Thermocapillary Motion of Bubbles Inside Drops

1981 ◽  
Vol 9 ◽  
Author(s):  
N. Shankar ◽  
Robert Cole ◽  
R. Shankar Subramanian
Keyword(s):  
Free Fall ◽  
Temperature Fields ◽  
Drop Surface ◽  
Thermocapillary Motion ◽  
Thermocapillary Migration ◽  
Axisymmetric Temperature

ABSTRACTThe quasi-static thermocapillary migration of a bubble located inside a drop in free fall is considered for arbitrary axisymmetric temperature fields prescribed on the drop surface. Some results are presented, and an approximation based on the superposition of simpler solutions is discussed.

Thermocapillary migration of a bidisperse suspension of bubbles

1994 ◽  
Vol 261 ◽  
pp. 47-64 ◽  
Author(s):  
Y. Wang ◽  
R. Mauri ◽  
A. Acrivos
Keyword(s):  
Volume Fraction ◽  
Single Bubble ◽  
Conducting Liquid ◽  
Typical Size ◽  
Thermocapillary Motion ◽  
Volume Fractions ◽  
Thermocapillary Migration ◽  
Asymptotic Expressions ◽  
Mixed Suspension ◽  
Spherical Bubbles

We consider the thermocapillary motion of a well-mixed suspension of non-conducting spherical bubbles of negligible viscosity in a viscous conducting liquid under conditions of vanishingly small Reynolds and Marangoni numbers. Recently, Acrivos, Jeffrey & Saville (1990) showed that when all the bubbles are of identical size, the ensemble-averaged migration velocity $\bar{U}_{1}$ of a test bubble of radius a1 within the suspension equals $U^{(0)}_1[1-\frac{3}{2}c_1+O(c^2_1)]$, where c1 is the volume fraction of the bubbles and U1(0) is the thermocapillary velocity of single bubble given by Young, Goldstein & Block (1959). Here we extend this result to a bi-disperse suspension containing bubbles of radii a1 and a2 ≡ λa1 in which case $\bar{U}_1 = U^{(0)}_1[1-\frac{3}{2}c_1 - S(\lambda)c_2+\ldots]$, where c1 and c2 are the corresponding volume fractions of the two sets of bubbles. Values for S(Λ) are presented for some typical size ratios Λ, and asymptotic expressions for S(Λ) are derived for Λ → 0 and for Λ → ∞.

Thermocapillary migration of droplets and bubbles in a viscous liquid (review)

2020 ◽  
Vol 15 (3-4) ◽  
pp. 144-158
Author(s):  
E.Sh. Nasibullaeva ◽  
S.F. Urmancheev
Keyword(s):  
Surface Tension ◽  
Temperature Gradient ◽  
Viscosity Coefficient ◽  
Theoretical Work ◽  
Point Of View ◽  
Temperature Fields ◽  
Physical Point ◽  
Practical Applications ◽  
Thermocapillary Migration ◽  
Gradient Fields

Investigation of the process of accumulation of gas bubbles in the aria of a heat source is, from a physical point of view, quite interesting problem that leads to important conclusions for practical applications. The peculiarity of the process under consideration is that the surface tension of the bubble changes in an alternating temperature field, which, in turn, leads to the appearance of a flow in the boundary layer of the liquid. In the world scientific literature, the discovery and description of the effect of gas bubble migration in the direction of the temperature gradient is usually associated with the experimental work of Yang, Goldstein and Block (1959). Without diminishing its significance, we note that the effect was first predicted in the theoretical work of Fedosov (1956) as a result of solving the problem of the onset of a microflow of a liquid near plane and spherical interphase boundaries in the presence of a temperature gradient. In both works, a significant factor in explaining the described phenomenon was the dependence of surface tension on temperature. After some time, after which it was realized the need to take into account the migration of not only bubbles, but also droplets, in inhomogeneous temperature fields in space technologies, biomedical and other applications, there was a significant number of publications on this subject, and this phenomenon was called thermocapillary migration. This review is devoted to the analysis of the main, in the opinion of the authors of the article, results of experimental, theoretical and applied research to establish the mechanism of migration bubbles and drops in temperature gradient fields. In most works, it is assumed that there is no dependence of the physical properties of a liquid, except for surface tension, on temperature. There are only a few studies where the influence of the temperature dependence of the viscosity coefficient was considered, which gives a new impetus to the continuation of research and the development of the theory of the effect, taking into account the thermorheological properties of working media.

