Single Liquid Drop Research Articles

Novel Method to Obtain Contact Angles of Tumor Biopsies.

Characterizing the strength of a solid-liquid interface can be done by depositing a single drop of liquid on a planar solid surface and measuring the angle of the formed semicircle, called the contact angle. The contact angle of pure water is indicative of a surface's hydrophobicity and is a useful metric in biomedical applications such as tissue scaffolding and drug/tissue interactions. However, the roughness and inhomogeneity of most biological surfaces make obtaining accurate contact angles of such materials challenging. Here, we developed an instrument and methodology to obtain contact angles of tissue sections. Breast cancer tumor and nearby healthy tissue sections were used as the model biological surface. The custom instrument was built on existing equipment by improving drop dispensing accuracy in the nanoliter range, an XYZ stage, additional side view cameras, and microscope-based sample visualization. The method takes into account the inherent surface inhomogeneity and topology of tissue and the required method of illumination for contact angle acquisition. As such, the system uses an inverted microscope with a high sensitivity camera, an XYZ stage for accurate droplet placement on tissue, and multiple cameras to obtain contact angles around the entire perimeter of the drop. We tested the system with breast cancer biopsies and adjacent normal tissue from 75 patients and report here a trend of tumor exhibiting higher water contact angles, and thus higher hydrophobicity, compared to their respective normal adjacent tissue. The system described here can be used to characterize any type of biological tissue, which can be sectioned, with any liquid including water or solutions with dissolved or suspended therapeutic molecules and particles.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ВЫСОКОТЕМПЕРАТУРНОЙ СУШКИ КАПЛИ ОКАЛИНОМАСЛОСОДЕРЖАЩЕГО ШЛАМА ПРИ ЕЕ ДВИЖЕНИИ В ЗАКРУЧЕННОМ ПОТОКЕ ГАЗА

The article presents an examination of the movement trajectory of a single liquid drop of sludge containing water, oil, and iron scale in a swirling high-temperature gas flow. Taking into account a two-phase transition area from liquid water to vapor, temperature fields in a drop are determined, as is an algorithm for calculating the movement trajectory of a drop in a swirling gas flow when heating it up according to a two-phase area of water evaporation. When designing a drying chamber for drops of scale- and oil-containing sludge, a mathematical model helps predict its typical size as well as control the drying process for drops produced by a disk atomizer.

Testing a Drop of Liquid Using Smartphone LiDAR

We present the first system to determine fluid properties using the LiDAR sensors present on modern smartphones. Traditional methods of measuring properties like viscosity require expensive laboratory equipment or a relatively large amount of fluid. In contrast, our smartphone-based method is accessible, contactless and works with just a single drop of liquid. Our design works by targeting a coherent LiDAR beam from the phone onto the liquid. Using the phone's camera, we capture the characteristic laser speckle pattern that is formed by the interference of light reflecting from light-scattering particles. By correlating the fluctuations in speckle intensity over time, we can characterize the Brownian motion within the liquid which is correlated with its viscosity. The speckle pattern can be captured on a range of phone cameras and does not require external magnifiers. Our results show that we can distinguish between different fat contents as well as identify adulterated milk. Further, algorithms can classify between ten different liquids using the smartphone LiDAR speckle patterns. Finally, we conducted a clinical study with whole blood samples across 30 patients showing that our approach can distinguish between coagulated and uncoagulated blood using a single drop of blood.

