Experiments in Fluids

, Volume 52, Issue 3, pp 795–807

Particle image velocimetry and infrared thermography in a levitated droplet with nanosilica suspensions

Research Article

DOI: 10.1007/s00348-011-1114-2

Cite this article as:
Saha, A., Basu, S. & Kumar, R. Exp Fluids (2012) 52: 795. doi:10.1007/s00348-011-1114-2

Abstract

Preferential accumulation and agglomeration kinetics of nanoparticles suspended in an acoustically levitated water droplet under radiative heating has been studied. Particle image velocimetry performed to map the internal flow field shows a single cell recirculation with increasing strength for decreasing viscosities. Infrared thermography and high speed imaging show details of the heating process for various concentrations of nanosilica droplets. Initial stage of heating is marked by fast vaporization of liquid and sharp temperature rise. Following this stage, aggregation of nanoparticles is seen resulting in various structure formations. At low concentrations, a bowl structure of the droplet is dominant, maintained at a constant temperature. At high concentrations, viscosity of the solution increases, leading to rotation about the levitator axis due to the dominance of centrifugal motion. Such complex fluid motion inside the droplet due to acoustic streaming eventually results in the formation of a ring structure. This horizontal ring eventually reorients itself due to an imbalance of acoustic forces on the ring, exposing larger area for laser absorption and subsequent sharp temperature rise.

1 Introduction

Vaporization of liquid droplets has been studied widely in the literature due to its applications in combustion, thermal coating, ink-jet printing, spray cooling, drug delivery, and surface patterning. Many of these studies involve wall-droplet or droplet–droplet interactions. It has been proven that binary droplet (containing solute) shows a preferential solute-migration pattern during drying process. Park and Moon (2006) discussed the role of competing effects of natural convection and Marangoni flow in creating different structures due to solute migration. A well known “coffee ring” phenomena has been studied by Deegan et al. (1997, 2000). They analyzed the ring formation around the edge of a vaporizing liquid pool (droplet) on a solid surface. They reported that the effects of surface tension gradient, solute diffusion, gravity are negligible for this ring formation. They showed that outer edge gets pinned to the solid surface. This results in an outward fluid flow due to squeezing of the free surface in order to compensate the evaporation loss. They also experimentally supported their theory of this contact line deposition of particles.

Containerless processing of materials also deals with liquid droplet evaporation without any interactions with surface or other droplets. Levitation is one of the adopted techniques to study vaporizing droplets in the absence of any surface effects. Studies on different levitation processes using magnetic, non-magnetic material and live animals have been performed extensively by several research groups (Brandt 2001; Xie and Wei 2007). In an acoustic levitator, small objects can be suspended with the help of a standing acoustic wave. The pressure difference between two poles of the objects counteracts the gravity. Yarin et al. (1998) showed through a detailed analytical work that acoustic streaming has a strong effect on the aspect ratio and vaporization characteristics of a suspended droplet. In addition to this work, Tian and Apfel (1996) experimentally studied the effect of acoustic streaming on the evaporation process which showed good agreement with the analytical work. However, these studies involved only pure liquid droplets.

Later Yarin et al. (2002) also studied natural drying process of liquid droplets containing glass beads. They delineated two distinct stages of evaporation: the first stage is due to pure vaporization of the solvent where the droplet diameter reduces with time, whereas in the later stage it becomes constant due to the formation of a porous solid shell of glass beads at the droplet surface. However, they noted that evaporation process still continues after the pure evaporation phase through the porous structure. They experimented with different concentrations of glass beads and observed shorter pure evaporation phase for higher concentration levels. They were able to obtain a correlation between porosity of the final precipitate, drying temperature, initial mass fraction and initial droplet size. Their work did not involve external heating.

Laser heating of liquid droplets has been studied by many authors in different contexts. Park and Armstrong (1989), Lage and Rangel (1993) studied in detail the heat transfer and hydrodynamics of irradiated water droplets. (Sazhin et al. 2000; Sazhin 2006) reported computational and theoretical analyses concerning radiative heating of fuel droplets. Recently, Basu and Cetegen (2008) reported a computational study on the radiative heating of water droplet containing non-volatile solute. Most of these studies are theoretical or computational in nature. Experimental work on hydrodynamics and heat transfer of an irradiated binary droplet exhibiting solute agglomeration has not been studied before.

In our recent work (Saha et al. 2010), we studied vaporizing cerium nitrate droplet under laser irradiation. Our study showed four distinct stages of heating. Initial stage of “pure evaporation” displayed a sharp decay in diameter. In the next stage of “evaporation with precipitation” surface precipitation occurs due to substantial evaporation of water, which slows down the vaporization rate. In the next stage, cerium nitrate goes through thermal decomposition releasing nitrogen oxides. This results in repeated expansion and contraction of the droplet during this stage of “chemical reaction and bubble formation”. The gas released from the droplet through the solid crust forms a porous precipitate at the next stage. The final stage of “porous precipitate” is calm and passive in nature with no change in shape and morphology.