On the Thermal Stresses Generated in Cylindrical Shells With Application to Gas Turbine Combustors

1982 ◽  
Author(s):  
H. A. Nied
Keyword(s):  
Gas Turbine ◽  
Thermal Stresses ◽  
Longitudinal Direction ◽  
Temperature Fields ◽  
Shear Stresses ◽  
Gas Turbine Combustor ◽  
Closed Form Solutions ◽  
Bending Stresses ◽  
Cooling Hole ◽  
Axisymmetric Temperature

The thermal stresses generated in a cylindrical shell due to axisymmetric temperature fields, which vary in the longitudinal direction, are examined by using an influence function formulation. Closed form solutions for the longitudinal, hoop and shear stresses are derived for any axially varying temperature distribution expressible by a Fourier expansion. The thermal stresses generated in a typical cylindrical gas turbine combustor cooled by periodically spaced circumferential bands of cooling holes are investigated using the derived solutions. It is shown that a critical pitch in the cooling hole spacing can create high bending stresses at the cooling holes which could contribute to thermal fatigue failure.

Near-contact thermocapillary motion of two non-conducting drops

1993 ◽  
Vol 256 ◽  
pp. 107-131 ◽  
Author(s):  
Michael Loewenberg ◽  
Robert H. Davis
Keyword(s):  
Contact Force ◽  
Relative Motion ◽  
Point Contact ◽  
Continuous Phase ◽  
Thermocapillary Motion ◽  
Asymptotic Formulae ◽  
Wide Range ◽  
Individual Drop ◽  
Gravity Driven ◽  
Axisymmetric Temperature

The axisymmetric, thermocapillary-driven motion of a pair of non-conducting, spherical drops in near contact is analysed for conditions of small Reynolds and Marangoni numbers. The pairwise motion and an associated contact force are computed by considering touching drops in point contact. Relative motion for nearly touching drops results from the contact force balanced by a lubrication resistance. A new, analytical solution is obtained for the axisymmetric temperature field around an unequal pair of non-conducting, tangent spheres embedded in an ambient temperature gradient. Numerical results for the pairwise migration velocity, contact force, and the relative and individual drop velocities are presented for all size ratios and a wide range of viscosity ratios, and asymptotic formulae are derived for small size ratios. For nearly equisized drops, the ratio of the relative velocity for two drops in near contact to that for widely separated drops is similar for thermocapillary-driven and gravity-driven motion. For small and moderate size ratios, however, this ratio is much larger for thermocapillary-driven relative motion than for gravity-driven relative motion, indicating that the former represents a more efficient coalescence mechanism. An explanation for this finding is provided in terms of the thermocapillary motion of the interface of the larger drop aiding the withdrawal of continuous phase from between the two drops.

Temperature fields in a liquid due to the thermocapillary motion of bubbles and drops

2001 ◽  
Vol 31 (1) ◽  
pp. 84-89 ◽  
Author(s):  
G. Wozniak ◽  
R. Balasubramaniam ◽  
P. H. Hadland ◽  
R. S. Subramanian
Keyword(s):  
Temperature Fields ◽  
Thermocapillary Motion

The growth of mica polytypes as studied by conventional and high-resolution TEM

1983 ◽  
Vol 41 ◽  
pp. 174-177
Author(s):  
A. Baronnet ◽  
M. Amouric
Keyword(s):  
Water Pressure ◽  
Point Of View ◽  
Temperature Fields ◽  
Natural Occurrence ◽  
Growth Mechanisms ◽  
Long Period ◽  
High Resolution Tem ◽  
Layer Stacking ◽  
Experimental Works ◽  
Potential Use

The origin of mica polytypes has long been a challenging problem for crystal- lographers, mineralogists and petrologists. From the petrological point of view, interest in this field arose from the potential use of layer stacking data to furnish further informations about equilibrium and/or kinetic conditions prevailing during the crystallization of the widespread mica-bearing rocks. From the compilation of previous experimental works dealing with the occurrence domains of the various mica "polymorphs" (1Mr, 1M, 2M1, 2M2 and 3T) within water-pressure vs temperature fields, it became clear that most of these modifications should be considered as metastable for a fixed mica species. Furthermore, the natural occurrence of long-period (or complex) polytypes could not be accounted for by phase considerations. This highlighted the need of a more detailed kinetic approach of the problem and, in particular, of the role growth mechanisms of basal faces could play in this crystallographic phenomenon.

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