Resonance oscillations of a drop or bubble in a viscous vibrating fluid

In the present work, we study the resonance oscillations of a single liquid drop or gas bubble relative to their equilibrium spherical shape, which arise as a result of harmonic, translational vibrations of a volume of liquid of different densities, containing such an inclusion. The parametric resonance of the forced translational mode with the main resonant frequency equal to the sum of two adjacent eigenfrequencies of capillary oscillations of the interface was previously discovered in an inviscid approximation [Lyubimov et al., “Resonance oscillations of a drop (bubble) in a vibrating fluid,” J. Fluid Mech. 909, A18 (2021)], also taking into account low viscosity using a phenomenological approach. Now, the effect of viscosity on the resonance is investigated by rigorous accounting for the viscosity in the dynamic boundary layer near the interface. The relations governing the evolution of the resonance modes near the threshold of instability excitation are determined. The equivalence of the two approaches taking viscosity into account is revealed: the rigorous one, built on a method of multiple scales, and the previously developed phenomenological approach, which is based on the artificial addition of the dissipative terms to the amplitude equations.

An experimental investigation of the heat transfer dynamics during evaporation of a single liquid drop on a sapphire substrate

The paper is devoted to an experimental study of the heat transfer dynamics during evaporation of a single liquid drop on a heated horizontal surface, which is a sapphire glass coated with a high heat-resistant black graphite paint. The method employed in research can be used to study the heat and mass transfer processes in the gas-liquid-solid contact line region with maximum heat transfer coefficient. Its particular feature as compared to the previously known methods is the solution of the initial-boundary problem for the heat conductivity equation, which in terms of mathematics is a correct problem. Using the thermography method, the sapphire surface temperature fields after single drop impingement are determined. The data obtained will be used to calculate the heat flux density in the region of the contact line of the drop.

Heat transfer modelling of dropwise condensation behaviour of magnesium vapours in the electrothermal production of magnesium

ABSTRACTDuring the extraction of magnesium by the electrothermal process, the condensation of magnesium vapours in the condenser is critical to achieve operational efficiency. In the present work, a mathematical heat transfer model has been developed to predict the growth rate of a single liquid metal drop during dropwise condensation (DWC) of magnesium vapours in the electrothermal process. Homogeneous DWC model has been developed considering negligible thermal resistance at the liquid–vapour interface for a single cycle of liquid magnesium layer formed at vapour–liquid interface. The heterogeneous DWC has been modelled taking into account all possible thermal resistances. The role of constriction resistance on transient droplet growth behaviour has been studied and the parametric sensitivity analysis has been conducted. Parameters i.e. degree of undercooling (ΔT), contact angle (θ), thickness of condenser wall (δ )and constriction effect cause (β) has been studied for droplet growth behaviour. Heat transfer and specially the constriction resistance was found to be quite significant for heterogeneous DWC of magnesium metal vapours. Alongwith other parameters, the thermally inactive region (β) on the condenser surface inversely affects the growth. The model-based predicted Mg droplet growth profiles during condensation have been validated with published data on similar DWC studies.

Impact dynamics and heat transfer characteristics of liquid nitrogen drops on a sapphire prism

Drops close to a hot solid surface can be prevented from making contact by the vapour generation in between them. This so-called Leidenfrost effect occurs at a minimal plate temperature which is referred to as the Leidenfrost temperature. In spray cooling, were one uses impacting drops to cool down the hot solid, this effect is very undesirable: the vapour layer forms an isolating layer and prevents effective heat transfer between the drop and the solid. We study this phenomenon by impacting a single liquid nitrogen drop on a smooth sapphire prism using high-speed frustrated total internal reflection imaging. In these cryogenic conditions, the prism behaves as a perfect thermal conductor, while its transparency enables us to study the contact behaviour during the impact and the spreading phase of the drop. By varying the prism temperature and impact velocity of the drops we obtain a phase diagram of the impact characteristics. Using the Stokes number for the vapour flow, we find good agreement with previous studies for non-cryogenic liquids. The phase diagram is then compared with a second type of experiment in which a stream of drops cools the prism over time. The results of the two different type of measurements agree well, from which we conclude that the cooling power of a drop is strongly related to the wetting behaviour of the impacting drops. Finally, by comparing the wetted area with the contact line length we show that heat transfer in contact and transition boiling is dominated by conduction rather than evaporation.

