Mechanism drop deformation

The mechanisms governing deformation and breakup of drops in Newtonian liquid systems are well understood. The viscosity ratio, X, critical capillary number, and the reduced time, t, are the controlling parameters. Within the entire range of X, it was found that elongational flow is more efficient than shear flow for breaking the drops. 

The mechanisms governing deformation and breakup of drops in Newtonian liquid systems are relatively well understood. However, within the range of compounding and processing conditions the molten polymers are viscoelastic liquids. In these systems the shape of a droplet is determined not only by the dissipative (viscous) forces, but also by the pressure distribution around the droplet that originates from the elastic part of the stress tensor. Therefore, the characteristics of drop deformation and breakup in viscoelastic systems may be quite different from those in Newtonian ones. Some of the pertinent papers on the topic are listed in Table 9.3. 

Consider now the drops whose size is smaller than the inner scale of turbulence (R Ao). It is obvious that the breakage of such drops can be caused only by pulsations with scale A < Aq, i.e. pulsations whose motion is accompanied by large forces of viscous friction. Therefore only the force of viscous friction at the drop surface can function as the main mechanism causing drop deformation. The criterion of strong deformation of a drop is the equality of forces of viscous friction and surface tension... 

H. A. Stone and L. G. Leal, The effects of surfactants on drop deformation and breakup. Journal of Fluid Mechanics, 220, 161-186, 1990. 

Although introducing micro-particles into an electrospun fiber mat enhances the hydrophobicity, the main problem associated with a fiber/particle hybrid membrane is that it is not robust mechanically under deformation and wear conditions, the disconnected particle component is readily lost from the membrane. Processing the fibers with a beaded morphology as described above solves the problem of wear, but it remains likely that the enhanced hydrophobicity is due to the introduction of beads rather than fibers as points of contact with the water drop. One way to enhance the hydrophobicity of electrospun hber mats without introducing microparticles (beads) is to make hierarchically roughened hber mats, where hner-scale structures (e.g. nanometer scale particles or pores) are decorated on a coarser-scale structure associated with the hbers. This is reviewed next. 

For K > 2 the drops deform into stable filaments, which only upon reduction of k disintegrate by the capillarity forces into mini-droplets. The deformation and breakup processes require time - in shear flows the reduced time to break is tb > 100- When values of the capillarity number and the reduced time are within the region of drop breakup, the mechanism of breakup depends on the viscosity ratio, A, - in shear flow, when X > 3.8, the drops may deform, but they cannot break. Dispersing in extensional flow field is not subjected to this limitation. Furthermore, for this deformation mode Kcr (being proportional to drop diameter) is significantly smaller than that in shear (Grace 1982). 

F. Mighri, M.A. Huneault, Drop deformation and breakup mechanisms in viscoelastic model fluid systems and polymer blends. Canad. J. Chem. Eng. 80, 1028-1035 (2002)... 

H.A. Stone, Dynamics of drop deformation and breakup in viscous fluids. Annual Review of Fluid Mechanics, 1994, 26, 65-102. 

As the pressure increases in the capillary, the trapped drop deforms and the pseu-doanulsion film thins. If the build up of the applied pressure, P pp, is slow, a condition of mechanical equilibrium will prevail so that the disjoining pressure in the... 

Even in the presence of coalescence, it is possible to predict the DSD for moderately concentrated systems. For cj) < 0.2, the drop phase does not appreciably affect the structure of the continuous phase flow field above the scale of the drop size. This allows single-phase flow concepts that describe the mechanical forces causing drop deformation, collisions, and film drainage to be used. 

Bentley, B. J., Leal, L. G. (1986). An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows. Journal of Fluid Mechanics, 167, 241-283. 

Figure 10.18. The rollback mechanism for oily soil removal surfactant adsorption at OfW and SAV interfaces acts to initiate drop deformation (a), followed by necking of the attached drop (b), and eventual detachment (c).

Drop deformation and breakup plays a decisive role in the evolution of polymer blend morphology. The breakup mechanism during polymer blending is very complex and is influenced by many variables, such as shear stress, viscosity ratio, stress ratio, Deborah numbo-and first normal force difference [1-3]. Visualization was used to get realtime information during the drop deformation and breakup process [1-5]. It is shown that drops can break up in simple shear flow via different modes such as breakup in the flow axis, erosion, parallel breakup, tip streaming and breakup along the vorticity axis [1-7]. 

Bubble and drop breakup is mainly due to shearing in turbulent eddies or in velocity gradients close to the walls. Figure 15.11 shows the breakup of a bubble, and Figure 15.12 shows the breakup of a drop in turbulent flow. The mechanism for breakup in these small surface-tension-dominated fluid particles is initially very similar. They are deformed until the aspect ratio is about 3. The turbulent fluctuations in the flow affect the particles, and at some point one end becomes... 

The necking mechanism has also been investigated using theoretical and numerical techniques. The theoretical approach, based on small deformation analysis (Barthes-Biesel and Acrivos, 1973) for the case of low Ca or high p shows the formation of lobes on the drop for Ca > Cacrit - Numerical techniques (Rallison, 1981) for p = 1 give similar results. The general conclusion is confirmation of the experimentally determined curve for Cacrit the drops in this case may break up rather than extend indefinitely. 

Contributions to pressure drop have also been studied by lattice Boltzmann simulations. Zeiser et al. (2002) postulated that dissipation of energy was due to shear forces and deformational strain. The latter mechanism is usually missed by capillary-based models of pressure drop, such as the Ergun equation, but may be significant in packed beds at low Re. For a bed of spheres with N — 3, they found that the dissipation caused by deformation was about 50% of that... 

Mechanically imposed oscillations at frequencies of 5-50 cycles sec. cause increases of up to 4 times in the rates of extraction of acetic acid from drops of CCI4 into water (79). The increase is due to the periodic deformation of the drops causing fluid circulation inside and outside, particularly at certain resonant frequencies. 

Break up of drops accelerated by air blasts (including shock waves) can occur by an inverted bag mechanism similar to that described in Section A above, for = UApd /a between about 16 and 10 (HI, H2, H4, L6). Reichman and Temkin (R7) give a detailed description of four stages of bag-type breakup. Under some circumstances, deformation preceding breakup appears more like a parasol than an inflating bag (SI2). The distance x moved by the drop is given approximately by... 

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