In this work, we present a detailed experimental study on laser heated nanosilica suspended water droplets. Our recent study (Kumar et al. 2010) showed preferential accumulation and agglomeration of suspended nano particles during heating process, which eventually forms ring or bowl shaped structures. These suspended nanosilica particles in the droplet do not undergo chemical reaction and phase transition as in our previous work (Saha et al. 2010) with cerium nitrate droplet. In the current study, we extended our previous work to delineate the effects of internal recirculation induced by acoustic streaming on solute migration and agglomeration through high speed imaging, IR thermography and particle image velocimetry. We will also present the details of the phase transitions of the nanosilica droplets (based on morphological and thermo-physical changes) as a function of concentration.

Optical diagnostics in levitated droplet have been reported by very few researchers. Omrane et al. (2004) studied naturally vaporizing droplet in the absence of external heating. They used 3rd and 4th harmonics of an Nd-YAG laser to perform optical measurements on the levitated droplet. They measured the temperature of the vaporizing droplet using Laser Induced Phosphorescence, and measured species concentration simultaneously using Laser Induced Fluorescence. However, owing to longer lifetime of phosphorescence they saw interference with the fluorescence signal. Yarin et al. (1997) used flow visualization technique to map the flow field outside of a droplet suspended in an acoustic levitator. They showed existence of vortex structures enclosing the levitated droplet induced by acoustic streaming. Recently, Abe et al. (2007) reported stereo PIV measurements in a levitated droplet of water and glycerol. They used droplet sizes of around 4 mm. Their study showed the presence of a strong single recirculation cell within the droplet.

Agglomeration of suspended particles is an important field of study in colloid science. Two important phenomena in this field are perikinetics and orthokinetics (Mason 1977). Perikinetics is a process of agglomeration of suspended particles due to Brownian rotation and diffusion. On the other hand, orthokinetics is an agglomeration process arising due to shear/velocity gradient within the liquid layers. He used numerical and experimental approach to understand different orthokinetic effects in rotational and irrotational flow in a dispersed flow field. Bremer et al. (1995) estimated time scale of macroscopic aggregation or the time scale when precipitation becomes visible. They also showed that the number of bond formed is as important as aggregation rate for the aggregation process. This led them to define a physical time scale based on orthokinetic sedimentation which did not include arbitrary parameters like visibility of precipitation.

The current work is an experimental analysis of an acoustically levitated droplet containing nanosilica solutions at different concentrations heated by a CO2 laser. Laser irradiation of the droplet shows agglomeration of suspended nanoparticles resulting in solid structures. This paper analyzes the effect of concentration on the shape of final structure using high speed imaging, IR thermography and particle image velocimetry.

2 Experimental set up

This work uses similar experimental setup used in our previous works (Saha et al. 2010; Kumar et al. 2010). The basic experimental setup employs an open ultrasonic levitator (Tec5 single axis ultrasonic levitator, 100 kHz, 154 dB) to levitate nanosilica suspended water droplets. The amplitude of the pressure field was kept constant at 154 dB throughout all experimental runs. A 30 W tunable CO2 laser which irradiates at wavelength of 10.6 μm was used to heat the droplet. As shown in Fig. 1, a high speed camera (Fastec TSHRMM with maximum frame rate of 16,000) was placed at an angle of 30° with the axis of the laser to image the heating event. To achieve a moderate resolution of 480 × 320 pixels, the framing rate was kept limited at 1,000 fps. A zoom lens assembly (Navitar 6000) was used to achieve high spatial resolution. A goose neck probe light was used to backlight the droplet.
Fig. 1

Experimental setup [adapted from our previous work, Saha et al. (2010)]

The temperature of the droplet was measured using an IR camera located perpendicular to the laser axis as shown in Fig. 1. The IR Camera (FLIR Silver: calibrated for a temperature range of −5 to 200°C) was attached to a special zoom lens to achieve 3× magnification at a working distance of 40 mm. A working temperature range used in the current experiment was 25–80°C, with an integration time of 1.173 ms. The IR camera was operated at 100 fps.

To facilitate minute spatial adjustments, the levitator and the high speed camera were placed on two separate XYZ stages. The IR camera was stationed on an XY platform. The cameras and the laser were synchronized using an external delay generator.

Most of the diameter and temperature profiles were measured with an initial dropsize of 500 (±30) μm in diameter. The PIV experiments were done for a drop size of 700 μm in diameter. Commercially available 15% vol concentrated nanosilica dispersion in water was sonicated for 15 min to make different homogeneous concentrations. The laser intensity was maintained at 0.85 MW/m2.

The high speed images were analyzed using an edge detection method to calculate an equivalent volume of the droplet to obtain the instantaneous diameter. From these high speed images, the diameter change with time was determined. High speed images were also used to identify morphological changes and reorientation of the structures formed by nanosilica agglomerates.

