Soap Bubbles Research Articles

Study of pressure wave dynamics in a channel with a spherical bubble cluster

The features of wave propagation in a bubbly liquid are associated with the combined interaction of nonlinear, dispersive, and dissipative effects. In a liquid with bubbles, the properties of a practically incompressible liquid, which is a carrier phase, change dramatically with a small volume (and even more so, mass) addition of gas (bubbles), which is a dispersed phase. The peculiarity of bubbly liquids is due to their high static compressibility while maintaining a high density close to that of the liquid, which in turn leads to a low equilibrium speed of sound. In this paper, we study two-dimensional axisymmetric wave perturbations in a channel with water containing a spherical cluster filled with a water-air bubble mixture and located at one of the end boundaries. Based on the results of numerical calculations, the dependence of the maximum pressure amplitude formed in the channel on the geometrical parameters of the cluster is analyzed. It has been established that the presence of a near-end bubble cluster can significantly both increase and decrease the effect of the wave signal incident on the wall, depending on the size of the cluster and its characteristics.

Transmission of an Acoustic Wave Through a Multilayer Medium Containing Layers of Bubble Liquid

Transmission of an Acoustic Wave Through a Multilayer Medium Containing Layers of Bubble Liquid

Modeling of co-axial bubbles coalescence under moderate Reynolds regimes: A Bi-phase SPH approach

Phenomena involving bubble flow play a significant role in numerous industrial, natural, and scientific systems. Thus, liquid–gas interfaces must be considered the influence of surface tension and buoyancy. This work analyzes a complete numerical study for bi-fluid flow problems in the deformation evolution of two bubbles coalescing in a viscous liquid. This study discusses diverse configurations of the coalescence bubbles process and their effect on the displacement of the center of mass, velocity, streamlines, and evolution of the morphologies’ deformation. The resulting simulations revealed the process of the coalescence bubbles regarding three stages: approaching, drainage, and rupture of the interface. These steps reach different morphologies, defined as oblate ellipsoid, prolate ellipsoid, and ellipsoidal cap shapes between the trailing, leading, and merging bubbles. Likewise, an approximated bi-phase 2D methodology using the Navier–Stokes equations with Smoothed Particle Hydrodynamics (SPH) method and associated with the Continuous Surface Force (CSF) method was employed to approach the interaction between the bubbles, the surrounding liquid, and cavity walls. This approach with SPH and CSF for fused bubbles and their liquid interaction are validated employing numerical benchmarks in situations with high and moderate regimes of the Reynolds (Re) and Eötvös (Eo) numbers, and different sizes of diameter between coalescence bubbles. Correspondingly, examples of bubbles merging around a liquid owing to gravitational are rarely treated in the literature of mesh-free methods, especially to characterize different viscosity, density and surface tension regimes at the bubble–liquid interface, the effect of the method precision (distance between particles, Δx), the size of the surrounding liquid cavity and the initial distance between lighter domains. According to the bubbles deformation, during the coalescence is observed significant influence of Δx resolution and the cavity size, there are instances of instabilities, such as lateral tails, droplets inside the lighter domain, break-up, and satellite bubble formation. Finally, it is provided a robust numerical study of the coalescence process with a bi-phase SPH for different surfaces tension regimes (5≤Eo≤200), viscosity and density ratios (5≤λ,Φ≤100) and initial conditions in merging bubbles problems with moderates Reynolds numbers (5≤Re≤50).

Diffraction Field and Radiation Force for a Liquid Bubble in a Dissimilar Fluid in an Infinite Cylindrical Cavity

Diffraction Field and Radiation Force for a Liquid Bubble in a Dissimilar Fluid in an Infinite Cylindrical Cavity

