Size Effect on Micro-Droplet Movement Due to Marangoni Effect

2003 ◽  
Author(s):  
Yuan-Tai Tseng ◽  
Fan-Gang Tseng ◽  
Ching-Chang Chieng

Fundamental physics are studied on the movement of droplets for sizes ranging from 0.1 μl to 1.0 μl on a solid surface subjected to temperature gradients using numerical computations and the comparison with experiments. The receding/advancing contact angles relating to the droplet size and shape are the key parameters of droplet moving and the differences subjected to the temperature gradients induce unbalanced recirculation zones inside the moving droplet, thus induces driving force to drag the droplet. It is found that droplet of smaller size moves faster with smoothly changing speed and the droplet of larger size moves with fluctuating speed and the average moving speed is roughly the same magnitude as that with two-dimensional heating.

1993 ◽  
Vol 58 (3) ◽  
pp. 496-505
Author(s):  
Ondřej Wein

Partial blocking of the transport surface under the stagnant (nerst) layer is simulated by periodically alternating bands of perfectly insulating zones and active zones with a constant potential of driving force. The numeric solution of the corresponding two-dimensional elliptic problem is represented by a simple empirical correlation for the transfer coefficients. The result is interpreted in terms of a simple electrochemical problem about limiting diffusion currents at electrodes with non-uniform surface activity.


2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.


1971 ◽  
Vol 50 (2) ◽  
pp. 321-334 ◽  
Author(s):  
James Witting

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.


1953 ◽  
Vol 45 (10) ◽  
pp. 2139-2145 ◽  
Author(s):  
S. D. Cavers ◽  
N. T. Hsu ◽  
W. G. Schlinger ◽  
B. H. Sage

1993 ◽  
Vol 18 ◽  
pp. 161-165 ◽  
Author(s):  
M.R. Albert

Preliminary estimates of the thermal signature of ventilation in polar firn are obtained from two-dimensional numerical calculations. The simulations show that spatially varying surface pressure can induce airflow velocities of 10−5m s−1at 1.5 m depth in uniform firn, and higher velocities closer to the surface. The two-dimensional heat-transfer results generally agree with our earlier one-dimensional conclusions that the thermal effects of ventilation tend to decrease the temperature gradient in the top portions of the pack. Field observations of ventilation through temperature measurements are most likely to be observed when the firn temperature at depths on the order of 10 m is close to the air temperature, since steep temperature gradients can mask the thermal effects of ventilation. Preliminary indications are that, as long as surface-pressure amplitude is sufficient to move the air about in the top tens of centimeters in the snow, the resulting temperature profile during ventilation is fairly insensitive to the frequency of the surface-pressure forcing for pressure frequencies in the range 0.1–10.0 Hz.


1973 ◽  
Vol 59 (4) ◽  
pp. 753-767 ◽  
Author(s):  
E. Pitts

We consider a drop of liquid hanging from a horizontal support and sandwiched between two vertical plates separated by a very narrow gap. Equilibrium profiles of such ‘two-dimensional’ drops were calculated by Neumann (1894) for the case when the angle of contact between the liquid and the horizontal support is zero. This paper gives the equilibrium profiles for other contact angles and the criterion for their stability. Neumann showed that, as the drop height increases, its cross-sectional area increases until a maximum is reached. Thereafter, as the height increases, the equilibrium area decreases. This behaviour is shown to be typical of all contact angles. When the maximum area is reached, the total energy is a minimum. It is shown that the drops are stable as long as the height and the area increase together.


2013 ◽  
Vol 88 (11) ◽  
Author(s):  
P. Delugas ◽  
A. Filippetti ◽  
A. Gadaleta ◽  
I. Pallecchi ◽  
D. Marré ◽  
...  

2014 ◽  
Vol 05 (supp01) ◽  
pp. 1441007 ◽  
Author(s):  
J. S. Espinoza Ortiz ◽  
H. Belich ◽  
M. T. D. Orlando ◽  
R. E. Lagos

Flow through a narrow bent channel may induce topological rearrangements in a two-dimensional monodispersed dry liquid foam. We use the Cellular Potts Model to simulate a foam under a variable driving force in order to investigate the strain-rate response from these rearrangements. We observe a set of foams' behaviors ranging from elastic, viscoelastic to fluid regime. Bubble's topological rearrangements are localized and their cumulative rearrangements change linearly with time, thus nonavalanches critical behavior is found. The strain-rate affects the rate of topological rearrangements, its dependence on the drag force is nonlinear, obeying a Herschel–Bulkley-like relationship below the foam's flow point.


1995 ◽  
Vol 101 (1-2) ◽  
pp. 58-68 ◽  
Author(s):  
David A. Everest ◽  
James F. Driscoll ◽  
Werner J.A. Dahm ◽  
Douglas A. Feikema

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