The IR camera captured surface temperature of the droplet depending on the intensity of thermal radiation recorded by the infrared sensor within the camera. The emissivity for DI water was found to be 0.95–0.98 in Bremson (1968), and Wolfe and Zissis (1978). For this range of emissivity, the error in temperature was found to be utmost 0.3°C. In the current experiments, the emissivity of water was kept at 0.98. Fourier Transform Infrared Spectroscopy (FTIR) confirmed that the absorption coefficient does not change by more than 1% for 10.6 μm (laser wavelength) among the different concentrations of nanosilica solutions. To obtain the temperature data from individual frames, a zone of interest was defined around the droplet edge and the maximum and average temperature were recorded. The IR images were out of focus sometimes due to the small depth of field of the camera. Only the in-focus images were considered for data analysis. The IR camera was capable of recording temperature with an accuracy of ±0.1°C. There was no direct way of measuring the effect of nanosilica concentration on the emissivity. When the droplets of different nanosilica concentrations were suspended in the levitator, they all were found to show the same temperature (using emissivity value of 0.98 and without any heating) as ambient air, which was measured using a thermocouple. Therefore, including the effects of potential emissivity changes, the total uncertainty in temperature measurements may be estimated to be ±0.4°C.

2.1 PIV setup and uncertainties

In this work, particle image velocimetry has been performed on levitated droplets to understand the effect of viscosity on the flow field inside the droplet. In this study, PIV was restricted to non-heating conditions using three different liquids of different viscosities. The setup described in the previous section was modified for PIV as shown in Fig. 2. A dual pulsed Nd-YAG laser with 70 mJ/pulse energy has been used as the light source. The 532 nm output (green) of the laser of 4 mm diameter was converted to an estimated 65 μm thick light sheet using a plano-convex lens as shown in Fig. 2. The levitator was placed at the focal length of the lens, so that the laser sheet was formed at the location where the droplet was suspended.
Fig. 2

Experimental set up for PIV

A CCD camera (LaVision Imager Intense, 1,376 × 1,040 resolution) was used for imaging the droplet. The camera was attached to the Navitar zoom lens assembly to enhance the spatial resolution. The CCD camera, operated at dual frame mode, was synchronized with the laser using a Programmable Timing Unit. The maximum frame rate of the PIV system was 5 fps. The droplets were seeded using polystyrene fluorescent spheres (1 μm average diameter). The laser and the acoustic levitator were placed such that the laser sheet intersected the droplet at the central plane. This was achieved by slowly moving the levitator with respect to the laser using the x–y–z stage. A set of 100 image-pairs were recorded and analyzed after background subtraction for each case. The vectors were generated using 32 × 32 pixel interrogation windows. To screen out unreliable vectors, a threshold value for displacement to noise peak ratio was set to be 1.5, below which the displacement peak was discarded.

The random error associated with this statistical method in determining the displacement vectors decreases with the ratio of maximum displacement and linear size of interrogation window. Scarano and Riethmuller (1999) reported that for displacements more than 2 pixel, this random error is limited to 1% in case of 32 × 32 window size. However, an increase in the displacement of particles within interrogation windows also results in loss of correlation peak (Raffel et al. 1998). Here, the maximum displacement was kept limited to 15 pixels using the PIV processing software.

The uncertainty originating from inherent grid generation, correlation and peak validation becomes insignificant when 100 image pairs were used to achieve good quality vectors. The uncertainty in the measured velocity is also dependent on particle sizes. If the particle images are smaller than the pixel size, then it would increase the bias error in correlation function owing to finite numerical resolution. On the other hand, if the particle size is too large, then the random error due to irregularities in the image will be significant (Prasad et al. 1992). Santiago et al. (1998) showed that for particle diameters around 3–4 pixel, the resultant uncertainty in determining particle displacement can be limited to within 1/10th of the particle image diameter. In our PIV measurements within suspended droplets, the camera recorded digital images with resolution of 1,376 × 1,040 pixel and each image corresponded to an area of 1,650 × 1,300 μm, i.e., each pixel had an area of ~1.5 μm2. The seed particles with a maximum diameter of 1 μm, occupied approximately 4 pixels. Thus, the uncertainty involved within displacement of each particle is 0.1 μm. The PIV experiments involved 200 μs pulse separation time on an average, which led to an uncertainty of 0.5 mm/s in velocity measurements.

The other aspect of the seeding particle which needs to be considered is its ability to flow with the fluid. The response time of the particles provides information on how fast the particles can react in a sharply accelerating flow. The first order response of these spherical particles in constant flow acceleration can be characterized by the response time, \( \tau ={d_{\text{p}}^{2} \rho_{\text{p}}}/\upmu_1 \), where dp is particle diameter, ρp is density of the particle and μl is viscosity of the fluid. In the current experiment, for a diameter of polystyrene sphere of dp = 1 μm and ρp = 1.03 gm/cc, the response time is τ ~ 10−7 s. The separation used between two pulses was 200 μs, which is 3 orders higher than the response time. The separation time between laser pulses was chosen based on the velocity range of 0–0.3 m/s in the experiment. Higher separation time can lead to errors in velocity as explained earlier. The particle response time depends on particle size, and for a response time of 10−7 s which is considerably smaller compared to the pulse separation, the particle follows the flow without much time delay.

3 Experimental results

This section is broadly divided into two sub sections. The first section reports PIV results inside droplets without external heating. PIV is also useful to understand the effect of acoustic streaming induced flow patterns inside the droplet. The second section discusses the behavior of nanosilica droplets under laser irradiation. Different phenomena observed during the heating process have been explained in detail using PIV results.

