The effect of surfactant on the terminal and interfacial velocities of a bubble or drop

Leven, M. Douglas; Newman, Jennifer F.

doi:10.1002/aic.690220411

Cited by 97 publications

(53 citation statements)

References 15 publications

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“…The specialization of this solution for the boundary conditions given in Eqs. 10,12 and 13 and suitable boundedness conditions already has been performed in another context by Levan and Newman (1976), who were interested in the slow buoyant migration of a fluid droplet in a continuous medium with a uniform concentration of surfactant far away from the droplet. Thus, the interested reader is referred to their article for details.…”

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confidence: 97%

Slow migration of a gas bubble in a thermal gradient

Subramanian

1981

AIChE Journal

146

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The steady migration velocity of a gas bubble placed in a liquid with a linear temperature field in the absence of gravity is obtained for small Marangoni Numbers using a matched asymptotic expansion procedure for solving the governing equations. A result good to O(N&,) is obtained, and in the limiting case of zero Marangoni Number, the results of Young, Goldstein and Block are recovered. R. S. SUBRAMANIAN Deportment of Chemical EngineeringClorkron College of Technology Potsdom, NY 13676 SCOPEWith the advent of orbital facilities for experimentation such as Spacelab to be flown aboard the Space Shuttle, and "Space Processing" applications, the migration of droplets and bubbles in a continuous phase due to forces other than buoyancy will become a subject of considerable interest.A theoretical development is presented for the description of bubble migration in a free fall environment due to interfacial tension gradients generated on the bubble surface by a temperature gradient in the surrounding liquid. The objective is to obtain a result for the migration velocity as a function of system parameters for a class of systems characteristic of glasses suggested for Space Processing. These systems, because of their high viscosities, possess very low Reynolds Numbers SO that the inertial terms in the equations of motion may be ignored* However, the Prandtl can be large; therefore, the convective transport terms in the energy equation are not usually negligible. CONCLUSIONS AND SIGNIFICANCEThe principal result of this work is Eq. 53 for the scaled migration velocity of the bubble. In addition to providing a quantitative expression for the buhhle velocity, this result identifies the influence of convective transport of energy in the system. The effect of such transport is to reduce the migration velocity over the value which would prevail were conduction to be the only mechanism. In the limit of zero Marangoni Number, when convective transport is negligible, the result derived here reduces to that of Young, Goldstein and Block utility in the description of bubble migration in space processing applications. Also, applications may be anticipated in the areas of bubble elimination in glass furnaces and in sealing operations where large thermal gradients are encountered. It is expected that this work will haveThe migration of a gas bubble (or a droplet in general) d u e to forces other than buoyancy in a surrounding fluid medium is a subject which so far has received only a small amount of attention. However, with the advent of the Space Shuttle, and the opportunity it provides for the conduct of experiments in a free fall environment, there is a need for developing improved descriptions of this process. In space experiments, it is expected that many occasions will arise where liquid bodies containing droplets of a second fluid, either liquid or gaseous, will be encountered. An example is in the manufacture of spaceprocessed glasses.It has been suggested that the containerless environment available in orbit can be used to make...

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confidence: 97%

Slow migration of a gas bubble in a thermal gradient

Subramanian

1981

AIChE Journal

146

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“…1 (b). For this geometry there exists a solution of the Stokes equation for the fluid flow field inside and outside of the droplet as well as the fluid velocity at the interface [35,36]. The solution at the interface is given in terms of the surface tension gradient:…”

Section: Diffusion-advection-reaction Equationmentioning

confidence: 99%

Swimming active droplet: A theoretical analysis

Schmitt¹,

Stark²

2013

EPL

101

145

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-Recently, an active microswimmer was constructed where a micron-sized droplet of bromine water was placed into a surfactant-laden oil phase. Due to a bromination reaction of the surfactant at the interface, the surface tension locally increases and becomes non-uniform. This drives a Marangoni flow which propels the squirming droplet forward. We develop a diffusionadvection-reaction equation for the order parameter of the surfactant mixture at the droplet interface using a mixing free energy. Numerical solutions reveal a stable swimming regime above a critical Marangoni number M but also stopping and oscillating states when M is increased further. The swimming droplet is identified as a pusher whereas in the oscillating state it oscillates between being a puller and a pusher.

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“…(6) as additional boundary condition to the general polynomial solutions an expression for the interfacial velocity reads [19,23] …”

Section: Flow Field Near a Dropletmentioning

confidence: 99%

“…This surface (Marangoni) stress has to be balanced by viscous stresses which are caused by a Marangoni flow tangential to the droplet surface. Thus the continuity of the tangential stress between the outer and inner bulk fluids in presence of Marangoni stresses at the surface has to be replaced by [18][19][20] …”

Section: Flow Field Near a Dropletmentioning

confidence: 99%

Self-propelled droplets

Seemann

Fleury

Maaß

2016

Eur. Phys. J. Spec. Top.

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Abstract. Self-propelled droplets are a special kind of self-propelled matter that are easily fabricated by standard microfluidic tools and locomote for a certain time without external sources of energy. The typical driving mechanism is a Marangoni flow due to gradients in the interfacial energy on the droplet interface. In this article we review the hydrodynamic prerequisites for self-sustained locomotion and present two examples to realize those conditions for emulsion droplets, i.e. droplets stabilized by a surfactant layer in a surrounding immiscible liquid. One possibility to achieve self-propelled motion relies on chemical reactions affecting the surface active properties of the surfactant molecules. The other relies on micellar solubilization of the droplet phase into the surrounding liquid phase. Remarkable cruising ranges can be achieved in both cases and the relative insensitivity to their own 'exhausts' allows to additionally study collective phenomena.

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The effect of surfactant on the terminal and interfacial velocities of a bubble or drop

Cited by 97 publications

References 15 publications

Slow migration of a gas bubble in a thermal gradient

Slow migration of a gas bubble in a thermal gradient

Swimming active droplet: A theoretical analysis

Self-propelled droplets

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