school system to examine the extent to which school demographics and principal leadership style helped explain variation in the rate of filed grievances per one hundred teachers. Results suggest that both demographic factors and principal leadership style were key determinants of filed grievances. Specifically, two aspects of principals\u27 leadership styles were important—those that reported engaging in Charisma/Inspirational leadership had more grievances files against them, while those with higher levels of Individualized Consideration had fewer grievances filed against them. Three demographic factors were also found to be important, with the most significant being that K–9 and K–12 schools had approximately 18 more grievances filed per one hundred teachers than elementary schools. In addition, those schools with a considerable number of office referrals (92–225) tended to have more filed teacher grievances, as did schools that had a comparatively large percentage of their student population from lower income families

Thermal Performance Analysis of an Underground Closed Chamber with Human Body Heat Sources under Natural Convection

In this article, a combined experimental and numerical study has been performed to investigate the thermal performance of a mine refuge chamber (MRC) under natural convection. In the current study, a 20-hour heating experiment is carried out in a fifty-person MRC laboratory and the heat lamps are utilized to simulate the human heat loss. A new analytical model is proposed to predict the air temperature and validated against the experimental data. Sensitivity analysis is performed to further investigate the effects of the thermal parameters of the rock. Results indicated that: (1) two different air temperature increase stages, rapid and slow increase stages, are observed in the MRC; (2) A new analytical method for predicting the air temperature in MRC under natural convection is proposed, it shows that the air temperature increasing trend becomes slow with the increase of the thermal conductivity, density and specific heat capacity of the rock; (3) the surface heat transfer coefficient on the vertical walls reaches the largest and it increases linearly with air temperature.Peer reviewe

Can longer gaze duration determine risky investment decisions? An interactive perspective

Can longer gaze duration determine risky investment decisions? Recent studies have tested how gaze influences people’s decisions and the boundary of the gaze effect. The current experiment used adaptive gaze-contingent manipulation by adding a self-determined option to test whether longer gaze duration can determine risky investment decisions. The results showed that both the expected value of each option and the gaze duration influenced people’s decisions. This result was consistent with the attentional diffusion model (aDDM) proposed by Krajbich et al. (2010), which suggests that gaze can influence the choice process by amplify the value of the choice. Therefore, the gaze duration would influence the decision when people do not have clear preference.The result also showed that the similarity between options and the computational difficulty would also influence the gaze effect. This result was inconsistent with prior research that used option similarities to represent difficulty, suggesting that both similarity between options and computational difficulty induce different underlying mechanisms of decision difficulty

Research on Rainfall Intensity Threshold of Occasional Debris Flow Based on Infiltration

The rainfall warning method for debris flows usually uses rainfall intensity and duration to establish an I-D relationship internationally and determine the rainfall warning threshold for debris flows. This method requires extensive rainfall data from debris flow events in the study area to establish the I-D relationship. However, some areas with occasional debris flows lack sufficient debris flow events to establish I-D relationships to determine rainfall warning thresholds. Therefore, this study uses the infiltration effect of water flow on gravel soil and establishes a rainfall intensity threshold judgment formula for debris flow initiation based on the limit equilibrium method. Taking the Taiqing debris flow that occurred in Laoshan, China, on June 13, 2018, as an example, the rainfall intensity and characteristics of the debris flow are analyzed. The maximum rainfall intensity during this rainfall process far exceeds the rainfall intensity threshold determined by the judgment formula. Using the judgment formula, it can be determined that the rainfall process will cause debris flow. The judgment result is consistent with the actual situation (where a debris flow occurred during the rainfall process). To further verify the accuracy of the judgment formula, the rainfall process of Typhoon Lichma on August 11, 2019, in the study area was analyzed. The rainfall process has a long history. Still, the rainfall intensity is much lower than the threshold of rainfall intensity for the initiation of debris flow, so this rainfall will not cause the occurrence of debris flow. The judgment result is consistent with the actual situation (no debris flow occurred during rains). Doi: 10.28991/CEJ-2023-09-09-02 Full Text: PD