3.1 PIV results inside a levitated droplet with no heating

As shown in our previous works (Kumar et al. 2010; Saha et al. 2010), flow induced by acoustic streaming plays an important role in solute migration in vaporizing droplet suspended in an acoustic levitator. The recirculation that results from acoustic streaming within the droplet depends on liquid properties such as viscosity and surface tension. Three types of fluid with an order of magnitude change in viscosity were considered for PIV studies as shown in Table 1. As will be noted later, viscosity increases with nanosilica concentration. However, the surface tension remains unaltered with increase in nanosilica concentration. Therefore, these fluids with nearly the same surface tension were used to mimic nanosilica suspensions of similar viscosity values so that the effects of viscosity can be delineated. Droplets with nanosilica suspension could not be used for PIV study since their presence within the droplet hindered the illumination of seed particles. This study was performed on three different liquids: Deionized Water, Cerium Nitrate solution (0.5 M) and Glycerol-water (3:2) solution. The surface tension and viscosity of these three liquids have been measured and tabulated in Table 1.
Table 1

Viscosity and surface tension of 3 liquids used for PIV

Fluid

Water

Cerium nitrate (0.5 M)

Glycerol-water solution (3:2)

μ/μwater

1

1.8

15

σ/σwater

1

1.02

1.08

Since only viscosity changes significantly in these fluids, it is expected that the current approach of performing PIV on these three liquids will correctly represent the velocity vectors expected in nanosilica suspensions at different concentrations.

Two-dimensional PIV was performed on a vertical plane intersecting the droplet at the center. The process has been detailed in Sect. 2.1. The resultant velocity vectors for these three liquids are shown in Fig. 3. Vectors fields depict the presence of a single recirculation zone around the droplet center. The predominant velocity component is in the tangential direction and the magnitude of the velocity increases with radius. Thus, the maximum velocity occurs at the droplet surface, and resembles the flow field of a forced vortex. Comparative analysis of velocity fields in three different liquids also reveals that with increase in viscosity the maximum and average velocity scale decrease. For the water droplet, the maximum velocity is 236 mm/s while for glycerol solution (15 cP), which has a viscosity 15 times that of water, maximum velocity reduces to 120 mm/s. For cerium nitrate solution with a viscosity of 1.8 times that of water, the magnitude of maximum velocity is 189 mm/s. The change in velocity is hence a nonlinear function of viscosity. This PIV analysis is also valid for initial stages of heating when solute agglomeration is not dominant. The PIV also provides a quantification of how the solute is transported by the flow field though in later stages with depletion of solvent, the flow structure is altered substantially with much reduced recirculation strength than what is shown in Fig. 3. However, it should be noted, that the relative difference in flow velocities as shown in Fig. 3 for different viscosity levels either remain unaltered or is exaggerated till the inception of the structure formation stage in nanosilica droplets.
Fig. 3

Velocity field inside the droplet for different viscosity levels

The velocity vectors measured here are in the vertical plane (Fig. 2). As reported in our previous works (Kumar et al. 2010; Saha et al. 2010), the droplet exhibits a rotation about vertical axis (levitator axis) as well. This will induce a velocity in a direction perpendicular to the plane of PIV measurement, which is not measured in the current study. Rednikov et al. (2006) studied the flow inside a levitated droplet analytically. Their work showed four recirculation zones within the droplet. However, they considered the flow field to be axisymmetric and did not consider the rotations. Trinh and Wang (1982) in their work on the oscillations of levitated droplet experimentally verified this four cell pattern as well. However, they also reported that when the oscillation reaches a critical value, the droplet starts rotating about its horizontal axis. This leads to a solid body rotation of the droplet, which can be observed as a single cell circulation in the center plane. Even after oscillation becomes significantly weaker, this rotation still persists. It is conjectured that the rotational instability arises from acoustic torque mainly due to (a) a possible misalignment or shift of droplet axis with levitator axis, (b) inhomogeneity in the droplet composition, (c) asymmetric heating (specific to our results involving directional laser heating). The proper alignment of the droplet with the levitator axis is rather difficult in a single axis levitator experiment. It is envisioned that the torque which imparts rotational motion on the droplet is primarily due to the misalignment of the drop from the levitator axis. In the current experimental work, high speed images show oscillations of the droplet as was also observed by Trinh and Wang (1982). For a single axis levitator, these oscillations and possible misalignment of the droplet axis with levitator become unavoidable, triggering solid-body rotation or single cell circulation. Furthermore, with reduction in drop size, the unbalanced torque imparts higher rotational speed due to smaller inertia. This was also observed in the PIV results for droplets with different diameters (not shown here). In the current experiments, the droplets were sub-millimeter in size, while Trinh and Wang (1982) used 10 mm droplets. During the nanosilica experiments, the asymmetric nature of heating further enhances the instability and unbalanced torque. Furthermore, the agglomeration of nanosilica leads to mass inhomogeneity across the top and bottom sectors of the droplet (as evidenced by the bowl shaped structure) leading to higher rotation rates.

It should be noted that the high speed images show rotation of the droplet about horizontal axis (Video 1) and vertical axis (Video 2) in addition to oscillations as also observed by Trinh and Wang (1982). It can therefore be safely inferred that oscillations and rotation lead to a break in symmetry and that the 4 cells predicted by Rednikov et al. (2006) merges into a single cell.

