scholarly journals Drag of a growing bubble at rectilinear accelerated ascension in pure liquids and binary solutions

2003 ◽  
pp. 177-192 ◽  
Author(s):  
Radomir Askovic
Keyword(s):  
Surface Tension ◽  
General Solution ◽  
Drag Coefficient ◽  
Critical Radius ◽  
Heat Diffusion ◽  
Binary Solutions ◽  
Diffusion Controlled

The problem of predicting the drag coefficient of a growing bubble at rectilinear accelerated ascension in uniformly super?heated pure liquids and in binary solutions with a non-volatile solute at large Reynolds and Peclet numbers is discussed. In the case of pure liquids, the general solution for the drag coefficient of an accelerated growing bubble from its inception at the critical radius and through the surface-tension-, inertia-, and heat-diffusion-controlled regimes is established, as well as some necessary adaptations in the case of binary solutions with a non-volatile solute. Two particular limiting regimes in the case of pure liquids, inertia-controlled and heat-diffusion-controlled regimes, respectively, are analyzed in details, with satisfactory results. .

scholarly journals On an evaluation of the drag force of a growing vapor bubble at rectilinear accelerated ascension

2002 ◽  
pp. 103-114 ◽  
Author(s):  
Radomir Askovic
Keyword(s):  
Drag Coefficient ◽  
Drag Force ◽  
Vapor Bubble ◽  
Bubble Growth ◽  
Simple Relation ◽  
Heat Diffusion ◽  
Diffusion Controlled

By applying the in viscid approximation, a simple relation for predicting the drag coefficient of a growing vapor bubble at rectilinear accelerated ascension in uniformly-superheated pure liquids was developed. The relation is valid in both regions: inertia controlled and heat diffusion controlled bubble growth, respectively. The drag coefficient decreases with time for all accelerations, as well as with augmentation of the bubble acceleration at each instant of time, independently of the internal vapor parameters.

An Investigation on the Profile of Microlens by the Thermal Reflow Process Due to Surface Tension and Gravity

2008 ◽  
Author(s):  
Jhy-Cherng Tsai ◽  
Yong-Sung Hsu
Keyword(s):  
Surface Tension ◽  
Critical Radius ◽  
Critical Size ◽  
Liquid Droplet ◽  
Bond Number ◽  
Diameter Ratio ◽  
Experimental Result ◽  
Critical Number ◽  
Reflow Process ◽  
Thermal Reflow

Microlens and its mold fabricated by thermal reflow using photoresist have been widely used for forming patterns in different scales. When the photoresist solidifies from melting condition, for example by the reflow process, its profile is formed based on the balance between surface tension and gravity. This research is aimed to investigate the influence of surface tension and gravity on the profile of microlens in thermal reflow process. Theoretical analysis based on the interaction between surface tension and gravity of liquid droplet is first investigated. The result showed that the height to diameter ratio (h/D), or the sag ratio, of the liquid droplet is affected by the Bond number (Bo), a number defined as the ratio of gravity to surface tension. The sag ratio is not sensitive to Bo when Bo is small but the ratio decreases as Bo increases if Bo is over the critical number. Based on the analysis, the critical number for the AZ4620 photoresist on a silicon substrate is 1, corresponding to the critical radius of droplet R = 2,500μm. When the size of the droplet is less then the critical size, the profile is mainly controlled by the surface tension and thus the sag ratio is about the same regardless the size. The profile, in contrast, is highly affected by the gravity if the size of the droplet is larger then the critical size. The sag ratio decreases exponentially with respect to Bo in this case. Experiments are also designed and conducted to verify the analysis. Experimental result showed that the sag ratio of the photoresist reduces to 0.065 from 0.095 when Bo increases from 0.0048 to 0.192. The results showed that the trend is consistent to the theoretical model.

Surface Tension and Parameters of Interatomic Interaction on Surfaces of Binary Solutions

2019 ◽  
Vol 83 (6) ◽  
pp. 749-751
Author(s):  
M. A. Shebzukhova ◽  
A. A. Shebzukhov ◽  
K. Ch. Bzhikhatlov ◽  
V. K. Lyuyev
Keyword(s):  
Surface Tension ◽  
Interatomic Interaction ◽  
Binary Solutions

Surface tension of binary solutions of non-electrolytes

1972 ◽  
Vol 40 (3) ◽  
pp. 424-428 ◽  
Author(s):  
Robert S Hansen ◽  
Laszlo Sogor
Keyword(s):  
Surface Tension ◽  
Binary Solutions

Dynamics of the Liquid Microlayer Underneath a Vapor Bubble Growing at a Heated Wall

2013 ◽  
Author(s):  
A. Guion ◽  
D. Langewisch ◽  
J. Buongiorno
Keyword(s):  
Quantitative Agreement ◽  
Heat Diffusion ◽  
Heated Wall ◽  
Interfacial Resistance ◽  
Governing Equations ◽  
Vapor Source ◽  
Phase Line ◽  
Diffusion Controlled ◽  
Vapor Recoil ◽  
Special Case

Evaporation of the liquid microlayer developing underneath a bubble in the initial (inertia controlled) phase of its growth can be a significant vapor source in the later (heat-diffusion controlled) phase of bubble growth. In the literature, representation of this microlayer is typically limited to a very short (order of microns) region near the apparent Triple Phase Line (TPL) between the bubble and the wall. However, experimental observations show that the microlayer may actually extend hundreds of microns beyond the TPL region. Guided by this observation, we develop a simple model to predict the time evolution of the extended microlayer, and the associated corresponding evaporation rate and heat flux underneath a bubble. The model is derived as a special case of the complete governing equations, which account for the complicated effects of disjoining pressure, capillarity, vapor recoil and interfacial resistance. The predictions of the model are in reasonable quantitative agreement with the experimentally observed behavior of the microlayer.

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