ДОСЛІДЖЕННЯ ФОРМИ ПОВІТРЯНОГО ПОТОКУ У ЗАБІРНОМУ ПРИСТРОЇ ДЛЯ ДОБУВАННЯ САПРОПЕЛЮ

For many years, global researches that focus on improving soil fertility have been conducted. Nowadays, innovative inculcations of environmentally (ecologically) friendly organic agriculture are becoming quite popular. One of the most effective indicators is the use of alternative types of fertilizers. As part of large-scale experiments, researchers propose to use fertilizers made from organic sapropel concentrated in freshwater lakes. Analysis of such studies shows that the impact of sapropel on soil fertility is significant and complex. The main problem they faced is the extraction of these deposits from underwater deposits (fields). Ukrainian scientists have proven the effectiveness of sapropel extraction by means of a pneumatic intake device. To substantiate the rational parameters of this device and visualize the processes, experimental studies of the work of the pneumatic working body were carried out. Namely, experimental studies of the determination of the trajectories of air bubbles in liquids of different viscosity were carried out. According to received trajectories, the boundaries of airflow and its shape are determined. Limpid liquids of different viscosities were used specially in order to see and fix the flow parameters, because it is impossible to observe such a phenomenon in sapropels placed in underwater deposits, due to their opacity and change of viscosity with depth of the bedding. Therefore, the experiment was considered as close as possible to the real one, and the environment of realization of the experiment was simulated. Water, industrial oil and concentrated detergent were selected as investigated liquids. Research data indicate that one can use a whirling airflow for better loosening of deposits of reduced humidity. Whirling occurs when there is a horizontal position of the outlet axis with a diameter in the range of 1-1.5 mm and air pressure of 300-400 kPa.

High pressure phase behavior and thermodynamic modeling of the carbon dioxide + chloroform + globalide system

The high-pressure phase behavior of the ternary system constituted by carbon dioxide + globalide + chloroform was studied. Experiments were conducted applying the synthetic-visual method in a variable-volume view cell at a mass ratios of globalide to chloroform of 0.5:1, 1:1, and 2:1, over a temperature range from 313.15 to 343.15 K, and pressures from 5.17 to 20.25 MPa. Phase transitions of vapor–liquid bubble point (VLE-BP), vapor–liquid dew point (VLE-DP), liquid–liquid (LLE), and vapor–liquid-liquid (VLLE) type were observed. Furthermore, through the P-w diagram, the phase behavior of the ternary system in chloroform free-basis was analyzed between 0.4250 to 0.9735 of carbon dioxide mass composition. It has been observed that high quantities of chloroform lead to lower transition pressures. Moreover, PT-diagrams efficiently displayed that higher pressures are necessary to achieve a single phase medium as temperature rises, which characterize LCST behavior. PR-vdW2 model was used to estimate binary interaction parameters. Additionally, the ternary system was compared with binary systems available in the literature. The data presented in this work provides necessary information for the optimization and improvement of poly(globalide) synthesis in supercritical media.

Development of fast scanning module with a novel bubble solution applied to scanning acoustic microscopy system for industrial nondestructive inspection

Scanning acoustic microscopy (SAM) system is a powerful nondestructive instrument owing to its capability to provide internal information and defect positions inside a material. In industrial applications of SAM, the scanning time plays an important role in enhancing efficient inspection of the product line. Several studies have used the traditional SAM system, which develops based on linear motor to inspect industrial samples, but the inspection time remained relatively long and cost-prohibitive. Herein, we reported a low-cost fast SAM (FSAM) system that provided the image results in a short time while maintaining their high resolution. In this design, FSAM fast scanning module (FSM) was developed by exploiting the slider-crank mechanism, which was optimized for a specific product to substantially reduce the inspection time. During the scanning process, bubbles were generated due to the rapid movement of transducer into the water, namely the bubble cavitation. The bubbles restricted the ultrasound wave propagation, which resulted in the bad image quality. The bubble cavitation phenomenon was examined using the incompressible flow theory to investigate the bubble inception, which was defined based on the pressure value around transducer. The bubbles appeared in areas where the pressure less than the vapor pressure. Using the OpenFOAM to analyze the pressure value, the bubble problem was solved by a novel solution that used a bubble reduction plate attaching to the transducer. The coin and aluminum samples with known dimensions and internal structure were prepared to scan using the FSAM system, which validated the simulation results and FSAM capabilities in providing good images with internal information and accurate measurements. Finally, FSAM system was designed and developed to successfully inspect industrial samples in a short time, such as an integrated circuit chip, printed circuit board, welded sheets, and silicon wafer. Using the FSAM system to scan welded sheets, the scanning time were reduced by approximately 77% compared to the traditional SAM system. These results demonstrate that the FSAM system is a potential instrument for industrial nondestructive inspection.