3.2 Heated droplets

Different concentrations of nanosilica have been used to delineate the effects of nanosilica concentration on the vaporization and agglomeration process. As the nanosilica droplets were heated by the laser and this heating process was recorded by high speed and infrared cameras. It will be shown in this section that depending on the concentration, the agglomerated nanoparticles may form two different structures, namely bowl and ring. Analysis of high speed images clearly shows the presence of two distinct stages during vaporization. During the first stage of pure evaporation, solvent (water) vaporizes, resulting in a sharp decay in diameter. On the other hand, after initial sharp reduction in diameter, the droplet takes the shape of a bowl with no further change is size. This point is considered to be the initiation of the second stage of structure formation.

3.3 Pure evaporation stage

Figure 4a shows diameter reduction plot for four different concentrations. It is clear that the time duration of the pure evaporation stage gets shorter with increase in concentration. Higher concentration of nanosilica reduces the amount of solvent to be vaporized leading to reduction in vaporization time. Higher solute concentration also results in the suppression of vapor pressure according to Raoults’ law. This slows down the vaporization rate, reducing the slope with increase in concentration as shown in Fig. 4a. As mentioned earlier, an increase in nanosilica concentration increases the viscosity of the solution as seen in Fig. 5. As shown in the previous section, the velocity scale of the flow field within the droplet gets reduced with increase in viscosity. Sirignano (1999), showed that mass vaporization rate from a vaporizing droplet depends on Sherwood number and Spalding mass transfer number.
$$ \dot{m} = 2\pi \rho_{\text{g}} D_{{{\text{g}}\infty }} r_{\text{s}} Sh^{*} \ln (1 + B_{\text{M}} ) $$
(1)
where \( \dot{m} \) is mass vaporization rate, ρg is density of air and vapor mixture surrounding the droplet, D is diffusivity of vapor phase into ambient, rs is instantaneous radius of the droplet, Sh* is modified Sherwood number and BM is Spalding mass transfer number. Sh* is a function of Reynolds number (Re) and Schmidt number (Sc) while BM is a function of solute concentration at the droplet surface. Reynolds number is defined based on the relative velocity of droplet and ambient. Since the acoustic frequency of the levitator remains constant, the flow induced by acoustic streaming around the droplet will remain the same for each concentration of nanosilica. On the other hand, Schmidt number defined as the ratio of kinematic viscosity and mass diffusivity will also remain the same for all concentrations. So, the effect of Sherwood number will be negligible as Reynolds number is found be of the order of ~1 for the current experimental setup. On the other hand, the scale for BM is around 10−3. Through semi-empirical correlations prescribed by Sirignano (1999), it can be seen that for low Reynolds number (i.e. Re ~ 1), if Reynolds number changes by 10%, Sh* will change by 0.1%.
Fig. 4

a Non-dimensional diameter reduction with time. (D0 = initial diameter 500 μm). b Non-dimensional diameter at the end of pure evaporation stage

Fig. 5

Viscosity of nanosilica suspensions at different concentrations

However, BM is strongly dependent on solute concentration. Sirignano (1999), showed with increase in surface concentration of solute, the value of BM decreases due to decrease in vapor pressure. Here, it is found that the value of BM changes from 1.63 × 10−3 to 1.51 × 10−3 if the silica concentration changes from 0.5 to 3%. Hence, mass vaporization rate also reduces by 7%. This calculation is based on the initial concentration level of nanosilica in the droplet. However, with heating, the surface concentration becomes much greater than the initial concentration, leading to further reduction in BM and mass vaporization rate. So, it can be inferred that the slower vaporization rate for higher concentration of nanosilica is primarily due to a decrease in vapor pressure. The increase in viscosity and the corresponding reduction in recirculation strength do not have such a strong effect on vaporization rate.

Figure 4b shows the final diameter at the end of pure evaporation stage. It shows that it increases with concentration owing to less solvent available for vaporization. In addition, the solute concentration buildup near the surface is significantly augmented at high concentrations. This solute layer near the droplet surface coupled with low mass diffusivity effectively halts any further regression of the droplet. However, the solvent continues to vaporize through the porous solute crust.

3.4 Structure formation stage

At the onset of the stage of structure formation, it is observed that the top half of the droplet collapses to form a bowl structure. Until this point of heating, all the cases at different concentrations behave similarly. But further heating shows different phenomena for different concentrations. It was observed that for concentrations <1.3%, the droplets form a bowl structure and remains in that form for the rest of the heating cycle. However, for concentrations more than 1.9%, initial bowl structure goes through a morphological change to form a horizontal ring (axis of the ring vertical). The horizontal ring keeps oscillating about the axis of the levitator (like a pendulum) and at one point of time it reorients itself to form a vertical ring (axis of the ring horizontal). For concentrations between 1.3 and 1.9%, formation of both bowl and ring structures are possible. This range of concentrations is termed as the transition zone. Figure 6 represents this transition phase diagram. This diagram has been prepared based on repeated experiments at different concentrations. The thick solid line (red triangle) represents the time at which pure evaporation ends for different concentrations. The other information captured in Fig. 6 is the ring formation time and the reorientation time. The dotted line (solid circle) shows the ring formation time, while the thin solid line (green square) represents the time when the ring reorients to form a vertical ring. It can be observed from the figure that for the same concentration, the reorientation time varies to some extent. This has been explained in the next section. Although the ring formation time has been shown as a line in the figure, but in reality it is a very fuzzy boundary between transformation of the bowl into a horizontal ring. High speed images show that this shape transformation occurs gradually over a period of time. On the other hand, in cases of evaporation time and ring reorientation time, the boundaries are much less fuzzy as evident from high speed images.
Fig. 6

