The problem of liquid droplet combustion-reexamination

The simple quasi-steady analysis of the combustion of a liquid fuel droplet in an oxidising atmosphere provides unsatisfactory explanations for several experimental observations. It's prediction of values for the burning constant (K), the flame-to-droplet diameter ratio ( ) and the flame temperature (Tf) have been found to be amgibuous if not completely inaccurate. A critical survey of the literature has led us to a detailed examination of the effects of unsteadiness and variable properties. The work published to date indicates that the gas-phase unsteadiness is relatively short and therefore quite insignificant.A new theoretical analysis based on heat transfer within the droplet is presented here. It shows that the condensed-phase unsteadiness lasts for about 20â??25% of the total burning time. It is concluded that the discrepancies between experimental observations and the predictions of the constant-property quasi-steady analysis cannot be attributed either to gas-phase or condensed-phase unsteadiness.An analytical model of quasi-steady droplet combustion with variable thermodynamic and transport properties and non-unity Lewis numbers will be examined. Further findings reveal a significant improvement in the prediction of combustion parameters, particularly of K, when consideration is given to variations of cp and λ with the temperature and concentrations of several species. Tf is accurately predicted when the required conditions of incomplete combustion or low ( ) at the flame are met. Further refinement through realistic Lewis numbers predicts ( ) meaningfully.

Numerical modeling of the non-isothermal liquid droplet impact on a hot solid substrate

The heat transfer from a solid phase to an impinging non-isothermal liquid droplet is studied numerically. A new approach based on an arbitrary Lagrangian-Eulerian (ALE) finite element method for solving the incompressible Navier Stokes equations in the liquid and the energy equation within the solid and the liquid is presented. The novelty of the method consists in using the ALE-formulation also in the solid phase to guarantee matching grids along the liquid solid interface. Moreover, a new technique is developed to compute the heat flux without differentiating the numerical solution. The free surface and the liquid solid interface of the droplet are represented by a moving mesh which can handle jumps in the material parameter and a temperature dependent surface tension. Further, the application of the Laplace-Beltrami operator technique for the curvature approximation allows a natural inclusion of the contact angle. Numerical simulation for varying Reynold, Weber, Peclet and Biot numbers are performed to demonstrate the capabilities of the new approach. (C) 2014 Elsevier Ltd. All rights reserved.

Modeling of the non-isothermal liquid droplet impact on a heated solid substrate with heterogeneous wettability

A comprehensive numerical investigation on the impingement and spreading of a non-isothermal liquid droplet on a solid substrate with heterogeneous wettability is presented in this work. The time-dependent incompressible Navier-Stokes equations are used to describe the fluid flow in the liquid droplet, whereas the heat transfer in the moving droplet and in the solid substrate is described by the energy equation. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the time-dependent incompressible Navier-Stokes equation and the energy equation in the time-dependent moving domain. Moreover, the Marangoni convection is included in the variational form of the Navier-Stokes equations without calculating the partial derivatives of the temperature on the free surface. The heterogeneous wettability is incorporated into the numerical model by defining a space-dependent contact angle. An array of simulations for droplet impingement on a heated solid substrate with circular patterned heterogeneous wettability are presented. The numerical study includes the influence of wettability contrast, pattern diameter, Reynolds number and Weber number on the confinement of the spreading droplet within the inner region, which is more wettable than the outer region. Also, the influence of these parameters on the total heat transfer from the solid substrate to the liquid droplet is examined. We observe that the equilibrium position depends on the wettability contrast and the diameter of the inner surface. Consequently. the heat transfer is more when the wettability contrast is small and/or the diameter of inner region is large. The influence of the Weber number on the total heat transfer is more compared to the Reynolds number, and the total heat transfer increases when the Weber number increases. (C) 2015 Elsevier Ltd. All rights reserved.

Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet

In this paper, the role of vertical component of Surface tension of a droplet on the elastic deformation of a finite-thickness flexible membrane was theoretically analyzed using Hankel transformation. The vertical displacement at the Surface was derived and can be reduced to Lester's or Rusanov's solutions when the thickness is infinite. Moreover, some Simulations of the effect of a liquid droplet on a membrane with a finite thickness were made. The numerical results showed that there exists a saturated membrane thickness of the order of millimeter, when the thickness of a membrane is larger than such a value, the membrane can be regarded as a half-infinite body. Further numerical calculations for soft membrane whose thickness is far below the saturated thickness were made. By comparison between the maximum vertical displacement of an ultrathin soft membrane and a half-infinite body, we found that Lester's or Rusanov's solutions for a half-infinite body cannot correctly describe Such cases. In other words, the thickness of a soft membrane has great effect on the surface deformation of the ultrathin membrane induced by a liquid droplet. (C) 2009 Elsevier Inc. All rights reserved.