Nonlinear ultrasound in liquid containing multiple coated microbubbles: effect of buckling and rupture of viscoelastic shell on ultrasound propagation

With promising applications in medical diagnosis and therapy, the behavior of shell-encapsula-ted ultrasound contrast agents (UCAs) has attracted considerable attention. Currently, second-generation contrast agents stabilized by a phospholipid membrane are widely used and studies have focused on the dynamics of single phospholipid shell-encapsulated microbubbles. To improve the safety and the efficiency of the methods using the propagation or targeted ultrasound, a better understanding of the propagation of ultrasound in liquids containing multiple encapsulated microbubbles is required. By incorporating the Marmottant–Gompertz model into the multiple scale analysis of two-phase model, this study derived a Korteweg–de Vries–Burgers equation as a weakly nonlinear wave equation for one-dimensional ultrasound in bubbly liquids. It was found that the wave propagation characteristics changed with the initial surface tension, highlighting two notable features of the phospholipid shell: buckling and rupture. These results may provide insights into the suitable state of microbubbles, and better control of ultrasound for medical applications, particularly those that require high precision.

The extreme bulk-modulus contrast of bubbly soft matter for underwater acoustic modulation

Bubbles in liquid and soft matter are excellent acoustic resonators with extremely low resonant frequencies. We find that bubbly soft matter (BSM) can enable full-phase (2π) modulation of incident acoustic waves just through changing the bubble size. Compared with the conventional solid–solid binary locally resonant metamaterial (SSM), due to the extreme bulk-modulus ratio of the bubbles and the soft matrix, the BSM has two distinguished merits. First, the size of the bubbly inclusions for the full-phase modulation is only about a third of the solid inclusions in the SSM; second, the range of variation of the bubbly inclusions to cover the full-phase modulation is two orders of magnitude wider than that of the solid inclusions. These features, combined with the salient advantage of wave-impedance match between soft matter and water, can realize compact and light-weight reflective and transmissive underwater bubble metasurfaces. At the lower limit 3 kHz of the active sonar operating frequency, an ultrathin reflective metasurface with a thickness of 1/50 the wavelength can redirect the incident waves at a given angle. Bubble resonance in soft matter opens a new avenue for underwater acoustic modulation at the deepest subwavelength.

Discrete $$\ell ^{1}$$ Double Bubble Solution is at Most Ceiling Plus Two of the Continuous Solution

Discrete $$\ell ^{1}$$ Double Bubble Solution is at Most Ceiling Plus Two of the Continuous Solution

Spinning Liquid Metal Droplets on Ice.

The non-contact and non-wetting droplet motion isolated from the solid surface has a high degree of freedom and thus can exhibit many peculiar interfacial phenomena. Here, an experimental phenomenon of spinning liquid metal droplets on an ice block is discovered, which adopts the dual solid-liquid phase transition of the liquid metal and the ice. The whole system is somewhat a variant of the classic Leidenfrost effect, which directly uses the latent heat released by the spontaneous solidification of the liquid metal droplet as a heat source to melt the ice and create an intervening lubricant water film. Interestingly, it is found that the droplets on ice become very mobile and undergo rapid spin as the solidification process proceeds. A series of comparative experiments clarify that the circumferential driving force comes from the escaping bubbles as the ice melts. Furthermore, by comparing the motion characteristics of different kinds of liquid metal droplets and solid balls on ice and investigating their physical properties and heat transfer, it is disclosed that the spin effect can be universal for objects of different materials, as long as the two necessary elements of rapid liquid film establishment and gas bubble release can be satisfied simultaneously.

Gas holdup, bubble size distribution, and mass transfer in an airlift reactor with ceramic membrane and perforated plate distributor

AbstractThe airlift reactor is one of the most commonly used gas–liquid two‐phase reactors in chemical and biological processes. The objective of this study is to generate different‐sized bubbles in an internal loop airlift reactor and characterize the behaviours of the bubbly flows. The bubble size, gas holdup, liquid circulation velocity, and the volumetric mass transfer coefficient of gas–liquid two‐phase co‐current flow in an internal loop airlift reactor equipped with a ceramic membrane module (CMM) and a perforated‐plate distributor (PPD) are measured. Experimental results show that CMM can generate small bubbles with Sauter mean diameter d32 less than 2.5 mm. As the liquid inlet velocity increases, the bubble size decreases and the gas holdup increases. In contrast, PPD can generate large bubbles with 4 mm < d32 < 10 mm. The bubble size and liquid circulation velocity increase as the superficial gas velocity increases. Multiscale bubbles with 0.5 mm < d32 < 10 mm can be generated by the CMM and PPD together. The volumetric mass transfer coefficient kLa of the multiscale bubbles is 0.033–0.062 s−1, while that of small bubbles is 0.011–0.057 s−1. Under the same flow rate of oxygen, the kLa of the multiscale bubbles increases by up to 160% in comparison to that of the small bubbles. Finally, empirical correlations for kLa are obtained.

