Droplet refractive index

Several theories have been developed to explain the rainbow phenomena, including the Lorenz-Mie theory, Airy s theory, the complex angular momentum theory that provides an approximation to the Lorenz-Mie theory, and the theory based on Huy gen s principle. Among these theories, only the Lorenz-Mie theory provides an exact solution for the scattering of electromagnetic waves by a spherical particle. The implementation of the rainbow thermometry for droplet temperature measurement necessitates two functional relationships. One relates the rainbow angle to the droplet refractive index and size, and the other describes the dependence of the refractive index on temperature of the liquid of interest. The former can be calculated on the basis of the Lorenz-Mie theory, whereas the latter may be either found in reference handbooks/literature or calibrated in laboratory. 

The fiber-taper coupling scheme was applied to liquid-immersed water-droplet microsphere resonators by Hossein-Zadeh and Vahala35. The water droplets of diameter 0.5 1 mm were generated by a syringe and immersed in a low refractive immiscible cladding liquid - an index matching oil with a refractive index of 1.3, and trapped on a silica sphere which was fixed to the bottom of a liquid container... 

Polarization ratioing thermometry has been proposed as a means of measuring the refractive index of a droplet and relating it to the droplet temperature. However, this approach does not have the... 

Chylek et al. (1983) showed that, by comparing experimental resonance spectra with spectra computed using Mie theory, the size and refractive index of a microsphere can be determined to about one part in 10. Numerous investigators have used resonance spectra to determine the optical properties of microspheres since Ashkin and Dziedzic observed resonances. A recent example is the droplet evaporation study of Tang and Munkelwitz (1991), who measured the vapor pressures of the low-volatility species dioctyl phthalate (DOP), glycerol, oleic acid, and methanesulfonic acid (MSA). This... 

Phase functions can also be used to measure the size and refractive index of a microsphere, and they have been used by colloid scientists for many years to determine particle size. Ray et al. (1991a) showed that careful measurements of the phase function for an electrodynamically levitated microdroplet yield a fine structure that is nearly as sensitive to the optical parameters as are resonances. This is demonstrated in Fig. 21, which presents experimental and theoretical phase functions obtained by Ray and his coworkers for a droplet of dioctylphthalate. The experimental phase function is compared with two... 

Note that the number of diffraction peaks decreases with time as the droplet diameter decreases, and the number density of peaks is very nearly proportional to the droplet size. The intensity of the scattered light also decreases with size. The resolution of the photodiode array is not adequate to resolve the fine structure that is seen in Fig. 21, but comparison of the phase functions shown in Fig. 22 with Mie theory indicates that the size can be determined to within 1% without taking into account the fine structure. In this case, however, the results are not very sensitive to refractive index. Some information is lost as the price of rapid data acquisition. 

Equations (126) and (127) can be used to calculate activity coefficients from evaporation data, for a, Zj, da fdt, and dz /dt are measurable quantities. The resonance spectrum of an evaporating droplet is highly sensitive to both size and refractive index, and the refractive index of a binary system is a unique... 

Allen et a/. (1991) performed these computations for 1-octadecene droplets, and they measured the evaporation rate of the droplets as a function of laser power. To determine the absolute irradiance /, of the laser beam, they also measured the force on the particle exerted by the laser beam using the techniques discussed above. The photon pressure force is given by Eq. (87), which involves the complex refractive index. The real component of the refractive index n was determined from optical resonance measurements, and the imaginary component was obtained iteratively. That is, they assumed a... 

Table III shows that the experimental and predicted evaporation rates are in good agreement at all beam intensities. There is some inconsistency at the highest power levels. It was difficult to maintain the droplet in the center of the laser beam at the highest power level, and the measured evaporation rate is somewhat low as a result of that problem. Additional computations demonstrate that the predicted evaporation rate is quite sensitive to the choice of the imaginary component of N, so the results suggest that this evaporation method is suitable for the determination of the complex refractive index of weakly absorbing liquids. For strong absorbers, the linearizations of the Clausius-Clapeyron equation and of the radiation energy loss term in the interfacial boundary condition may not be valid. In this event, a numerical solution of the governing equations is required. The structure of the source function, however, makes this a rather tedious task.

Tallin (1988) recognized that the refractive index change associated with the OCT/Brj reaction would affect optical resonances of a reacting droplet, so he carried out bromination experiments with levitated droplets using the apparatus shown in Fig. 43. 

The studies of Tallin and Buehler indicate that microparticle spectroscopic techniques can be used to follow gas/microparticle chemical reactions. The use of morphological resonances to determine the refractive index of a reacting droplet has limited applicability because there must be a unique relationship between composition and refractive index to allow the method to be used to follow chemical reactions. Raman spectroscopy has broader applications, but one must deal with morphological resonances if droplets are... 

Figure 3.7. State of aggregation of water and glycerol droplets in different oils (C H2 +2) as a function of n and of the absolute value refractive index mismatch Arir between the dispersed and the continuous phase. The surfactant concentration (SMO) is equal to 1 wt%. The droplet volume fraction is set at 5%. Water and glycerol droplets have a diameter close to 0.4 um. Black symbols, aggregated droplets empty symbols, dispersed droplets. (Adapted from [13].)...

Spin the samples with 200 000 x g at 4 °C for 15 -17 h. After the run, displace the gradient using a more dense solution, e.g., 40% sucrose in Soln. A, colored by a droplet Amido Black 10 B solution. The principle of a displacement apparatus is shown in Fig. 5.4. The RNA content of the fractions is measured either by reading the UV absorption at 260 nm or, if labeled material was used, by counting the radioactivity. To monitor the sucrose gradient, estimate the refractive index of the obtained fractions (concentration, density and refractive index of sucrose solutions are given in Table 8.17). 

Table 4.1 Scattering Coefficients for a Water Droplet in Air with Size Parameter x = 3 and Complex Refractive Index m = 1.33 + 10 8...

Three peaks, labeled a 0, aj0, a Q, in the real part of a60(x) for a water droplet are shown in Fig. 11.9 the real part of the refractive index is fixed but the imaginary part is varied. These optical constants could be obtained by, for example, adding a little dye (food coloring) to water this would increase k without appreciably changing n. Note that the horizontal scale is different for... 

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