An analytical model of heat and mass transfer from liquid drops with temperature dependence of gas thermo-physical properties

An analytical model for heating and evaporation of a single component liquid drop is developed. The model accounts for the temperature dependence of density, diffusivity, thermal conductivity and specific heat of the gas species. The effect of variable properties on heat and evaporation rates is analysed and a comparison with the prediction of the classical constant property model is reported for six different species and different operating conditions. The model allows to evaluate the effect of the choice of the gas mixture averaging parameter (the relative weight of free stream and drop surface conditions) on the prediction of the constant property model, and a way to optimise the choice is proposed. The results can be extended to non-spherical drop and examples are reported.

Residence time distribution in packed bed microreactor – Lattice Boltzmann model validation

An analytical model for heating and evaporation of a single component liquid drop is developed. The model accounts for the temperature dependence of density, diffusivity, thermal conductivity and specific heat of the gas species. The effect of variable properties on heat and evaporation rates is analysed and a comparison with the prediction of the classical constant property model is reported for six different species and different operating conditions. The model allows to evaluate the effect of the choice of the gas mixture averaging parameter (the relative weight of free stream and drop surface conditions) on the prediction of the constant property model, and a way to optimise the choice is proposed. The results can be extended to non-spherical drop and examples are reported.

Computational Fluid Dynamics Simulations of Single Drops in Confined Geometries

Understanding of drop rise in confined domains is important as it influences drop rise velocity and drag coefficient. In this work, the motion of a single liquid drop rising in a quiescent channel filled with water in the presence of a wall effect is studied numerically using the combined volume of fluid and level set method. The ratio of drop diameter to column diameter is used as a parameter to quantify the presence of the wall effect. Simulations were carried out for n-butanol and toluene drops. A reduction in rise velocity is seen in all the cases. It is seen that pressure profile, strain rate, and vorticity magnitude near the drop surface have a significant effect on the evolution of a drop shape in confined geometries. Drag coefficients have been calculated from the force balance equation. The correlation for the correction factor for the drag coefficient has been developed to account for the wall effect.

Effective Mass Layer of a Single Drop of Liquid Located on a Quartz Crystal Microbalance

Effective Mass Layer of a Single Drop of Liquid Located on a Quartz Crystal Microbalance

Numerical analysis and insight of drop impacting dynamics upon a liquid film

A single liquid drop impinging onto very thin spherical films was observed with the aid of a high-speed digital camera at $$10^{4}$$ frames per second. The liquid sheet produced at a high impact velocity was mainly concerned. Also more features and insights of the sheet were numerically studied using the coupled level set and volume of fluid method, considering effects of four non-dimensional parameters: Reynolds number, Weber number, dimensionless film thickness and drop–film curvature ratio. Results reveal that splashing can be suppressed by decreasing Reynolds number and Weber number. An increase in both the dimensionless film thickness and the film–drop curvature ratio is adverse to splashing onset. In addition, these four parameters can also greatly affect the geometrical shape and diameter of the sheet. In the second part, the air gap generated in the sheet–film contact neck region was investigated. It was noted that gas and liquid vortices produced near the liquid film surface render the film liquid to sink to form the air gap. Meanwhile, liquid accumulates inside the liquid sheet base gradually. Analysis in the velocity field suggests that the very thin preexisting film should be responsible for the vortex generation and the curvature ratio has minor effects on it, which is confirmed quantitatively as well.

Flow and heat transfer during a single drop impact on a liquid film

ABSTRACTA two-dimensional incompressible laminar computational model was established to analyze flow and heat transfer characteristics during a single liquid drop impinging onto a liquid film, with an underneath surface of relatively low temperature. Using the coupled level set and volume of fluid method, the gas–liquid interface at different time sequences can be obtained clearly. Concerning the heat transfer process, three different factors including impact velocity, film thickness, and drop diameter were discussed. Results indicate that liquid inside the film can be classified as three zones: the impact zone, the transition zone, and the static zone, specifically according to different heat flux. Average surface heat flux can be increased by increasing impact velocity, while effects of film thickness and drop diameter are minor. Corresponding mechanisms were interpreted as well. For heat flux distribution in the impact and transition zones, both film thickness and drop diameter influence the distribution greatly. With an increment in film thickness and drop diameter, heat flux in the impact zone decreases, while heat flux in the transition zone appears to be an opposite trend. Also in the transition zone, the fluctuation amplitude of the heat flux rises as the two factors are reduced.