Identification of swirling air flow velocity by non-neutrally buoyant tracer particle based on machine learning

In the non-intrusive measurement of swirling air flow, helium-filled soap bubbles (HFSBs) are ideal neutrally buoyant tracer particles However, there are some researchers that do not use HFSBs in the non-intrusive measurement of swirling air flow, leading to some kind of measurement inaccuracy. Since the flow velocity data has been implicitly included in the physical equations of any kind of tracer particles, it is possible to extract such hidden flow velocity from particle trajectory. In this study we propose a physics-informed procedure of adopting SINDy algorithm to identify the hidden physical equations of non-neutrally buoyant particle dynamics, so that the implicit flow velocity can be discovered. First of all, the numerical experiment is conducted to generate particle trajectory in a 2D swirling air flow in small cyclone separator. Based on the numerical experiment trajectory data, the input variables for SINDy algorithm are properly constructed. The output of SINDy algorithm, which are the identified physical equations, are evaluated and validated on two different-density particle trajectory data. Our results show that the physical equations of tracer particle dynamics can be identified and the discovered flow velocity data has a maximum deviation of 1.4% from the truth (R2≥0.999). The proposed method may remove the requirement of NB tracer particle in non-intrusive measurement of swirling air flow, and may be applied to recognize the physical equations of complex particle laden flow.

Effect of liquid elasticity on nonlinear pressure waves in a viscoelastic bubbly liquid

The importance of viscoelasticity of biological media that are used in medical ultrasounds has been discussed in the literature. Furthermore, the use of microbubbles in biological media drastically improves the efficiency of both diagnostic and therapeutic ultrasounds. Weakly nonlinear wave equations for ultrasound propagation in liquids containing microbubbles have long been studied, although the viscoelasticity of the liquid phase has been ignored for simplicity. In this study, we derived a nonlinear wave equation for ultrasound propagation in a viscoelastic liquid containing microbubbles by considering the effect of the elasticity of the liquid. Additionally, we evaluated how the elasticity of the liquid modifies the nonlinear, dissipation, and dispersion effects of the ultrasound in a few tissue models (i.e., liver, muscle, breast cancer, fat, and skin models and that without shear elasticity). The results revealed that liquid shear elasticity decreases the nonlinear and dissipation effects and increases the dispersion effect, and this tendency is more significantly observed in the breast cancer tissue compared with other tissues. Furthermore, we numerically solved the nonlinear wave equation and investigated the changes in ultrasonic wave evolution with and without shear elasticity.

Derivation and stability analysis of two-fluid model equations for bubbly flow with bubble oscillations and thermal damping

The two-fluid model with bubble oscillations, proposed by Egashira et al. (2004), can explain the properties of cavitating bubbly flow and pressure wave propagation in the bubbly liquid. However, the viscous effect as well as energy conservation leading to temperature changes inside the bubble with bubble oscillations have not yet been considered. Hence, this study aimed to incorporate the viscous (bulk viscosity and drag) and thermal effects to the previously proposed two-fluid model with bubble oscillations. Bulk viscosity was considered by averaging the shear stress term in the single-phase momentum conservation for a Newtonian fluid, and the drag was introduced by transforming the interfacial shear stress. We derived the averaged energy conservation for a general two-phase flow with a thermal conduction inside bubbles and heat transfer between the two phases, and limited this equation to that for a bubbly flow by closing the interfacial temperature gradient term via constitutive equations for a single bubble. Furthermore, we investigated the stability of our proposed one-dimensional model equations using the dispersion analysis. This analysis provided the following insight: (i) The difference in the temperature gradient models had a slight effect on the stability of the proposed model equations; (ii) the thermal conduction inside the bubbles was dominant in the thermal damping in bubbly flows rather than the heat transfer between the two phases; (iii) incorporating both the bulk viscosity and drag stabilized the proposed model equations. Our results provide insights into the development of mathematical models to investigate the thermal effects in bubbly flow with bubble oscillations, such as cavitating bubbly flow and wave propagation in bubbly liquids.