Structural changes in the droplet over time at different solute concentration

Based on the aforementioned observation of ring and bowl formation, Fig. 6 has been divided into a number of zones. These zones are indicated with different colors which represent different structures. For a given concentration at a given time instant during the heating cycle, the most probable structure can be predicted using this phase diagram.

3.5 Formation mechanisms of ring and bowl shaped Structures

Circulation induced by acoustic streaming within the droplet promotes preferential solute migration during the evaporation phase resulting in initial bowl formation. The velocity scale due to Marangoni convection inside the droplet is given by
$$ u_{\text{M}} \sim \frac{\alpha }{{r}}Ma\sim \frac{{{\text{d}}\sigma }}{{{\text{d}}T}}\left( {\frac{\Updelta T}{{\mu_{\text{drop}} }}} \right). $$
(2)
uM = velocity due to Marangoni flow; α = thermal diffusivity; Ma = Marangoni number; dσ/dT is measured in our experiment as −0.2 N/m°C. Saha et al. (2010), Kumar et al. (2010) showed by an order of magnitude analysis that Marangoni convection inside the droplets is negligible compared to velocities of the flow induced by acoustic streaming. In this work, we also used PIV results to show the presence of a single cell recirculation zone centered at the droplet center with negligible Marangoni convection. Although the PIV has been performed in the absence of external heating, the flow pattern will remain similar as Marangoni effects are negligible.
To understand the bowl and ring formation mechanisms, a time scale, τrecirc, can be defined, which is the time needed for a fluid element to reach the bottom of the droplet from the equator as shown in Fig. 7. If we define the recirculation velocity to be Vrecirc, the time scale is
$$ \tau_{\text{recirc}} \approx \frac{r}{{V_{\text{recirc}} }} $$
(3)
Fig. 7

Rotation of the droplet about levitator axis and recirculation velocity acting on a fluid element

On the other hand, due to rotation about the vertical axis of the droplet, there would be a dominant centrifugal force which would try to carry the fluid element towards the outer periphery of the droplet near the equator. If we define the rotation speed to be ω, then the time scale for carrying the droplet towards the periphery of the droplet, τcentrifugal can be defined as,
$$ \tau_{\text{centrifugal}} \approx \frac{1}{\omega } $$
(4)
It can be argued that whether a bowl or ring structure is formed depends on which time scale is dominant. To form a bowl structure, the τrecirc has to be smaller than τcentrifugal resulting in faster accumulation of particles at the bottom of the droplet. On the other hand if τrecirc is higher than τcentrifugal then the particles would accumulate around the periphery of the droplet near the equatorial plane creating a horizontal ring. Thus, the criterion for bowl and ring formation may be written as follows,
$$ \begin{gathered} \frac{r}{{V_{\text{recirc}} }} < \frac{1}{\omega }({\text{bowl}}) \hfill \\ \frac{r}{{V_{\text{recirc}} }} > \frac{1}{\omega }({\text{ring}}) \hfill \\ \end{gathered} $$
(5)

High speed images confirm that the rotational speed ω is similar for initial stages of the heating when the amount of solvent is substantial. PIV results show that Vrecirc decreases with increase in viscosity. Figure 5 confirms that the initial viscosity of the solution increases with increase in nanosilica concentration.

As a first order estimate, the decrease in recirculation velocity (from 236 to 189 mm/s) is about 50 mm/s for a 1.8 times increase in viscosity. Viscosity ratio of 1.8 corresponds to that when solute concentration of nanosilica is increased from 0.5 to 5% volume. The corresponding increase in τrecirc can be calculated as τrecirc, 5%recirc, 0.5% = 1.25, which implies a 25% increase in the timescale for recirculation. Assuming that the centrifugal timescale governed by the rotation of the droplet about the levitator axis is constant across all concentrations, the implication is that the propensity of droplets to form ring shaped structures increases with concentration. However, the exact cross-over from bowl to ring shaped is very hard to pinpoint as there exists a fuzzy boundary between 1.3 and 1.9% concentration droplets. However, concentrations more than 1.9% always results in ring formation and concentrations <1.3% shows repeated bowl formations. It should be noted that the initial structure in all droplets is a bowl, and a ring only forms for the higher concentration values. The phase diagram also confirms this observation. It is also possible that the recirculation which is initially strong gets diminished (as the solvent vaporizes, thus increasing the concentration with time) due to increase in viscosity and onset of aggregation. It may also be argued that during the initial formative stages, the strong recirculation present for all concentrations (0.5–5%) lead to a generic bowl shaped structure. It is only later that weakening of recirculation (due to combined viscosity increase and solute aggregation) especially at higher concentrations leads to a ring formation according to Eq. 5. Interestingly, high speed images suggest that rotational speed remains almost a constant during the entire cycle of bowl formation and bowl to ring transition. This confirms that an increase in τrecirc makes the centrifugal effect relatively more dominant leading to solute migration in the equatorial plane forming ring shaped structures. It is worth mentioning that the rotation about the horizontal axis decays as agglomeration or bowl formation event is triggered due to the depletion of liquid. However, rotation about the vertical axis persists due to the asymmetry in the bowl shaped structure and hence the unbalanced acoustic torque.