Boiling from liquid drops impact on a heated wall

With aid of high-speed imaging, boiling phenomena near the Leidenfrost point from a single liquid drop impact on a heated solid wall were identified, including reflection rebound, explosive rebound and explosive detachment. Wall temperature was ranging in 182–384°C, and water, butanol, ethanol and 5.21% NaCl solution were adopted as the fluids due to their different properties. Transitions in the three boiling phenomena were determined concerning effects of Weber number and wall temperature, respectively. For the process of reflection rebound, the maximum spread factor and resident time of the drop are independent of wall temperature. With an increment in Weber number, the maximum spread factor rises, while its effect on the resident time is minor. Empirical correlations were acquired to predict the maximum spread factor and its corresponding dimensionless time as well as the dimensionless resident time. Moreover, formation of the central liquid jet was observed using the NaCl solution drop, which was interpreted by bubble entrainment with violent nucleating. Finally, preliminary discussions regarding drop detaching time in the explosive detachment process were undertaken. Results revealed that the drop detaching time decreases with Weber number, and wall temperature also can affect it.

Crown and drop rebound on thin curved liquid films

Experimental and theoretical work was conducted to enrich the previous study concerning a single liquid drop impinging on curved liquid films. Two typical outcomes including crown sheet at high impact velocity and drop rebound at low impact velocity were mainly discussed. Different from the traditional crown on a flat film, the crown on curved films has larger upper size but smaller base size. Increasing Weber number produces a positive influence on crown diameter when sphere-drop curvature ratio is higher than 0.303. While this effect is minor for curvature ratio of less than 0.114. By reducing curvature ratio, crown diameter first increases then remains unchanged. An empirical formula was also provided to predict the crown scale. With respect to drop rebound, a physical model was established to assist theoretical derivations. Based on energy conservation, a theoretical formula for predicting the inferior limit of rebound thresholds was obtained to offset deficiency in experiments, which involves Froude number and a deformation factor. In this work, the inferior limit of the critical Weber number is 0.8, applied to drop bouncing off both a curved film and a flat film.

Impact of a single drop on a flowing liquid film.

The impact of a single liquid drop on a flowing liquid film is experimentally and theoretically studied. The drop impact produces a crownlike rising liquid sheet, which radially expands. Small droplets can be formed from the crown sheet, resulting in splash. The present study results in three major contributions. (1) A theoretical model is developed to predict the expansion of the crown base. The model with an introduced energy loss factor is shown to be in satisfactory agreement with our experimental observations of drop impact on both stationary and flowing films. The energy loss factor is correlated to the properties of the film and drop. (2) Analysis is conducted to derive an equation for evaluating the stretching rate of the rising crown sheet, which is the local gradient of the rising velocity at the top edge of the crown sheet. It shows that the highest stretching rate appears where the drop spreading flow is right opposite to the film flow, which helps explain why the same location is most probable for splash to take place. (3) A parameter as a function of modified Weber and Reynolds numbers is defined to predict splash and nonsplash of drop impact on flowing films. The two nondimensional numbers evaluate the competition of the two flows (drop and film) against viscosity and surface tension effects. A threshold value of the parameter is found for the occurrence of splash impact on flowing films.

