Dependency of the apparent contact angle on nonisothermal conditions

Krahl, Rolf; Gerstmann, Jens; Behruzi, Philipp; Bänsch, Eberhard; Dreyer, Michael

doi:10.1063/1.2899641

Cited by 12 publications

(10 citation statements)

References 13 publications

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“…Many practical applications, for example, in microfluidic devices 1-3 or in orbital spacecrafts, 4,5 involve actuation of droplets immersed in another fluid medium or attached on a solid substrate. One mechanism to drive the droplets is to use thermocapillarity, which refers to the variation of surface tension coefficient with temperature.…”

Section: Introductionmentioning

confidence: 99%

Moving towards the cold region or the hot region? Thermocapillary migration of a droplet attached on a horizontal substrate

Sui

2014

Physics of Fluids

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We study computationally thermocapillary migration of a two-dimensional droplet attached on a horizontal substrate with a constant temperature gradient. A level-set approach is employed to track the droplet interface and a Navier slip boundary condition is imposed to alleviate a stress singularity at the moving contact lines. The present numerical model allows us to consider droplets with large contact angles and to take into account effects of the fluid outside the droplet, both have not been well studied so far. In the limits of a zero contact angle hysteresis and a small viscosity ratio of the fluids outside and inside the droplet (μout/μin ⩽ 0.1), we find the droplet finally migrates towards the cold region, and both the steady migration speed and the velocity field inside the droplet obtained from numerical simulation agree very well with the lubrication theory of Ford and Nadim [“Thermocapillary migration of an attached drop on a solid surface,” Phys. Fluids 6, 3183–3185 (1994)] when the contact angles are small (⩽45°). Beyond this regime, increasing the contact angles leads to increased deviations between numerical simulation and the lubrication theory, and the steady migration speed of the droplet towards the cold side decreases with the contact angles. The simulation results show that the droplet could fall in a motionless regime when its contact angles are around 100° even without any contact angle hysteresis. It is very interesting to find that a droplet with even larger contact angles migrates towards the hot region in a steady speed. We also find the transition of the migration direction of a droplet could strongly depend on the viscosity ratio. With increasing the viscosity of the external fluid, the transition could happen at much smaller values of contact angles. We summarize the results in a phase diagram and discuss the effects of other system parameters, including the contact angle hysteresis, the effective Marangoni number, the Prandtl number, and the slip length, on thermocapillary migration of the droplet.

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Section: Introductionmentioning

confidence: 99%

Moving towards the cold region or the hot region? Thermocapillary migration of a droplet attached on a horizontal substrate

Sui

2014

Physics of Fluids

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“…More details can be found in (Gerstmann and Dreyer 2007;Krahl and Bänsch 2005;Krahl et al 2008). The characteristic temperature differences for start and end point of time are sketched in Fig.…”

Section: Deformation Of the Free Surfacementioning

confidence: 97%

Description of the Sounding Rocket Experiment—SOURCE

Fuhrmann

Dreyer

2008

Microgravity Sci. Technol

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A SOUnding Rocket Compere Experiment (SOURCE) is prepared for launch in spring 2008 and shall deliver approximately 360 s of microgravity time. The experiment is intended to partially fulfill the scientific objectives of the European Space Agency Microgravity Applications Program project AO-2004-111 (Convective boiling and condensation). One of the tasks of this experiment is the investigation of capillary dominated flow at a heated wall. The SOURCE experiment will also serve the needs of the COMPERE research group whose mandate is to investigate the behavior of propellant in spacecraft tanks. SOURCE is a benchmark type of experiment on fluid behavior in tanks to test hypotheses and numerical predictions (quantitative results on a tank scale). Several work packages have been distributed to the Center of Applied Space Technology and Microgravity (ZARM) to manage a part of the preparation of this experiment. Since ZARM acts also as a principal investigator, the subject of surface tension driven flows is one of the main topics. It includes the design of the experimental setup to study free surface behavior as well as the numerical predictions to quantify the heat transfer at a non-isothermal boundary condition in the absence of gravity.

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“…(Krahl et al 2008 (Ostrach 1982), that the Reynolds number can be substituted by the Reynolds-Marangoni number Re M here in this case for the boundary layer flow type. Furthermore the heat transfer between wall and liquid due to convection can be characterized by the Nusselt number Nu.…”

Section: Dimensionless Numbersmentioning

confidence: 98%

Heat Transfer by Thermo-Capillary Convection

Fuhrmann

Dreyer

2009

Microgravity Sci. Technol.

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This paper describes the results of a sounding rocket experiment which was partly dedicated to study the heat transfer from a hot wall to a cold liquid with a free surface. Natural or buoyancy-driven convection does not occur in the compensated gravity environment of a ballistic phase. Thermo-capillary convection driven by a temperature gradient along the free surface always occurs if a non-condensable gas is present. This convection increases the heat transfer compared to a pure conductive case. Heat transfer correlations are needed to predict temperature distributions in the tanks of cryogenic upper stages. Future upper stages of the European Ariane V rocket have mission scenarios with multiple ballistic phases. The aims of this paper and of the COMPERE group (French-German research group on propellant behavior in rocket tanks) in general are to provide basic knowledge, correlations and computer models to predict the thermo-fluid behavior of cryogenic propellants for future mission scenarios. Temperature and surface location data from the flight have been compared with numerical calculations to get the heat flux from the wall to the liquid. Since the heat flux measurements along the walls of the transparent test cell were not possible, the analysis of the heat transfer coefficient relies therefore on the numerical modeling which was validated with the flight data. The coincidence between experiment and simulation is fairly good and allows presenting the data in form of a Nusselt number which depends on a characteristic E. Fuhrmann · M. Dreyer (B)

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Dependency of the apparent contact angle on nonisothermal conditions

Cited by 12 publications

References 13 publications

Moving towards the cold region or the hot region? Thermocapillary migration of a droplet attached on a horizontal substrate

Moving towards the cold region or the hot region? Thermocapillary migration of a droplet attached on a horizontal substrate

Description of the Sounding Rocket Experiment—SOURCE

Heat Transfer by Thermo-Capillary Convection

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