3.6 Reorientation of ring shaped structure

It is important to mention here that the rotation around the axis of the levitator (vertical axis rotation) still persists even after the formation of ring. The non-uniform accumulation of solute around the periphery of the ring leads to an imbalance in the pressure force around the ring circumference causing the ring to oscillate back and forth in the vertical plane. As shown in stage 1 of Fig. 8, Fz, the acoustic force in z direction balances W, the weight of the ring. The radial forces cause the oscillation about the axis of the levitator. It was shown by Lierke and Holitzner (2008) that the acoustic force in the radial direction is given by
$$ F_{\text{r}} (r,z) \approx - \frac{{k_{\text{r}} }}{2}\sin (k_{\text{r}} r)\cos (2k_{\text{z}} z) $$
(6)
where r and z are distances from the levitator axis and antinode, respectively. Parameters kr and kz depend on acoustic frequency and are constant. The sinusoidal nature of the force at a fixed ‘z’ explains the oscillatory motion of the levitator about the levitator axis.
Fig. 8

Different stages of ring reorientation for 3% nanosilica concentration

However, it so happens that the ring reaches a point far enough from the levitator axis where the acoustic field imposes an unbalanced turning moment causing it to reorient from a horizontal position to a vertical position. Different stages of this reorientation are shown in Fig. 8. Just before the reorientation, the oscillating ring becomes tilted. This is shown as stage 2 in Fig. 8. This inclination results from the combined effect of oscillation about the levitator axis and rotation about its own axis. Once the ring is tilted, the forces become highly imbalanced. The free body diagram at this instant is shown in Fig. 8. The vertical force Fz still balances the weight of the ring, W. The two radial forces, Fr1 and Fr2 act at the outer and inner edge of the ring, respectively. At this point it is worth mentioning that the levitated object under gravity shows a finite amount of shift from the antinode. This has been reported by Rednikov et al. (2006), Lierke and Holitzner (2008). Assuming Δz is the shift of the center of gravity of the ring from the antinode, at the inclined position two extremes of the ring will be at different ‘z’ location as shown in Fig. 8b. Considering Z1 and Z2 as the distances of outer and inner extreme distances of the ring from the plane of antinode, one can see Z1 < Z2.

From Eq. 5, we can write
$$ \begin{gathered} F_{{{\text{r}}1}} \approx - \frac{{k_{\text{r}} }}{2}\sin (k_{\text{r}} r)\cos (2k_{\text{z}} Z_{1} ) \hfill \\ F_{{{\text{r}}2}} \approx - \frac{{k_{\text{r}} }}{2}\sin (k_{\text{r}} r)\cos (2k_{\text{z}} Z_{2} ) \hfill \\ \end{gathered} $$
(7)

Now Z1 < Z2 implies that Fr1 > Fr2. This creates a moment, M, around the center of gravity of the ring resulting in reorientation. Once reoriented in the vertical plane, the ring returns to the axis of the levitator as shown as stage 3 in Fig. 8. The vertical ring now starts rotating due to acoustic forces about the axis of the levitator.

Bowl shaped structures do not experience this reorientation. Figure 6 shows the ring re-orientation time for different concentrations. It is worth noting that the reorientation has been observed for all the cases of ring formation. However, the reorientation phenomenon being a result of instability caused by asymmetry of the ring structure, time instant for this orientation does not follow a particular trend. That is the reason for wide variations of reorientation time that can be observed between different experiments at the same concentration.

3.7 Temperature history

Analysis of IR images shows a very similar trend for temperature history for all concentrations. Figure 9 shows temperature profile for four different concentrations of nanosilica. At the onset of heating, the average temperature of droplet surface sharply rises from room temperature and attains a maximum value around 40–42°C. Afterwards the average surface temperature starts decreasing at a very slow rate until most of the solvent vaporizes. This behavior can be explained by comparing the latent heat and sensible heat budgets. At the beginning of the heating process, the droplet surface temperature is low resulting in slower vaporization rate. Thus, the droplet needs a small amount of latent heat. The sensible heat being higher, the temperature rises very fast. However, with increase in temperature, vaporization rate also increases, thus, the latent heat requirement increases. At some point, all the heat absorbed through laser irradiation is used for latent heat in vaporizing the droplet. From this point onwards, latent heat dominates sensible heat resulting in a slight decrease of droplet average temperature.
Fig. 9

Average temperature during the heating cycle for various nanosilica concentrations

In cases of ring formation, it was observed that the temperature again rises very sharply after the reorientation of the ring as shown in Fig. 9. It can be explained from the point of view of area exposed to laser irradiation. As long as the ring remains horizontal, the surface area which is being irradiated remains constant. However, after reorientation, the surface area absorbing the laser irradiation increases. This, in turn, increases the amount of heat transfer into the ring structure. At this point, the structure does not contain any solvent to vaporize, thus, the entire amount of absorbed heat helps to increase the temperature of the structure resulting in a sharp rise in surface temperature.

