Evaporation of stationary droplets in high temperature surroundings

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The prediction of the rate of evaporation of liquids in high-temperature surroundings is important in an increasing number of processes such as spray drying and flash drying, combustion of atomized liquid fuels, cyclone evaporation, and in operations carried out in gas-conveyed systems, such as in the atomized suspension technique (1 ) . Theoretically at least, the problem is capable of solution if sufficient knowledge exists concerning the boundary-layer flow pattern and the rate of heat transfer by radiation and convection at every point of the system.As pointed out by Hoffman ( 2 ) , most of the numerous investigations which have been reported in this field were concerned with low transfer rates and generally fall into two broad classes: measurement of the rate of heat and mass transfer from stationary liquid drops in surroundings at a temperature only moderately higher than that of the drop, and measurement of the rate of heat and mass transfer from liquid and solid spheres in a flowing medium under forced convection conditions.Virtually all of these studies, the most pertinent of which have been reviewed in reference 2 and will not be listed here, have assumed that the two transfer mechanisms did not affect one another. With work at high rates of mass transfer, Hoffman has, however, shown that the rate of heat transfer is governed by the effect of the evolved vapors on the boundary-layer flow.The present investigation was undertaken specifically to study the vaporization of liquids at high rates of mass transfer and to provide a better understanding of the complex interaction of the two transfer mechanisms. A theoretical analysis of this problem will first be presented, from which the various dimensionless groups governing the process will be deduced. This will be followed by the description of an experimental study on the rates of evaporation from stationary spheres in high-temperature surroundings. D. C. T. Pei is ANALYSIS OF PROBLEMIn an analysis of the convectivetransfer problem, the fundamental approach is to consider the equations which govern the transfer of momentum, heat, and mass in the boundary layer. To simplify matters the case of two-dimensional incompressible flow along a curved surface will be considered. With a curvilinear orthogonal system of coordinates whose x-axis will be in the direction of the wall, it can be shown that, in general, the boundary-layer equations for a flat wall may be applied to the case of a curved wall as well, provided that there are no large variations in curvature. When applied to a sphere, this approach is only an approximation which should indicate the nature of the dimensionless parameters on which the solution should depend. Thus, assuming constant physical properties, the expressions are Navier-Stokes momentum equation derived from a force balance

Section: ( T -T M ) / ( 7 ' W -T M ) (24)supporting

confidence: 81%

Section: A1che Journalmentioning

confidence: 96%

Section: Where B = ( G a T ) / ( X -Q T / I )mentioning

confidence: 98%

Section: A1che Journalmentioning

confidence: 99%

Section: Where B = ( G a T ) / ( X -Q T / I )mentioning

confidence: 99%

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Natural convection evaporation from spherical particles in high‐temperature surroundings

Pei¹,

Gauvin²

1963

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The evaporation of drops of pure liquids at elevated temperatures: Rates of evaporation and wet‐bulb temperatures

Downingm

1966

A r l z and pointing into the phase of interest. The fractional rate of change of area of surface element 4xi\zBy taking the limit as ( A x , A z ) approach zero, this expression may be rewritten for any point u, w in the interfacial surface as (A2)For an incompressible fluid this expression may be rewritten with the aid of the continuity relation to obtain auX au, u,lt) ax az The rates of evaporation and the wet-bulb temperatures have been correlated for drops of pure liquids evaporating in streams of high-temperature air. The four liquids studied were acetone, benzene, n-hexane, and water. The drops were of the order of a millimeter in diameter and were suspended in a free jet of dry, vapor-free air that ranged in temperature from 27" to 340°C. Reynolds numbers ranged from 24 to 325. Corrections to the Nusselt number to account for the heat lost to the outwardly diffusing vapor ranged up to about 35%.The correlation of the phenomena characterizing the evaporation of liquid drops under conditions leading to high heat and mass fluxes would be of interest in many fields of cominercial importance, but probably the greatest utility of such a correlation woiild be in relation to spray-drying and droplet-combustion studies. The present paper presents a simplified approach to such a correlation, being concerned solely with the evaporation of isolated pure liquid drops at atmospheric pressure. DROP EVAPORATION RATESA heat balance taken on a differential shell about a spherically symmetrical model of a drop undergoing steady state evaporation leads to the differential equation (constant film properties) ma1 conductivity of the film, is constant. In the general case, however, k will be a function of both composition and temperature. In order to maintain the simple form of Equation (1) , it is therefore necessary to define an effective average thermal conductivity of the film, to be evaluated at some appropriate composition and temperature which are as yet undefined. By designating this average thermal conductivity of the film as kf, the solution of Equation (1) is (13)To-Tl exp(-a' (RJRo)) -exp(-a') Equation ( 2 ) may now be differentiated to obtain the temperature gradient at the drop surface:The expression for the heat balance at the drop surface is (4)

Evaporation of liquid droplets containing surface impurities

Shih¹,

Coughanowr²

1968

The evaporation of a single droplet into still air has been summarized by Green and Lane (1) and by Orr ( 2 ) . If (9) pointed out that "the distance A is never clearly defined and the limits of validity of the treatment are not apparent."It is well known that surface impurities retaid the rate of evaporation in a flat surface ( l o ) , but there is no quantitative discussion of the effect of surface impurities on the evaporation of a droplet. Such a detailed discussion is given in this report, which also discusses the effect of surface tension. EFFECT OF SURFACE IMPURITIES AND SURFACE TENSIONThe effect of curvature on the vapor pressure of a liquid is described by the Kelvin equation ( , l l ) , which may be written for a spherical surface as Substitution of Equations (4) and (5) into Equation ( 3 )gives "A more important effect on the rate of evaporation is the accumulation of surface impurities, which form a layer or coating, on the surface. As the drop diameter decreases during the evaporation, the thickness of the impurity layer increases. Since the amount of surface impurities in turn is proportional to the surface area of the initial drop, one may write01'where we have assumed that the thickness of the impurity layer, d, is much smaller than the diameter of the drop; K1 is a constant.In the following treatment we assumed that the resistance to diffusion through the impurity layer is proportional to its thickness. We also neglected the effect of curvature. HenceA combination of this with Equation (8) Although this is of the same form as the Langmuir equation, Equation ( l ) , the actual concentration at the surface has been used. If surface impurities are not present, Equation (10) reduces to Equation ( 1 ) . The quasisteady state approach has been used in the derivation of Equation (10). The validity of this approach has been checked by Luchak and Langstroth ( 1 2 ) , who showed that at low diffusion flux the time-variable boundary approach gives almost the same results as the quasisteady state approach.Combination of Equations (a), (9), and (10) gives