Drop deformation and breakup in flows with shear

A Volume of Fluid (VOF) method is applied to study the deformation and breakup of a single liquid drop in shear flows superimposed on uniform flow. The effect of shearing on the breakup mechanism is investigated as a function of the shear rate. Sequential images are compared for the parameter range studied; density ratios of liquid to gas of 20, 40, and 80, viscosity ratios in the range 0.5–50, Reynolds numbers between 20, a constant Weber number of 20, and the non-dimensional shear rate of the flow G=0–2.1875. It is found that while shear breakup remains similar for all values of shear rate considered, other breakup modes observed for uniform flows are remarkably modified with increasing shear rate. The time required for breakup is significantly decreased in strong shear flows. A simple model predicting the breakup time as a function of the shear rate and the breakup time observed in uniform flows is suggested.

What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion

Typical Hamiltonian liquids display exponential "Lyapunov instability", also called "sensitive dependence on initial conditions". Although Hamilton's equations are thoroughly time-reversible, the forward and backward Lyapunov instabilities can differ, qualitatively. In numerical work, the expected forward/backward pairing of Lyapunov exponents is also occasionally violated. To illustrate, we consider many-body inelastic collisions in two space dimensions. Two mirror-image colliding crystallites can either bounce, or not, giving rise to a single liquid drop, or to several smaller droplets, depending upon the initial kinetic energy and the interparticle forces. The difference between the forward and backward evolutionary instabilities of these problems can be correlated with dissipation and with the Second Law of Thermodynamics. Accordingly, these asymmetric stabilities of Hamilton's equations can provide an "Arrow of Time". We illustrate these facts for two small crystallites colliding so as to make a warm liquid. We use a specially-symmetrized form of Levesque and Verlet's bit-reversible Leapfrog integrator. We analyze trajectories over millions of collisions with several equally-spaced time reversals.

Effects of dispersed phase viscosity on drop deformation and breakup in inertial shear flow

The deformation and breakup of a single liquid drop subjected to simple shear flow is studied numerically using a diffuse interface free energy lattice Boltzmann method. The effect of dispersed phase viscosity on the behavior of the drop at a drop Reynolds number Re=10 is investigated over the range of viscosity ratios λ=0.1−2 (dispersed phase viscosity over continuous phase viscosity) with a focus on λ<1. For every λ the critical capillary number Cac for breakup is determined. For the range of λ considered, Cac decreases as λ increases. Both the extent of deformation and the breakup mechanism depend on the viscosity ratio and the capillary number. At the highest subcritical capillary number, the drop becomes less elongated and more inclined towards the vertical axis as the viscosity ratio increases. The changes in the drop breakup process are examined as the capillary number increases from the lowest supercritical Ca~Cac, to 1.2, 1.5 and 2Cac. Drops break by the end-pinching mechanism, except for λ=2 at Ca=2Cac where the drop undergoes capillary wave breakup.

A study of a single liquid drop impact on inclined wetted surfaces

Experimental observations concerning various outcomes during a single liquid drop impact on inclined wetted surfaces are performed using a high-speed digital camera. A 30 vol% glycerol/water solution, butanol and heptane are adopted as the fluids. At an impact angle ranging in 28.0°–74.7°, outcomes after impact including spreading, the jet sheet and splashing definitely emerge in succession with the Weber number increasing, whereas both rebound and partial rebound are random through numerous repeatable tests and they can only be observed at smaller impact angle, lower Weber number and higher viscosity. The increment in the Ohnesorge number results in smaller spreading factors, and its effect becomes weak at the small impact angle. The decrement in the impact angle leads to a rising front spreading factor, while the back one shows the opposite trend. In addition, the front spreading factor also can be increased by increasing the Weber number, but the back one varies less. Finally, several three-dimensional simulations are undertaken. Results reveal that the spreading factor in the normal direction can be decreased by reducing the impact angle, whereas the Weber number influences are minor. Also the decrement in the impact angle will enhance the pressure accumulation in the front direction inside the pre-existing film. This research provides some basic particularities for a drop impact on inclined surfaces.