A self-control mechanism that stabilizes the size of Rhodamine B-doped water microdroplets standing on a superhydrophobic surface is demonstrated. The mechanism relies on the interplay between the condensation rate that was kept constant and evaporation rate induced by laser excitation which critically depends on the size of the microdroplets. The radii of individual water microdroplets (>5 um) stayed within a few nanometers during long time periods (up to 455 seconds). By blocking the laser excitation for 500 msec, the stable volume of individual microdroplets was shown to change stepwise.
With their almost spherical geometries and smooth surfaces, liquid microdroplets are naturally attractive to function as optical microcavities. They host high quality whispering gallery modes (WGMs) which inspired various applications in areas as: laser diagnostics 1, 2 , atmospheric science, biology, and interfacial chemistry. Size control has been an important challenge in applications using microdroplets of liquids with relatively high vapor pressures.
This hindered detailed studies of the dynamics at specific gas-liquid interfaces. Only very recently single water microdroplets were analyzed for long time periods 3,4 . In these experiments, microdroplets with initial salt concentations between 0.04-1.28 M reached to a stable volume by evaporation in a humidity controlled chamber.
We have previously demonstrated the tunability of WGMs of water microdroplets on superhydrophobic surfaces in a large spectral window 5 . Here, we show that the observed volume stability of dye-doped water microdroplets is due to the ambient humidity and size dependent laser absorption, and we introduce a mechanism that allows the volume of microdroplets to be changed stepwise without the need for any complex position control scheme such as optical tweezing 3,4 or electric field 6 trapping.
Scattering of a plane electromagnetic wave by a dielectric sphere is explained by Lorenz -Mie theory. Derivation of Lorenz -Mie theory has been extended to incorporate an incident focused Gaussian beam 7,8 . Enhanced internal field intensities have been predicted from these analyses when resonance conditions (spectral, spatial, and polarization) are met between the excitation laser beam and specific WGMs. The resulting enhanced absorption was demonstrated using Rhodamine 6G doped ethanol microdroplets in air 9 . Microdroplets having a critical size showed much larger absorption efficiencies compared to microdroplets with diameters differing by 4 nm.
Size dependent absorption phenomenon plays a crucial role in the realization of the reported high precision volume stabilization mechanism. Figure 1 shows the calculated absorption efficiency ( abs Q ) and modified absorption efficiency ( abs Q ~) as a function of radius (R) for a sphere having a refractive index equal to that of 50 µM Rhodamine B-doped water (n=1.33+4⋅10 -5 i) 10 . In Fig. 1a, calculation results are presented for a plane wave excitation (λ = 532 nm, transverse polarized), where TE and TM modes appear. Fig. 1b-c simulate our experiment, with a tightly focused Gaussian beam (λ = 532 nm, ω 0 = 250 nm, linearly polarized along the x direction), and were calculated using the localized model developed by Gouesbet et al. 11 with an algorithm introduced by Lock 12 . abs Q and abs Q ~ are the ratios of the total power absorbed by the sphere to the power incident upon the projected area of the sphere and to the total power of the incident beam respectively. In Fig. 1a the first order modes are suppressed due to the high absorption coefficient. For an absorbing sphere, the suppression of the higher quality lower order modes with increasing absorbance of the dielectric medium has also been reported previously [13][14][15] . In Fig. 1b-c
An ultrasonic nebulizer sprayed 50 µM Rhodamine B-doped water microdroplets (diameters between ~ 1-30 µm) into a home-built current controlled mini humidity chamber 5 .
Generated microdroplets landed on a superhydrophobic surface where they rested with a nearly spherical shape. A nichrome wire resistor attached to the liquid reservoir of the nebulizer allowed for control of the ambient humidity, and hence condensation rate of water microdroplets. Superhydrophobic surfaces were prepared by spin coating hydrophobically coated silica nanoparticles (Degussa AG, Aeroxide LE1) on thin glass substrates from 50 mg/ml dispersions in ethanol 17 . Resulting films had nanometer scale surface roughness and were transparent to visible light. The average contact angle of 2 mm diameter water droplets on these surfaces was measured to be 152.6 °.
Single microdroplets were excited with a continuous wave green laser (λ = 532 nm, spolarized) within resolution limited spots located away from the center in the direction shown as x in Fig. 1 and in the inset of Fig. 2. For microdroplets discussed in Fig. 234, the laser focus was positioned in the vicinity of the microdroplet’s rim while for the microdroplet discussed in Fig. 5 the laser focus was positioned at almost half-radius. Upon excitation, Rhodamine B in the microdroplets served for two purposes: (i) as the absorbing agent for volume stabilization, and (ii) as the fluorescent probe enabling the observation of the WGMs in the fluorescent spectra collected from individual water microdroplets 18 . Changes in the microdroplet volume were monitored through these WGMs. A high numerical aperture microscope objective (60x, NA=1.4) was used in the inverted geometry both for excitation and collection of the fluorescence. The c
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