Evaporation rates of volatile liquids in a laminar flow system: Part II. Liquid mixtures

Clark, Michael W.; King, C. Judson

doi:10.1002/aic.690160115

Cited by 4 publications

(6 citation statements)

References 16 publications

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“…( 2 ) and f ( 7 ) = function representing the variation of u with y, Equation ( 2 ) ; given by Equation (22) f' (7) and f " ( 7 ) = first and second derivatives of f (7) with respect to 7 G = S/d, represents accumulation in the surface g ( 7 ) = function representing the variation of C' with y, Equation ( 3 ) ; given by Equation (23) g'(7) and g"(7) = first and second derivatives of g ( 7 ) Page 772…”

Section: Acknowledgmentmentioning

confidence: 99%

“…Using Equations ( 1 ) , (7), and ( l l ) , Equation ( In order to reduce the surface diffusion term to this form, it is necessary to employ Pearson's Equation (14) : Equation (13) contains four dimensionless groups which influence this problem…”

Section: Theorymentioning

confidence: 99%

“…The function W(7) is readily obtained by differentiating Equation (24) with respect to 7. Similarly, Equation (22) is differentiated first once and then twice to produce the functions f' (7) and f " ( 7 ) . This is quite straightforward, and the functions (which will not be written out here) are then all evaluated at 7 = 1 in Equations (29), (31), and (32).…”

Section: B = -mentioning

confidence: 99%

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Effect of gibbs adsorption on marangoni instability

Brian

1971

AIChE Journal

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SCOPEIn the transfer of mass from one fluid phase to another, solute concentration gradients or temperature gradients may produce surface tension gradients, resulting in cellular convection at the interface. In liquid-liquid extraction systems the convection may become so intense that it causes the break-up of the interface, resulting in "spontaneous emulsification." Often referred to as Marangoni instability, convection driven by surface tension gradients also occurs frequently in gas-liquid mass transfer systems and has been known to enhance the mass transfer rate more than tenfold.A theoretical understanding of Marangoni instability should lead ultimately to the prediction of its occurrence and of its effect upon the mass transfer rate when it occurs, permitting this important phenomenon to be properly accounted for and perhaps even exploited in the design and development of processes involving interphase mass transfer.Previous workers have made substantial progress toward defining the conditions under which the instability occurs, usually measured by the critical value of the Marangoni number. These workers have employed small disturbance hydrodynamic stability theory to predict the point of convective instability. Recent experimental measurements of the critical Marangoni number in desorbing surface tensionlowering solutes from water, however, were found to be several orders of magnitude greater than the theoretical predictions. One speculation offered to explain the discrepancy involved the Gibbs adsorption layer. Because previous theoretical work had not considered the effect of Gibbs adsorption, the present study was undertaken to evaluate the effect of Gibbs adsorption on the theoretically predicted critical Marangoni number. SUMMARYThe influence of Gibbs adsorption has been incorporated into a small disturbance hydrodynamic stability analysis of Marangoni convection. The model used was the first and perhaps the simplest model studied by previous workers, the mass transfer analog of the problem studied by Pearson (9). In this model, the unperturbed state is a horizontal liquid layer at rest, from which a surface tensionlowering solute is desorbing into a gas phase above. The concentration gradient within the liquid layer is linear, and it is assumed that the planar gas-liquid interface is not deformed. The fluid mechanics of the gas phase are not considered, mass transfer in the gas phase being represented by a constant mass transfer coefficient which is unaffected by convection in the liquid phase. These simplifications appear to be adequate for gas-liquid systems, and in any event they are appropriate for this initial analysis of the effect of Gibbs adsorption.The present theory, therefore, involves the incorporation of the effect of Gibbs adsorption into Pearson's hydrodynamic stability analysis. The influence of Gibbs adsorption enters the problem in the boundary condition which Correspondence concerning this article should be addressed to Profes-represents a solute material balance on a small elemen...

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Section: Acknowledgmentmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: B = -mentioning

confidence: 99%

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Effect of gibbs adsorption on marangoni instability

Brian

1971

AIChE Journal

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“…A Schlieren photographic observation of the suppression of the interfacial motion was made by Fujinawa et al (1958). Subsequently, much theoretical and experimental work has been reported (Berg and Acrivos, 1965;Clark and King, 1970;Fujinawa, 1974a, 1974b;Westwater, 1961, 1962;Zeren and Reynolds, 1972). Recently, an examination has been carried out on the Marangoni convection caused by the interfacial tension gradient in the production of materials used in the electronics industry (Ostrach, 1983).…”

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confidence: 99%

Effect of interfacial velocity and interfacial tension gradient on momentum, heat and mass transfer

1989

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The effect of interfacial velocity and interfacial tension gradient on momentum, heat and mass transfer was studied theoretically. After reviewing current knowledge regarding interfacial velocity effects, the interfacial tension gradient effect is discussed as a numerical solution of the laminar boundary layer equations. The enhancement and suppression of interfacial mobility, and the rates of interphase momentum, heat and mass transfer were related to the Marangoni number. A diagram showing the effect of interfacial tension gradient on momentum, heat and mass transfer is presented.

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“…Only recently Í Bakker et al. 1966;Brian <?i al., 1967;Clark and King, 1970) has work begun on the important problem of determining quantitatively the effect of the convection upon the mass transfer coefficients, which is the objective of this investigation.…”

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confidence: 99%

Cellular Convection in Desorbing Surface Tension-Lowering Solutes from Water

Brian¹,

Vivian²,

Mayr³

1971

Ind. Eng. Chem. Fund.

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The effect of cellular convection, driven by surface tension gradients, upon the gas-liquid•mass transfer rate was studied by desorbing four surface tension-lowering solutes from aqueous solution and monitoring the transfer process in each phase by the simultaneous transfer of tracer components. kL was enhanced as much as 3.6-fold by the cellular convection when the Marangoni number was increased above its critical value. kfi was unaffected by the cellular convection, in agreement with predictions based on estimation of the linear and velocity scales of the cellular convection. Critical Marangoni numbers showed the expected dependence on Hk(*/kL* and the surface tension equilibration time but were very much larger than theoretically predicted values.Cellular convection driven by surface tension gradients has for a number of years been recognized as having an

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Evaporation rates of volatile liquids in a laminar flow system: Part II. Liquid mixtures

Cited by 4 publications

References 16 publications

Effect of gibbs adsorption on marangoni instability

Effect of gibbs adsorption on marangoni instability

Effect of interfacial velocity and interfacial tension gradient on momentum, heat and mass transfer

Cellular Convection in Desorbing Surface Tension-Lowering Solutes from Water

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