Turbulence, interfacial

The effect, which arises in cases where the interfacial tension is strongly dependent on the concentration of diffusing solute, will generally be dependent on the direction (sense) in which mass transfer is taking place. 

The mass transfer rate at the surface of the sphere at time t 

Tills phenomenon, frequently referred to as the Marangoni Effect, explains some of the anomalously high mass transfer rates reported in the literature. 

The effect may be reduced by the introduction of surfactants which tend to concentrate at the interface where they exert a stabilising influence, although they may introduce an interface resistance and substantially reduce the mass transfer rate. Thus, for instance, hexadecanol when added to open ponds of water will collect at the interface and substantially reduce the rate of evaporation. 

Such effects are described in more detail by Sherwood, Pigford and Wilke(271. 

On the basis of each of the theories discussed, the rate of mass transfer in the absence of bulk flow is directly proportional to the driving force, expressed as a molar concentration difference, and, therefore  

---

Information on the coefficients is relatively undeveloped. They are evidently strongly influenced by rate of drop coalescence and breakup, presence of surface-active agents, interfacial turbulence (Marangoni effect), drop-size distribution, and the like, none of which can be effectively evaluated at this time. 

Insulation see also lagging 554 Intelligent transmitters 240,241,242 Intensity of turbulence 701 Interface evaporation 484 Interfacial turbulence 618 Internal energy 27,44... 

Sternling and Sc riven 13 1 have examined interfacial phenomena in gas absorption and have explained the interfacial turbulence which has been noted by a number of workers in... 

Interfacial turbulence [60] Due to a nonuniform distribution of surfactant molecules at the interface or to local convection currents close to the interface, interfacial tension gradients lead to a mechanical instability of the interface and therefore to production of small drops. 

These equations, referring to completely unstirred systems, are not usually valid in practice complications such as spontaneous interfacial turbulence and spontaneous emulsification often arise during transfer, while, if external stirring or agitation is applied to decrease Ri and R2, the hydrodynamics become complicated and each system must be considered separately. The testing of the above equations will be discussed below, after a consideration of overall coefficients and of interfacial turbulence. 

The second complicating factor is interfacial turbulence (1, 12), very similar to the surface turbulence discussed above. It is readily seen when a solution of 4% acetone dissolved in toluene is quietly placed in contact with water talc particles sprinkled on to the plane oil surface fall to the interface, where they undergo rapid, jerky movements. This effect is related to changes in interfacial tension during mass transfer, and depends quantitatively on the distribution coefficient of the solute (here acetone) between the oil and the water, on the concentration of the solute, and on the variation of the interfacial tension with this concentration. Such spontaneous interfacial turbulence can increase the mass-transfer rate by 10 times 38). 

When acetic acid is diffusing from a 1.9 iV solution in water into benzene, spontaneous emulsion forms on the aqueous side of the interface, accompanied by a little interfacial turbulence. Results can be obtained with this system, however, if in analysing the refractive index gradient near the surface a correction is made for the spontaneous emulsion the rate of transfer is then in excellent agreement (57) with Eq. (20) (Fig. 6). Consequently there is no appreciable energy barrier due to re-solvation of the acetic acid molecules at the interface, nor does the spontaneous emulsion affect the transfer. With a monolayer of sodium lauryl... 

The extraction of uranyl nitrate from 1 M aqueous solution into 30% tributylphosphate in oil is accompanied by an initial interfacial turbulence (41), with more transfer than calculated, even though re-solvation of each uranyl ion at the interface must be a relatively complex process. If the turbulence is suppressed with sorbitan mono-oleate, transfer proceeds at a rate in excellent agreement with theory. 

The conclusions we may draw from these results are that, in general, interfacial turbulence will occur, and that it will increase the rate of mass transfer in these otherwise unstirred systems. Monolayers will prevent this turbulence, and theory and experiment are then in good agreement, in spite of spontaneously formed emulsion. There are no interfacial barriers greater than 1000 sec. cm. due to the presence of a mono-layer, though polymolecular films can set up quite considerable barriers. Usually there are no appreciable barriers due to re-solvation however, in the passage of Hg from the liquid metal into water, the change between the metallic state and the Hg2++ (aq) ion reduces the transfer rate by a factor of the order 1000. 

This continual replacement of liquid is readily visible with talc particles sprinkled on to the interface though stationary on the average (if the stirrers in phases 1 and 2 are contra-rotated at appropriate relative speeds), they make occasional sudden, apparently random, local movements, which indicate that considerable replacement of the interface is occurring by liquid impelled into the interface from the bulk. Spontaneous interfacial turbulence, associated with such processes as the transfer of acetone from solvent to water, may further increase the rate of transfer by a factor of two or three times (44, 48, 51). Other systems (48), such as benzoic acid transferring (in either direction) between water and toluene, give transfer rates only about 50% of those calculated by Eq. (26), suggesting either that this equation is not valid or that there is an interfacial resistance. This point is discussed in detail below. 

