Droplet deformation characteristics

Atomization, or generally speaking droplet generation, is an extremely complex process that cannot yet be precisely predicted theoretically. The lack of general theoretical treatment of droplet processes has led to the development of numerous empirical correlations for droplet properties as a function of process parameters and material properties. In this chapter, empirical and analytical correlations for the prediction of droplet properties, such as droplet size distribution and droplet deformation characteristics will be summarized from experimental observations and theoretical analyses in available literature. 

Better accounting is needed of wetted perimeter, droplet deformation, vapor flow momentum and frictional forces on droplets, and geometric characteristics. 5. This rather qualitative presentation serves primarily to indicate the magnitude of Dpt and. more importantly, to... 

Examining the various timescales involved shows that droplet evaporation is commonly diffusion limited. Since the characteristic vapor diffusion times are well below the typical droplet evaporation times [2], the vapor concentration is assumed to adapt instantaneously to a droplet deformation, and within the so-called quasisteady approach, the dynamics of the evaporation is controlled solely by the diffusional mass transport from the droplet surface into the ambient gas phase. A characteristic vapor distribution above the droplet, obtained by finite-element simulations, is shown in Fig. la. The... 

To constitute the We number, characteristic values such as the drop diameter, d, and particularly the interfacial tension, w, must be experimentally determined. However, the We number can also be obtained by deduction from mathematical analysis of droplet deforma-tional properties assuming a realistic model of the system. For a shear flow that is still dominant in the case of injection molding, Cox [25] derived an expression that for Newtonian fluids at not too high deformation has been proven to be valid ... 

The time tb for a droplet to undergo deformation prior to secondary breakup is a function of Ohd and a characteristic time... 

If the droplet or bubble is deformable (Ca is not negligible), then the emulsion will be viscoelastic, even if the two fluids composing it are both Newtonian. The characteristic... 

If flow is continuous, or strains are large, droplets or domains deform greatly or burst, and the above expressions for the moduli are inapplicable. Although there have been some experimental and theoretical studies of the droplet size and size distributions in such flows (see Section 9.2.2), there seem to be few theoretical results that allow prediction of the stresses in such flows. These flows are immensely complex the stresses depend not only on the viscoelastic characteristics of the two components of the emulsion, but also on the micromorphology of the phases, which, in turn, depends on the history of the flow. 

The characteristic relaxation time t = 1 /(Hp was found to be insensitive to the droplet size a, weakly dependent on the continuous-phase viscosity, and perhaps weakly dependent on r and M also. Although the complete scaling law for r cannot be deduced from this limited set of data, it is evidently influenced by lubrication flow of liquid in the thin films between the deformed droplets, and perhaps also by the circulatory flow in the viscous droplets. 

The pendant of equation (1.5.11 has been experimentally verified by O Konski and Gunther ) for the case of hanging drops. Moriya et al. ) studied the time dependence of the deformation in very viscous fluids. This relaxation can be well represented by multiplying the r.h.s. with a factor (1 - exp(-t/r)l where t is the time and T a characteristic relaxation time, proportional to the sum of the viscosities of droplet and medium. It is recalled that t/r is just the reciprocal Deborah number De" . 

The importance of FIPI is twofold. It can be used to promote phase inversion without changing the thermodynamics of the system to obtain a higher entropy state, or it is possible to delay phase inversion while reducing the system entropy. The characteristics of the microstructure formed (such as emulsion droplet size) are dependent on the type of microstructure and deformation (shear, extension, or combined), as well as the deformation rate. To maximize the fluid micro-structure/flow field interactions, the flow fleld must be uniform, which requires the application of the flow field over a small processing volume, which can be achieved by using MFCS mixers or CDDMs. 

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. 

Drawing is a process similar to dry-spinning, in which nanofibres are drawn slowly from the droplet of a polymer solution by a micropipetter. The polymer solution is made from a viscoelastic material (i.e., one exhibiting both viscous and elastic characteristics upon deformation) that can accommodate the extensive deformation caused by drawing and retain the integrated form of an ultrafine fibre (Ondarcuhu and Joachim, 1998). 

The majority of microfluidic methods produce droplet using passive devices generating a uniform, evenly spaced, continuous stream of droplet, whose volume ranges from femtoliters to nanoliters. Their operational modes take advantage of the characteristics of the flow field to deform the interface and promote the natural growth of interfacial instabilities, avoiding in this way the necessity of any local external actuation. Droplet polydispersity, defined as the ratio between the standard deviation of the size distribution and the mean droplet size, can be as small as l%-3%. 

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