The water cavitation line as predicted by the TIP4P/2005 model.

The formation of vapor bubbles in a metastable liquid, cavitation, is an activated process due to the free energy cost of having both phases at contact. Such an energetic penalty enables the existence of the liquid beyond its thermodynamic borders. Establishing the stability limits of a liquid as ubiquitous as water has important practical implications and has thereby attracted a lot of attention. Different experimental strategies and theoretical analyses have been employed to measure and predict the cavitation line, or the pressure-temperature kinetic stability border of liquid water. Understanding the location of the cavitation line requires knowing the cavitation rate dependence on pressure and temperature. Such dependency is difficult to obtain in experiments, and we use molecular simulations with the TIP4P/2005 model to fill this gap. By deeply overstretching liquid water below the saturation pressure, we are able to observe and quantify spontaneous cavitation. To deal with a lower overstretching regime, we resort to the Seeding technique, which consists of analyzing simulations of a liquid containing a vapor bubble under the theoretical framework of Classical Nucleation Theory. Combining spontaneous cavitation with Seeding, we get a wide overview of the cavitation rate. We study two different temperatures (450 and 550K) and complement our perspective with the results previously obtained at 296.4K [Menzl et al., Proc. Natl. Acad. Sci. 113, 13582 (2016)] to establish a broad simulation-experiment comparison. We find a good agreement between simulations and both isobaric heating and isochoric cooling experiments using quartz inclusions. We are, however, unable to reconcile simulations with other experimental techniques. Our results predict a decrease in the solid-liquid interfacial free energy as the liquid becomes increasingly overstretched with a temperature independent Tolman length of 0.1nm. Therefore, the capillarity approximation underestimates the nucleation rate. Nonetheless, it provides a fair indication of the location of the cavitation line given the steep rate vs pressure dependence. Overall, our work provides a comprehensive view of the water cavitation phenomenon and sets an efficient strategy to investigate it with molecular simulations.

Estimation of bubble cavitation rates in a symmetrical Lennard-Jones mixture by NVT seeding simulations.

The liquid-vapor transition starts with the formation of a sufficiently large bubble in the metastable liquid to trigger the phase transition. Understanding this process is of fundamental and practical interest, but its study is challenging because it occurs over timescales that are too short for experiments but too long for simulations. The seeding method estimates cavitation rates by simulating a liquid in which a bubble is inserted, thus avoiding the long times needed for its formation. In one-component systems, in the NpT ensemble, the bubble grows or redissolves depending on whether its size is larger or smaller than the critical size, whereas in the NVT ensemble (i.e., at constant number of particles, volume, and temperature), the critical bubble can remain in equilibrium. Provided that a good criterion is used to determine the bubble size, this method, combined with the Classical Nucleation Theory (CNT), gives cavitation rates consistent with those obtained by methods independent of the CNT. In this work, the applicability of NVT seeding to homogeneous cavitation in mixtures is demonstrated, focusing on a partially miscible symmetrical binary Lennard-Jones (LJ) liquid at a temperature within the mixing regime. At the same stretching pressure, cavitation rates are higher in the binary mixture than in the pure liquid due to the lower interfacial free energy of the mixture. Curiously, the cost of creating a bubble is similar in the pure and binary LJ liquids at the same metastability, Δμ/Δμspin, with Δμ being the difference in chemical potential between the metastable liquid and coexistence, and Δμspin between the spinodal and coexistence.

Accurate mass flow and density of bubbly liquids using speed of sound augmented Coriolis technology