Study in a stirred cell of the transfer of uranyl ions from water to organic solvents confirms the result for unstirred cells that transfer is faster than theoretical when interfacial turbulence is visible (53). After long times, in systems showing no visible turbulence, the transfer coefficients decrease, becoming less than those calculated from Eqs. (25) and... 

For the reverse process of the extraction of the metal salts from n-butanol to water, there is spontaneous interfacial turbulence which raises the mass-transfer coefficient to about twice the value expected from the correlation 54). 

Study of the eflSciency of packed columns in liquid-liquid extraction has shown that spontaneous interfacial turbulence or emulsification can increase mass-transfer rates by as much as three times when, for example, acetone is extracted from water to an organic solvent (84, 85). Another factor which may be important for flow over packing has been studied by Ratcliff and Reid (86). In the transfer of benzene into water, studied with a laminar spherical film of water flowing over a single sphere immersed in benzene, they found that in experiments where the interface was clean... 

With all three types of oscillations superimposed, the final result has a random appearance. Since a sphere has the smallest area per unit volume, all oscillatory movements cause an alternate creation and destruction of interfacial area. The rate of mass transfer is thereby enhanced for oscillating drops. Since surface stretch due to oscillations is not uniformly distributed, all such oscillations produce interfacial turbulence (see Section VII, E). 

An excellent discussion of the phenomenon of spontaneous emulsion has been included in a recent book by Davies and Rideal (D2). Interfacial turbulence has been advanced (D2, 01) as a possible cause but has been eliminated in at least one ease (D2). Diffusion and stranding seems... 

A good model is needed for mass transfer during the formation of new area, whether this area be created by circulation, oscillations, formation stretch, interfacial turbulence, or any other mechanism. 

What is the mechanism which results in rapid coalescence if mass transfer occurs from the drops but slow or no coalescence if both phases are mutually saturated Interfacial turbulence caused by local gradients in interfacial tension looks promising. 

On the interface between quiescent fluids, interfacial motions may take the form of ripples (E4, 02) or of ordered cells (B5, L5, 02, S22). Slowly growing cells may exist for long periods of time (B5, 02), or the cells may oscillate and drift over the surface (L6, L7). When the phases are in relative motion, interfacial disturbances usually take the form of localized eruptions, often called interfacial turbulence (M3). This form of disturbance can also be observed at the interface of a drop (S8). A thorough review of interfacial phenomena, including a number of striking photographs, has been presented by Sawistowski (S7). 

Mass transfer rates are increased in the presence of eruptions because the interfacial fluid is transported away from the interface by the jets. For mass transfer from drops with the controlling resistance in the continuous phase, the maximum increase in the transfer rate is of the order of three to four times (S8), not greatly different from the estimate of Eq. (10-4) for cellular convection. This may indicate that equilibrium is attained in thin layers adjacent to the interface during the spreading and contraction. When the dispersed-phase resistance controls, on the other hand, interfacial turbulence may increase the mass transfer rate by more than an order of magnitude above the expected value. This is almost certainly due to vigorous mixing caused by eruptions within the drop. 

The maximum effect of interfacial turbulence on the mass transfer coefficient can be estimated using the correlation of Davies and Rideal (D6) for the initial spreading velocity, of a surface tension-lowering material spreading at the interface between two fluid phases ... 

In this equation. Act is taken as the maximum possible surface tension lowering. Hence for a solute-free continuous phase, Aa is the difference between the interfacial tension for the solvent-free system and the equilibrium interfacial tension corresponding to the solute concentration in the dispersed phase. Equation (10-6) indicates a strong effect of the viscosity ratio k on the mass transfer coefficient as found experimentally (LI 1). For the few systems in which measurements are reported (Bll, Lll, 04), estimates from Eq. (10-6) have an average error of about 30% for the first 5-10 seconds of transfer when interfacial turbulence is strongest. 

Third, turbulent transport is represented as a succession of simple laminar flows. If the boundary is a solid wall, then one considers that elements of liquid proceed short distances along the wall in laminar motion, after which they dissolve into the bulk and are replaced by other elements, and so on. The path length and initial velocity in the laminar motion are determined by dimensional scaling. For a liquid-fluid interface, a roll cell model is employed for turbulent motion as well as for interfacial turbulence. 

---