After ring reorientation, the structure keeps rotating about the levitator axis. However, it is observed that the rotational speed initially stays slow immediately after reorientation and gradually increases. This change in speed also has an effect on temperature rise. It can be argued that the rotational speed dictates the average duration of exposure of any point on the surface to laser irradiation. Faster the rotation, longer is the average exposure duration and hence faster is the temperature rise.

For the 3% concentration reported in Fig. 9, the reorientation occurs after 5.5 s as shown also in Fig. 6. The average temperature of the droplet at this instant is 38°C. From high speed images, it was evident that immediately after reorientation, the rotation about the levitator axis is slower. For this particular case, the average rotational speed immediately after reorientation was found to be 1.2 rps (based on video images similar to Video 2 shown). However, high speed images show that after 7.1 s the vertical ring starts rotating faster with an average speed of 9 rps. The temperature plots show a sharp change in slope at 7.2 s. The temperature after 7.2 s (for slow rotation) is 41.5°C. With increase in rotation speed to 9 rps, the temperature rises to 70°C in approximately 2 s. It shows that the rate of temperature rise is 1.67°C/s during slow rotation and 15.83°C/s during faster rotation. So, it shows that 7 times increase in rotational speed causes a 9.5 times increase in the rate of temperature rise, suggesting that the rate in temperature increase is probably proportional to the rotational speed about the levitator axis.
$$ \frac{{{\text{d}}T}}{{{\text{d}}t}} \sim \omega $$
(8)
Figure 10 shows sample IR and high speed images at different time instants during the heating phase for different concentration levels. The initial stage of pure evaporation is marked by a sharp decrease in diameter before reaching a constant value. This stage is dominated by internal recirculation rising from acoustic streaming. At this stage, the droplet takes the shape of a bowl with collapsed top half. The next stage of structure formation is dominated by orthokinetic aggregation or agglomeration of particles. Due to increase in viscosity coupled with weaker recirculation, higher concentration of nanosilica (more than 1.9%) solution shows morphological transformation to form a horizontal ring, which eventually reorients itself to become a spinning vertical ring. However, lower concentrations (<1.3%) do not show such a transformation and remains in bowl shape for rest of the heating cycle.
Fig. 10

Infrared camera and high speed camera images at different time instants of the heating cycle for various nanosilica concentrations

4 Conclusions

In this work, an acoustic levitator was used to study evaporating nanosilica suspended droplets heated by laser irradiation. At first, particle image velocimetry was used to understand the flow structure inside the levitated droplet. Results show the presence of a single recirculation around droplet center. The velocity magnitude was found to increase with radius. PIV on droplets with different viscosity shows that maximum velocity decreases with increase in viscosity in a non-linear fashion.

Heating of nanosilica suspended solutions with different initial concentration shows a fascinating agglomeration and structure formation. In the initial stages of heating when significant evaporation has not taken place, the hydrodynamic effects caused by acoustic streaming is stronger compared to other effects such as aggregation. Soon, the evaporate rate becomes stronger resulting in a sharp diameter reduction. At the end of this stage, accumulation of nanosilica sets in as the droplet takes the shape of a bowl due to acoustic pressure difference, and the drop size stops reducing further. As the solvent is depleted, the hydrodynamic effect becomes weaker. This marks the onset of the structure formation stage which is dominated by aggregation or agglomeration of nanosilica particles. The current results show two different structures depending on the initial solute concentration. For nanosilica concentration of <1.3%, the droplet maintains the bowl structure. On the other hand, for concentration >1.9%, the initial bowl transforms into a horizontal ring. For the concentrations between 1.3 and 1.9, the droplet either forms a ring or a bowl. The formation of ring can be explained as follows. Further increase in viscosity with concentration decreases the strength of recirculation. The centrifugal effect due to droplet rotation about the levitator axis becomes stronger than recirculation resulting in the accumulation of particles around the droplet equatorial plane. Thus, a horizontal ring is formed due to asymmetries in mass distribution. The horizontal ring first starts oscillating within the acoustic field and eventually reorients itself to form a vertical ring due to an imbalance of forces.

Acknowledgments

The authors wish to acknowledge Mr. Erick Tijerino for the data acquired in Fig. 6.

Supplementary material

348_2011_1114_MOESM1_ESM.avi (75.2 mb)
Supplementary material 1 (AVI 77,019 kb)
348_2011_1114_MOESM2_ESM.avi (18.9 mb)
Supplementary material 2 (AVI 19,303 kb)

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Abhishek Saha
    • 1
  • Saptarshi Basu
    • 2
  • Ranganathan Kumar
    • 1
  1. 1.Department of Mechanical Materials and Aerospace EngineeringUniversity of Central FloridaOrlandoUSA
  2. 2.Department of Mechanical EngineeringIndian Institute of ScienceBangaloreIndia

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