Equilibration of a liquid droplet-vapor-gas mixture downstream of a shock wave

The equations of motion for the flow of a mixture of liquid droplets, their vapor, and an inert gas through a normal shock wave are derived. A set of equations is obtained which is solved numerically for the equilibrium conditions far downstream of the shock. The equations describing the process of reaching equilibrium are also obtained. This is a set of first-order nonlinear differential equations and must also be solved numerically. The detailed equilibration process is obtained for several cases and the results are discussed.

Modelling electromagnetically levitated liquid droplet oscillations

This work comprises accurate computational analysis of levitated liquid droplet oscillations in AC and DC magnetic fields. The AC magnetic field interacting with the induced electric current within the liquid metal droplet generates intense fluid flow and the coupled free surface oscillations. The pseudo-spectral technique is used to solve the turbulent fluid flow equations for the continuously dynamically transformed axisymmetric fluid volume. The volume electromagnetic force distribution is updated with the shape and position change. We start with the ideal fluid test case for undamped Rayleigh frequency oscillations in the absence of gravity, and then add the viscous and the DC magnetic field damping. The oscillation frequency spectra are further analysed for droplets levitated against gravity in AC and DC magnetic fields at various combinations. In the extreme case electrically poorly conducting, diamagnetic droplet (water) levitation dynamics are simulated. Applications are aimed at pure electromagnetic material processing techniques and the material properties measurements in uncontaminated conditions.

Enhanced Nanoparticle Detection with Liquid Droplet Resonators

Whispering gallery mode particle sensing experiments are commonly performed with solid resonators, whereby the sensing volume is limited to the weak evanescent tail of the mode near the resonator surface. In this work we discuss in detail the sensitivity enhancements achievable in liquid droplet resonators wherein the stronger internal fields and convenient means of particle delivery can be exploited. Asymptotic formulae are derived for the relative resonance shift, line broadening and mode splitting of TE and TM modes in liquid droplet resonators. As a corollary the relative fraction of internal and external mode energy follows, which is shown to govern achievable sensitivity enhancements of solute concentration measurements in droplet sensors. Experimental measurements of nanoparticle concentration based on whispering gallery mode resonance broadening are also presented.

Observation Of Diffusion Process Of A Water Droplet Immersed In Protein Solution In Microgravity

Pure liquid - liquid diffusion driven by concentration gradients is hard to study in a normal gravity environment since convection and sedimentation also contribute to the mass transfer process. We employ a Mach - Zehnder interferometer to monitor the mass transfer process of a water droplet in EAFP protein solution under microgravity condition provided by the Satellite Shi Jian No 8. A series of the evolution charts of mass distribution during the diffusion process of the liquid droplet are presented and the relevant diffusion coefficient is determined.

The Head-On Colliding Process Of Binary Liquid Droplets At Low Velocity: High-Speed Photography Experiments And Modeling

The experimental and theoretical studies are reported in this paper for the head-on collisions of a liquid droplet with another of the same fluid resting on a solid substrate. The droplet on the hydrophobic polydimethylsiloxane (PDMS) substrate remains in a shape of an approximately spherical segment and is isometric to an incoming droplet. The colliding process of the binary droplets was recorded with high-speed photography. Head-on collisions saw four different types of response in our experiments: complete rebound, coalescence, partial rebound With conglutination, and coalescence accompanied by conglutination. For a complete rebound, both droplets exhibited remarkable elasticity and the contact time of the two colliding droplets was found to be in the range of 10-20 ms. With both droplets approximately considered as elastic bodies, Hertz contact theory was introduced to estimate the contact time for the complete rebound case. The estimated result Was found to be on the same order of magnitude as the experimental data, which indicates that the present model is reasonable. (C) 2008 Elsevier Inc. All rights reserved.

Deformation Of Pdms Membrane And Microcantilever By A Water Droplet: Comparison Between Mooney-Rivlin And Linear Elastic Constitutive Models

In this paper, we studied the role of vertical component Of Surface tension of a water droplet on the deformation of membranes and microcantilevers (MCLs) widely used in lab-on-a-chip and micro-and nano-electromechanical system (MEMS/NEMS). Firstly, a membrane made of a rubber-like material, poly(dimethylsiloxane) (PDMS), was considered. The deformation was investigated using the Mooney-Rivlin (MR) model and the linear elastic constitutive relation, respectively. By comparison between the numerical solutions with two different models, we found that the simple linear elastic model is accurate enough to describe such kind of problem, which would be quite convenient for engineering applications. Furthermore, based on small-deflection beam theory, the effect of a liquid droplet on the deflection of a MCL was also studied. The free-end deflection of the MCL was investigated by considering different cases like a cylindrical droplet, a spherical droplet centered on the MCL and a spherical droplet arbitrarily positioned on the MCL. Numerical simulations demonstrated that the deflection might not be neglected, and showed good agreement with our theoretical analyses. (C) 2008 Elsevier Inc. All rights reserved.

