Abstract

An evolution of the alignment of the spherical micro-suspensions of an evaporating microdroplet wasstudied by observing the scattered intensity of laser light. The studied aqueous microdroplet of standardizedsuspensions was a random structure of an arrangement changing with time. The droplet was kept inside theelectrodynamic trap and was illuminated with the two orthogonally polarized laser beams. Interferencescatterograms in the four (paralel- and cross-) polarization geometries were registered with a CCD camera.

The performed analysis of interference fringes of the scatterograms for s polarization allowed us to findthe temporal evolution of droplet radius. The resulting evaporation rate temporal dependence enabledevaluation of the surface pressure evolution of the droplet of suspension during evaporation. A numericalmodel of surface structure formation, based on our observations, was proposed.

The presence of cross-polarized light results from multiple scattering by inclusions, or by multiplestructures formed by inclusions, inside the droplet or on droplet surface. The changes of depolarized lightintensity are associated with the evolution of the fractal dimension of structures (scatterers) formed within thedroplet.

[1] G. Derkachov, K. Kolwas, D. Jakubczyk, M. Zientara, and M. Kolwas, Drying of a Microdroplet of Water Suspension of Nanoparticles: from SurfaceAggregates to Microcrystal, J. Phys. Chem. C, 112, 16919 (2008)

[2] D. Jakubczyk, M. Kolwas, G. Derkachov, K. Kolwas, Surface states of micro-droplet of suspension, J. Phys. Chem. C, 113(24) 10598 (2009)[3] D. Jakubczyk, G. Derkachov, M. Zientara, M. Kolwas, K. Kolwas. Determination of mass and thermal accommodation coefficients from evolution of

evaporating water droplet. Proc. SPIE, 5849 162 (2005).[4] D. Jakubczyk, G. Derkachov, M. Zientara, M. Kolwas, K. Kolwas. Light scattering by microdroplets of water and water suspensions. Proc. SPIE, 5849 62

(2005)

LIGHT SCATTERING BY A SPHERE OF RANDOM STRUCTURE WITH EVOLVING ARRANGEMENT.

Gennadiy Derkachov, Anastasiya Derkachova, Daniel Jakubczyk, Krystyna Kolwas, Maciej KolwasInstitute of Physics, Polish Academy of Sciences,

Al. Lotników 32/46, 02-668 Warsaw

The dynamics of evaporation-driven nanostructures assembly was numerically simulated (in MATLAB andSIMULINK) for the water droplet containing 1500 polystyrene nanosphere of 200 nm diameter. Thedynamics of nanoparticle assembly and the shapes of intermediate and final structures are determined bythe relative timescales of evaporation, and nanoparticle mobility in the medium. The random Brownianmovements of nanospheres in liquid leads to their sticking. The movement of inclusions is described withthe Newton equation with the flow resistance defined by the viscosity coefficient. As the nanosphere hitsthe liquid interface it is, in our model, additionally subjected to the surface adsorbing force, which isassumed to be proportional to the distance between the nanosphere center and the interface. The rate ofwater evaporation from the droplet was taken from the experiment (smoothed a(t)). A survey of snapshotsof aggregate morphologies obtained is provided in Figure

Simulation of Topographic Nanostructure Patterning

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Drying Droplet Size Evolution.

The droplet radius temporal dependence a(t)was derived from the analysis of thefrequency of the spatial modulation of thescattered light intensity Ivv(Θ,t) correspondingto successive frames of the registered video.The droplet radius is found from spatialfrequency of the scatterograms. The methodis based on the simple relationship betweenthe spatial frequency ωs of Ivv(Θ) and the sizeparameter X=2πa/λ, where λ is thewavelength of the scattered light field. Thisrelationship was derived with a little help ofMie scattering theory but can be perceived aspartially phenomenological. In the range ofsize parameters 0 < X < 300, this relationshipcan be expressed as:

ωs = kX with k = 4.83×10-3. ωs can be found by applying the fast Fouriertransform (FFT) in respect Ivv(Θ)- the intensityof interference fringes. This relationship ispractically independent of the (effective)refractive index of the droplet. The method ofspatial frequency analysis providedtrustworthy information on the dynamics ofthe effective size evolution as long as thedistinct interference pattern was visible. Aslong as the droplet can be treated as aspherical, globally homogeneous object, itsradius can be found with the accuracy betterthan 8%.

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By analyzing the evaporation rate of a droplet (withinthe framework of a model that we adopted), we wereable to determine the effective surface pressureevolution (changes of surface tension). As the droplet ofsuspension looses water and evolves from liquid to dryaggregate of inclusions, its surface undergoes transitionsthrough various surface thermodynamic states.

Drying Droplet Size Evolution

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Evolution of Fractal Dimension

Experimental Setup

The schematic diagram of the experimental setup is presentedin the Figure above. Single droplets of homogeneous aqueoussuspension of standardized nanospheres were injected with apiezoelectric injector into the quadrupole electrodynamic trapmounted in a small climatic chamber. The climatic chamberprovided stable and homogeneous temperature field. Twocounterpropagating laser beams of orthogonal polarizationswere used simultaneously for monitoring the dropletevolution. These were a He-Ne laser beam of 632 nmwavelength (red light, polarized perpendicularly to theobservation plane), ∼18 mW CW, and a Nd: YAG laser beam of532 nm wavelength (green light, polarization parallel to theobservation plane)), ∼25 mW CW. Two linear polarizers wereused in the detection channel: first with the polarizationdirection parallel to the laser beam polarization (upper half ofthe channel) and the second perpendicular to it (the lower halfof the channel). The spatial distribution of the intensity wasregistered with the 12-bit color digital CCD camera. It allowedus to separate spectrally the elastically scattered light andattribute it to appropriate incident beam polarization.

Some examples of the interferencepatterns of light scattered by thetrapped droplet/crystalite at differentstages of water evaporation.

Green and red fringes/speckles in thedetection channel

The droplet of suspension is a random structure of anarrangement changing with time. As the droplet ofsuspension looses water, the randomly volume distributedinclusions evolve trough various ordering states. Apolarization degree of light scattered by a droplet followssome changes in inclusions ordering. The correlationfunction of suspension density is related to the polarizationdegree of the scattered light [5]. It allows us to describe thestructures formed during evaporation by one number: thefractal dimension D.

The fractal dimension evolution is shown in the figureabove.

[5] C.M. Sorensen Aeros. Sci. and Tech. 35: 648-687 (2001)