Interfacial tension driven flow

For the case of a thread at rest, the initial growth of a disturbance can be relatively well characterized by linear stability theory. In the initial stages, the deformation of the thread follows the growth of the fastest growing disturbance (Tomotika, 1935). Eventually the interfacial tension driven flow becomes nonlinear, leading to the formation of the smaller satellite drops (Tjahjadi et al., 1992). 

In this paper, we now report measurements of heat transfer coefficients for three systems at a variety of compositions near their lower consolute points. The first two, n-pentane--CO2 and n-decane--C02 are supercritical. The third is a liquid--liquid mixture, triethylamine (TEA)--H20, at atmospheric pressure. It seems to be quite analogous and exhibits similar behavior. All measurements were made using an electrically heated, horizontal copper cylinder in free convection. An attempt to interpret the results is given based on a scale analysis. This leads us to the conclusion that no attempt at modeling the observed condensation behavior will be possible without taking into account the possibility of interfacial tension-driven flows. However, other factors, which have so far eluded definition, appear to be involved. 

In Table II, we list the various dimensionless groups defined above and the two criteria for enhancement of the heat transfer coefficient by interfacial tension-driven flow. Calculated values are given for the three mixtures for which we presented experimental data. All values pertain to a temperature difference AT of 10 K. 

Upon cessation of flow, well-known interfacial tension driven flow instabilities set in and cause catastrophic breakup of the strings into droplets. 

A second, new class of processes is that of membrane and micro-channel emulsification. A to-be-dispersed phase is here pushed through pores of a membrane or through micro-engineered micron-scale channels. At the pore or channel mouth, droplets are formed. These droplets can spontaneously detach from the pore or channel mouth (interfacial tension driven snap-off), due to the distortion of the droplet shape when it is still attached to the mouth. At higher fluxes or with channel mouths not giving a strong shape distortion, droplets are sheared off by a cross-flowing continuous phase. 

For solids with continuous pores, a surface tension driven flow (capillary flow) may occur as a result of capillary forces caused by the interfacial tension between the water and the solid particles. In the simplest model, a modified form of the Poiseuille flow can be used in conjunction with the capillary forces equation to estimate the rate of drying. Geankoplis (1993) has shown that such a model predicts the drying rate in the falling rate period to be proportional to the free moisture content in the solid. At low solid moisture contents, however, the diffusion model may be more appropriate. 

Mechanisms of coalescence in polymer blends are generally not well understood [56, 57]. Flow induced coalescence has been discussed briefly above. Under quiescent conditions such as cooling of a strand or an injection molded part, mechanisms such as Smoluchowski coalescence or Ostwald ripening may be important [58]. However, under manufacturing conditions, relaxation of flow stresses and interfacial tension driven changes in domain shape are probably of more importance. 

Note 2 Representative mechanisms for coarsening at the late stage of phase separation are (1) material flow in domains driven by interfacial tension (observed in a co-continuous morphology), (2) the growth of domain size by evaporation from smaller droplets and condensation into larger droplets, and (3) coalescence (fusion) of more than two droplets. The mechanisms are usually called (1) Siggia s mechanism, (2) Ostwald ripening (or the Lifshitz-Slyozov mechanism), and (3) coalescence. 

If indeed one of the phases has broken up into droplets, then slow diffusive processes are the only coarsening mechanisms possible. However, if both phases are still interconnected and are both fluids, then coarsening can occur by the faster process of capillary flow, which is driven by the interfacial tension acting on the curved surfaces between the two fluids (Siggia 1979). The typical pressure drop Ap produced by capillarity is Ap Tja. The velocity produced by this pressure drop is V aApfrj Y/t], where is an average viscosity. The domains grow at a rate da/dt jr] hence... 

Equations (9-43) and (9-44) account for the effects of flow on interfacial area and orientation, but omit interfacial shrinkage, or coarsening, which is driven by interfacial tension. Additional terms to account for coarsening must be added to the right sides of Eqs. (9-43) and (9-44). On dimensional grounds, such terms are proportional to r/t]o, Doi and Ohta chose arbitrary, but simple, terms consistent with this ... 

Finally, we consider the problem of Marangoni instability, namely convection in a thin-fluid layer driven by gradients of interfacial tension at the upper free surface. This is another problem that was discussed qualitatively in Chap. 2, and is a good example of a flow driven by Marangoni stresses. 

In this section, we begin by considering the buoyancy-driven motion of a single gas bubble or drop through an otherwise stationary viscous fluid under the assumption that the bubble or drop shape is nearly spherical. We denote the viscosities and densities of the two fluids as /x, /x, p, and p with the variables with carets corresponding to the fluid inside the drop. In this section, we also assume that the interfacial tension, which we denote as y, is uniform at the drop surface, and that the Reynolds numbers for both the interior and exterior flows are sufficiently small that the creeping-motion approximation can be applied for both fluids. Under these circumstances, experimental evidence shows (and we will assume) that the drop or bubble will translate with a constant velocity U. In addition, though we must consider the shape of the drop to be unknown, we may also anticipate that it will be axisymmetric about an axis that is collinear with the velocity vector U. 

Mechanisms of liquid-liquid phase separation were studied in the binary styrene-acrylonitrile copolymer/poly(methyl methacrylate) system. Evidence is presented which suggests that spinodal decomposition occurs in this system. The Cahn theory provides an interpretation of key experimental results. Both a dispersed, two-phase structure and a highly interconnected, two-phase structure can be formed. These two structures coarsen at significantly different rates. The dispersed-phase structure coarsens by Ostwald ripening, an extremely slow process in the polymer-polymer system. The interconnected structure coarsens more rapidly. Data suggest that the mechanism of coarsening is viscous flow driven by interfacial tension. 

Once composition equilibration has been reached, a mechanism for particle coarsening is available to highly interconnected structures which is unavailable to dispersed-phase structures. This mechanism involves viscous flow driven by interfacial tension. It will be shown that rates of coarsening by this mechanism can be orders of magnitude faster than Ostwald ripening for dispersed phase structures. 

After phase equilibration has been reached, the high level of phase interconnectivity provides a coarsening mechanism unavailable to the dispersed phase structures. This mechanism is viscous flow driven by interfacial tension. One objective of the experimental program was to investigate particle coarsening characteristics of both dispersed and interconnected structures. 

At values above a critical Ca number (Ca 0.015) the shear-driven mechanism also contributes to the droplet formation (De Menech et al. 2008). The shear stress acts to tear off the tip of the dispersed phase, whilst the interfacial tension acts to minimize its surface area. Although a T-shaped configuration favours the formation of plug flow, further increase on the flow rate ratio leads to a change on the flow regime and thus parallel flow will be observed. 

Gradients in surface (or interfacial) tension can accelerate the spreading of fluids, enhance the stability of surfactant-laden films of liquid, emulsions, and foams, and increase rates of mass transport across interfaces. The motion of fluid driven by a gradient in surface tension is referred to as a Marangoni flow . We have demonstrated that electrochemical reduction of IF to IF at an electrode that... 

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