Controlled growth of silicon nanowires by solid-liquid-solid method and their formation mechanism

High quality silicon nanowires (SiNWs) were grown directly from n-(111) silicon single crystal substrate by using Au film as a metallic catalyst. The diameter and length of the formed nanowires are 30-60 nm and from several micrometers to sereral tens of micrometers, respectively. The effects of Au film thickness, annealing temperature, growth time and N-2 gas flow rate on the formation of the nanowires were experimentally investigated. The results confirmed that the silicon nanowires with controlled diameter, length, shape and orientation can be obtained via reasonably choosing and optimizing various technical conditions. The formation process of the silicon nanowires is analyzed qualitatively based on solid-liquid-solid growth mechanism.

Droplet size control with methanol-repellent surface in a sampling device for continuous annular electrochromatography

The eluent droplet size defines the number of sampling compartments in a continuously operated annular electrochromatograph and therefore influences separation efficiency. In this work, an assembly of two capillaries, a feeding capillary on the top and a receiving capillary placed under it, has been investigated to control droplet size. The receiving capillary prevents the liquid droplet formation beyond a critical size, which reduces the volume of sampling compartment as compared with the case of the electrolyte flow driven solely by gravity. With a receiving capillary, the electrolyte droplet size was reduced from 1.5 to 0.46 mm. Further decrease of droplet size was not possible due to a so-called droplet jump upwards effect which has been observed on a hydrophilic glass surface with water. A typical electrolyte used in CAEC has high methanol content. In an attempt to improve the methanol-repellent properties of the glass surface, two approaches have been implemented: (i) self-assembled chemisorbed monolayers of an alkylsiloxane and (ii) fabrication of a nano-pin film. The methanol-repellent surface of the feeding capillary suppressed the droplet jump upwards effect. The surface remained methanol repellent in different solutions with lower polarity than that of water.

LIQUID MARBLES GRANULATED USING SUPER-HYDROPHOBIC METAL POWDERS

Superhydrophobic (SH) particles based on a copper substrate were prepared by a silver deposition technique of different particle sizes from 10µm to 425µm. Such SH particles were found to be pH-responsive and liquid marbles formed using the SH copper substrate destabilised under certain pH conditions. The exposure to high concentrations of acidic or basic gases caused immediate collapse of the liquid marble. However, low concentrations of acidic and basic gases could diffuse across the shell of liquid marbles without adversely affecting the structure. Liquid marbles formed with large SH particles (425
µm) did not fully form a mono-layer around the liquid droplet. This phenomenon, whereby SH particles slide down the surface of the water droplet until an equilibrium position is reached, was studied using a mathematical approach, which related the angle to the vertical axis of the SH particles at t
he equilibrium F, to the shape of liquid marble and the contact angle, ?.

Colorimetric determination of sulfur dioxide in air using a droplet collector of malachite green solution

The measurement of sulfur dioxide in air at the parts-per-billion level is described. The experimental arrangement consists of two optical fibers placed on opposite sides of a liquid droplet of malachite green solution. After light has been passed through the droplet, the transmitted light is measured by a referenced photodetection arrangement. The light used in this absorption process is from a monochromatic source (lambda(max) 625 nm). This arrangement permits the variation of color in the droplet to be measured. The sulfur dioxide in the sample is collected by the droplet; it reacts with malachite green resulting in a colorless dye. The decoloration of the solution is proportional to the concentration of sulfur dioxide sampled. The signal depends on the sample flow rate. The present technique is simple, inexpensive, and permits a fast and near real time measurement while consuming very little reagent, (C) 1999 Academic Press.

Colorimetric determination of ambient ozone using indigo blue droplet

A simple and sensitive method based on a liquid droplet is described for the measurement of atmospheric ozone. A 30 μL drop of indigo blue solution is suspended in a flowing-air sampling stream. The ozone collected reacts with the indigo solution resulting in its decolorization. The colorimetric sensor is composed of two optical fibers and the source of monochromatic light was a red LED (625 nm). The calibration curve was constructed with ozone standard concentrations ranging from 37 - 123 ppbv. The detection limit achieved was 7.3 ppbv. The method considered here showed itself to be easy to apply with a fast response and a total analysis time of only 5 minutes.