Speed of sound augmented Coriolis technology utilizes a process fluid sound speed measurement to improve the accuracy of Coriolis meters operating on bubbly liquids. This paper presents a theoretical development and experimental validation of speed of sound augmented Coriolis meters. The approach utilizes a process fluid sound speed measurement, based on a beam-forming interpretation of a pair of acoustic pressure transducers installed on either side of a Coriolis meter, to quantify, and mitigate, errors in the mass flow, density, and volumetric flow reported by two modern, dual bent-tube Coriolis meters operating on bubbly mixtures of air and water with gas void fractions ranging from 0% to 5%. By improving accuracy of Coriolis meters operating on bubbly liquids, speed of sound augmented Coriolis meters offer the potential to improve the utility of Coriolis meters on many existing applications and expand the application space of Coriolis meters to address additional multiphase measurement challenges.The sources of measurement errors in Coriolis meters operating on bubbly liquids have been well-characterized in the literature. In general, conventional Coriolis meters interpret the mass flow and density of the process fluid using calibrations developed for single-phase process fluids which are essentially incompressible and homogeneous. While these calibrations typically provide sufficient accuracy for single-phase flow applications, their use on bubbly liquids often results in significant errors in both the reported mass flow, density and volumetric flow. Utilizing a process fluid sound speed measurement and an empirically-informed aeroelastic model of bubbly flows in Coriolis meters, the methodology developed herein compensates the output of conventional Coriolis meters for the effects of entrained gas to provide accurate mass flow, density, volumetric flow, and gas void fraction of bubbly liquids.Data presented are limited to air and water mixtures. However, by influencing the effective bubble size through mixture flow velocity, the bubbly liquids tested exhibit decoupling characteristics which spanned theoretical limits from nearly fully-coupled to nearly fully-decoupled flows. Thus, from a non-dimensional parameter perspective, the data presented is representative of a broad range of bubbly liquids likely to be encountered in practice.

Definition of Bubbly Liquids Parameters for the Optimization of Their Nonlinear Effects on Ultrasound

The aim of this paper is to optimize the generation of frequencies obtained nonlinearly from the propagation of ultrasound in a bubbly liquid. A study is presented for which the number and size of the gas bubbles in the liquid are varied to determine the optimal medium, which is the one that allows the highest amplitude for these frequency components. We use a previously developed numerical software that tracks the nonlinear behavior of both ultrasound and bubble vibrations in time to carry out several simulations. We focus our attention on two one-dimensional configurations, a resonator of length set at a quarter of the wavelength with a free-wall condition and a cavity of length set at sixteen wavelengths with open-field condition. In each case, we analyze the generation of the 2nd, 3rd, and 4th harmonics of the source frequency. Our results show that, in both cases, the use of higher source amplitudes and lower source frequencies is more useful to increase the harmonic amplitudes. Moreover, smaller bubbles are more adequate when the void fraction is kept constant for this purpose in the first configuration, whereas the modification of void fraction has no influence in the second configuration, for which given a void fraction value, bubble sizes whose ratio are f0/f≈5, f0/f≈7, and f0/f≈9 maximize the 2nd, 3rd, and 4th harmonics, respectively. These conclusions could be of interest for some applications.

Accuracy of different cytoarchitectural features in the diagnosis of papillary thyroid carcinoma by fine needle aspiration

Fine needle aspiration (FNA) has about 90% diagnostic accuracy for papillary thyroid carcinoma (PTC) in an adequate sample. Ignorance of relative significance of individual cytologic features may lead to misdiagnosis due to reliance on a single or few features. Our objective was to determine the usefulness of individual and most appropriate combined cytologic features, for diagnosis of PTC. H&E stained FNA smears of fifty cases each, of consecutive histologically confirmed PTC and benign thyroid cases (controls), reported over 3 years, were retrieved from the files. A total of 31 architectural, cytological and background features were assessed, blind to the final diagnosis and compared amongst the two groups. The statistical significance (p<0.05) of each parameter was determined by chi-square and odds ratio and combinations quality assessed by ROC curves.: Twenty features were found to be statistically significant. Fourteen highly significant (p<0.000) features included flat syncytial sheets, anatomical borders, true papillae, cellular swirls, individually dispersed cells with eosinophilic cytoplasm, anisonucleosis, elongated oval nuclei, powdery chromatin, nuclear outline irregularity, thickened nuclear membranes, crescent shaped nuclei, intranuclear inclusions, histocytoid cells and soap bubble cytoplasmic vacuolation. The six statistically significant features (p<0.05) included micro-acinar structures, cellular crowding, nuclear overlapping, nuclear grooves, squamoid cells and bubble gum colloid. The control group also showed some of these single cytologic features. All the combinations of ≥ 4 features had a statistical significance of p=0.000 and specificity and PPV of 100% with ROC showing excellent results. Using correct combination of cytologic features will increase accuracy of FNA diagnosis of PTC.