Droplet polydisperse distribution

Light Scattering Technique. Properties of the light scattered by a large number of droplets can be used to determine droplet size distribution. Dobbins et al. 694 first derived the theoretical formulation of scattering properties of particles of arbitrary sizes and refractive indices in polydispersions of finite optical depth. Based on... 

It is probable that numerous interfacial parameters are involved (surface tension, spontaneous curvature, Gibbs elasticity, surface forces) and differ from one system to the other, according the nature of the surfactants and of the dispersed phase. Only systematic measurements of > will allow going beyond empirics. Besides the numerous fundamental questions, it is also necessary to measure practical reason, which is predicting the emulsion lifetime. This remains a serious challenge for anyone working in the field of emulsions because of the polydisperse and complex evolution of the droplet size distribution. Finally, it is clear that the mean-field approaches adopted to measure > are acceptable as long as the droplet polydispersity remains quite low (P < 50%) and that more elaborate models are required for very polydisperse systems to account for the spatial fiuctuations in the droplet distribution. 

The preliminary results obtained show that the initiation limits for polydispersed mixtures and stability of flame propagation strongly depend on inhomogeneity of particles (droplets) concentration distribution typical for the majority of practical cases wherein the ignition and combustion of polydispersed mixtures take place. Thus to ensure stable ignition and combustion characteristics... 

DOP polydisperse aerosol generated by blowing air through liquid dioctyl phthalate (DOP) at room temperature. The approximate light-scattering mean droplet size distribution of the aerosol is ... 

On the other hand, for a polydisperse collection of condensation nuclei (particles > 0.1 p,m in diameter), it can be seen from Eq. 15.15 that the rate of growth of small droplets will be faster than the rate of growth of larger droplets. Thus, as long as there is an excess of vapor for condensation, there will be a tendency for condensing droplet size distributions to become more homogeneous. 

Valentas and Amundson (V3) studied the performance of continuous flow dispersed phase reactors as affected by droplet breakage processes and size distribution of the droplets. Various reaction cases with and without mass transfer were studied for both completely mixed or completely segregated dispersed phase. Droplet size distribution is shown to have a considerable effect on the efliciency of a segregated reaction system. They indicated that polydispersed drop populations require a larger reactor volume to obtain the same conversion as a monodispersed system for zero-order (or mass-transfer-controlled) reactions in higher conversion regions. As the dispersed phase becomes completely mixed, the distribution of droplet sizes becomes less important. These interactions are un-... 

This results from the finite solubility of the liquid phases. Liquids which are referred to as being immiscible often have mutual solubilities which are not negligible. In the case of emulsions, which are usually polydisperse, the smaller droplets will have a greater solubility compared to the larger droplets (due to curvature effects). With time, however, the smaller droplets will disappear and their molecules will diffuse to the bulk and become deposited on the larger droplets. With time, the droplet size distribution wiU shift to a larger value. 

The theoretical description in terms of spherical harmonics also yields a relation between the size polydispersity index p of the microemulsion droplets and the bending elastic constants [43]. The quantity p is accessible by SANS [51, 52, 59-61]. For polydisperse shells as obtained by using deuterated oil and heavy water for the preparation of the microemulsion (contrast variation), one can account for the droplet polydispersity by applying an appropriate form factor, e.g. containing a Gaussian function to model the size distribution [52, 59, 62]. A possible often-used choice is the following form factor... 

Here, t is a parameter describing the thickness of the surfactant layer and a (or p) contains the information about the size polydispersity of the micro emulsion drops. R0 is the mean value of the shell inner and outer radii. Besides this approach other distribution functions were also already applied to model the droplet polydispersity [52]. The absolute scattering intensity I(q), which is the experimentally observed quantity is given by... 

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%. 

Emulsions with PEG-12 content of 1.5 to 2.5wt.% (0.1 wt.% acrylate) stiU have a broad but monomodal droplet size distribution (Fig. 6C) and at PEG-12 concentrations >3.5 wt. % monomodal size distributions (Fig. 6F) with a lower degree of polydispersity appear. A similar behavior for model emulsions is reported in [35]. 

For emulsions with low acrylate (0.1 wt. %) and PEG-12 concentrations up to 5.0wt. % the t mean values of aged emulsions are higher than in fresh emulsions. This is consistent with results from [18] and [28]. The droplet size distributions of the aged emulsions SE47-01-05-17 to SE47-01-50-12 reveal a polydispersity similar to that of fresh emulsions but the distributions are bimodal (compare Eig. 7A) with a clear increase of larger droplets with diameters of approx. 30-40 xm. This indicates droplet coalescence over the 12-month storage. 

White AJ, Hounslow MJ (2000) Modelling droplet size distributions in polydispersed wet-stream flows. Int J Heat Mass Transfer 43(11) 1873-1884... 

Polydispersity is a measure of the uniformity of a droplet size distribution and typically varies from 0.0 to 1.0 (unit-less) (Constantinides and Yiv, 1995), where values of 0.000 to 0.02 indicate a monodisperse or nearly monodisperse distribution, values of 0.02-0.08 are common for narrowly-distributed droplet sizes, and values higher than 0.08 indicate broad distributions. Despite microemulsions being polydispersed, they are frequently interpreted as being monodispersed to simplify analysis. 

Experiments have been conducted on emulsions containing 20% v/v of a mixture of heptane (90% v/v) and hexadecane (10% v/v), emulsified with 0.35% nonionic surfactant in the aqueous phase. The aqueous phase also contained 0.2% sodium azide as preservative. The emulsions were prepared using a Waring Blender, and their droplet size distribution revealed a polydisperse distribution, with weight mean radius 2 im. The emulsion was stable to coalescence during the timescale of the experiments. 

The destruction of dense emulsions is a rich domain. A large variety of behavior is observed. At the macroscopic scale, the system may exhibit a demixtion, as represented by Figure 8.21, or an homogeneous destruction (the emulsion remains macroscopically homogeneous at any time). At the colloidal scale, the droplet size distribution may change from almost bimodal to polydisperse or very monodis-perse. In addition, when the continuous phase spinodally decomposes, one phase may cause severe destruction, as described in Section 8.4. 

Emulsions are dispersions of two immiscible liquids into each other. They are thermodynamically unstable, but the addition of surfactant molecules can provide significant kinetic stability. Emulsions are extensively used in food, cosmetic, and pharmaceutical industries, just to name a few. Because of the thermodynamic penalty, emulsion formation requires an energy input. In bulk systems, this can most easily be achieved by vigorous stirring or shaking of the whole oil/water/surfactant system. This approach leads to an pulsion with broad droplet size distribution. Microfluidics allows for the minimization of polydispersity and the creation of droplets that are virtually identical in size. 

In order to characterize quantitatively the polydisperse morphology, the shape and the size distribution functions are constructed. The size distribution function gives the probability to find a droplet of a given area (or volume), while the shape distribution function specified the probability to find a droplet of given compactness. The separation of the disconnected objects has to be performed in order to collect the data for such statistics. It is sometimes convenient to use the quantity v1/3 = [Kiropiet/ ]1 3 as a dimensionless measure of the droplet size. Each droplet itself can be further analyzed by calculating the mass center and principal inertia momenta from the scalar field distribution inside the droplet [110]. These data describe the droplet anisotropy. 

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