Motion of a drop in a vertical temperature gradient at small Marangoni number – the critical role of inertia

2001 ◽  
Vol 448 ◽  
pp. 197-211 ◽  
Author(s):  
LU ZHANG ◽  
R. SHANKAR SUBRAMANIAN ◽  
R. BALASUBRAMANIAM
Keyword(s):  
Temperature Field ◽  
Temperature Gradient ◽  
Small Parameter ◽  
Asymptotic Expansions ◽  
Peclet Number ◽  
Marangoni Number ◽  
Matched Asymptotic Expansions ◽  
Vertical Temperature Gradient ◽  
Vertical Temperature ◽  
Singular Behaviour

When a drop moves in a uniform vertical temperature gradient under the combined action of gravity and thermocapillarity at small values of the thermal Péclet number, it is shown that inclusion of inertia is crucial in the development of an asymptotic solution for the temperature field. If inertia is completely ignored, use of the method of matched asymptotic expansions, employing the Péclet number (known as the Marangoni number) as the small parameter, leads to singular behaviour of the outer temperature field. The origin of this behaviour can be traced to the interaction of the slowly decaying Stokeslet, arising from the gravitational contribution to the motion of the drop, with the temperature gradient field far from the drop. When inertia is included, and the method of matched asymptotic expansions is used, employing the Reynolds number as a small parameter, the singular behaviour of the temperature field is eliminated. A result is obtained for the migration velocity of the drop that is correct to O(Re2 log Re).

scholarly journals Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

2017 ◽  
Vol 835 ◽  
pp. 170-216 ◽  
Author(s):  
Sayan Das ◽  
Shubhadeep Mandal ◽  
Suman Chakraborty
Keyword(s):  
Temperature Field ◽  
Temperature Gradient ◽  
Poiseuille Flow ◽  
Peclet Number ◽  
Marangoni Number ◽  
Stream Velocity ◽  
Small Surface ◽  
Péclet Number ◽  
Surfactant Transport ◽  
The Cross

The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactant-laden droplet. The droplet speed and direction of motion are strongly influenced by the interfacial transport of surfactant, which is governed by surface Péclet number. The present study is focused on the following two limiting situations of surfactant transport: (i) surface-diffusion-dominated surfactant transport considering small surface Péclet number, and (ii) surface-convection-dominated surfactant transport considering high surface Péclet number. Thermocapillary-induced Marangoni stress, the strength of which relative to viscous stress is represented by the thermal Marangoni number, has a strong influence on the distribution of surfactant on the droplet surface. The present study shows that the motion of a surfactant-laden droplet in the combined presence of temperature and imposed Poiseuille flow cannot be obtained by a simple superposition of the following two independent results: migration of a surfactant-free droplet in a temperature gradient, and the motion of a surfactant-laden droplet in a Poiseuille flow. The temperature field not only affects the axial velocity of the droplet, but also has a non-trivial effect on the cross-stream velocity of the droplet in spite of the fact that the temperature gradient is aligned with the Poiseuille flow direction. When the imposed temperature increases in the direction of the Poiseuille flow, the droplet migrates towards the flow centreline. The magnitude of both axial and cross-stream velocity components increases with the thermal Marangoni number. However, when the imposed temperature decreases in the direction of the Poiseuille flow, the magnitude of both axial and cross-stream velocity components may increase or decrease with the thermal Marangoni number. Most interestingly, the droplet moves either towards the flow centreline or away from it. The present study shows a critical value of the thermal Marangoni number beyond which the droplet moves away from the flow centreline which is in sharp contrast to the motion of a surfactant-laden droplet in isothermal flow, for which the droplet always moves towards the flow centreline. Interestingly, we show that the above picture may become significantly altered in the case where the droplet is not a neutrally buoyant one. When the droplet is less dense than the suspending medium, the presence of gravity in the direction of the Poiseuille flow can lead to cross-stream motion of the droplet away from the flow centreline even when the temperature increases in the direction of the Poiseuille flow. These results may bear far-reaching consequences in various emulsification techniques in microfluidic devices, as well as in biomolecule synthesis, vesicle dynamics, single-cell analysis and nanoparticle synthesis.

scholarly journals Analysis of Sunshine Temperature Field of Steel Box Girder Based on Monitoring Data

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hailin Lu ◽  
Jing Hao ◽  
Jiwei Zhong ◽  
Yafei Wang ◽  
Hongyin Yang
Keyword(s):  
Temperature Field ◽  
Temperature Distribution ◽  
Temperature Gradient ◽  
Maximum Temperature ◽  
Temperature Model ◽  
Bridge Site ◽  
Vertical Temperature Gradient ◽  
Vertical Temperature ◽  
Box Girder ◽  
Steel Box Girder

In this study, based on the recorded meteorological data of the bridge site, a spatial-temporal temperature model of a 3-span steel box girder is developed through applying the thermal analysis software TAITHERM. Firstly, the rationality and dependability of the proposed spatial-temporal temperature model are adequately verified by means of implementing the comparison with the measurement data. Then the temperature distribution of the steel box girder is analyzed and discussed in detail. The analytical results show that the time of the bottom of pavement reaching the daily maximum temperature lags behind the top of pavement by 2 or 3 hours due to the thermal insulation effect of pavement, and the maximum vertical temperature gradient of the structure exceeds the existing standards. Moreover, with the help of the analytical model, a parametric study of comprehensively meteorological factors is also performed. The results of the sensitivity analysis indicate that solar radiation is the most significant factor affecting the maximum vertical temperature gradient of the steel box girder, followed by air temperature and wind speed. After that, with the representative values of the extreme meteorological parameters during 100-year return period in Wuhan City in China being considered as the thermal boundary conditions, the temperature distribution of the steel box girder is further studied for investigation purpose. The results demonstrate that the heat conduction process of the steel box girder has distinct “box-room effect,” and it is of great necessity to consider both the actual weather conditions at the bridge site and the “box-room effect” of steel box girder when calculating thermal behaviors of bridge structures. Finally, it is related that the particular method proposed in this paper possesses a satisfactory application prospect for temperature field analysis upon various types of bridges in different regions.

Effects of Age and Overhead Illumination on Temperatures Preferred by Underyearling Rainbow Trout, Salmo gairdneri, in a Vertical Temperature Gradient

1978 ◽  
Vol 35 (11) ◽  
pp. 1430-1433 ◽  
Author(s):  
Wen-Hwa Kwain ◽  
Robert W. McCauley
Keyword(s):  
Rainbow Trout ◽  
Temperature Gradient ◽  
Temperature Gradients ◽  
Salmo Gairdneri ◽  
Vertical Temperature Gradient ◽  
Temperature Preference ◽  
Vertical Temperature ◽  
Preferred Temperature ◽  
Distribution Of Fish ◽  
Vertical Gradients

During their first 12 mo of life rainbow trout, Salmo gairdneri, preferred progressively cooler temperatures as they grew older; 19 °C was selected during the 1st mo and the selected temperature declined by intervals of 0.5 °C for each of the following months up to the 3rd mo. Fish swam higher in temperature gradients exposed to overhead illumination than in those in total darkness. This trend was reversed during the following 9 mo. These findings demonstrate the important role that age plays in the temperature preference of this species and the influence that overhead light may have on the distribution of fish in vertical gradients. Key words: preferred temperature, age, Salmo gairdneri, light gradients

scholarly journals The isothermal layer of the atmosphere and atmospheric radiation

1909 ◽  
Vol 82 (551) ◽  
pp. 43-70 ◽  
Keyword(s):  
High Pressure ◽  
Temperature Gradient ◽  
Temperature Change ◽  
Atmospheric Temperature ◽  
Atmospheric Radiation ◽  
Average Height ◽  
Vertical Temperature Gradient ◽  
Vertical Temperature ◽  
Temperature Changes ◽  
Isothermal Layer

The investigation of the upper air by means of balloons carrying self-recording instruments, which have furnished values for the atmospheric temperature up to heights between 15 and 20 kilometres, has revealed the existence of an abnormal change in the vertical temperature gradient. After a fairly uniform fall, with increasing altitude, of about 6° C. per kilometre, a height is reached above which the temperature changes very little, sometimes increasing, sometimes diminishing slowly. The phenomenon was first noticed by M. Teisserenc de Bort in a communication to the Société de Physique in June, 1899. He improved his apparatus and made further investigations, in many cases sending up the balloons by night to eliminate any possible insolation effects. He found the average height, at which the change began, to be about 11 kilometres. He discovered also that the height was greater near the centre of high pressure areas than in low pressure areas, the average heights for the two cases being 12-5 and 10 kilometres respectively. More recently he found that the height increased with approach towards the equator and that near the equator, ballons-sondes , ascending to 15 kilometres, had failed to reach this layer if it existed there. He proposed to call this layer, in which little temperature change occurred, the “Isothermal Layer of the Atmosphere,” and the name has been generally accepted.

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