Shape Of Liquid Meniscus Research Articles

A new spray current control for the reliable operation of a single-capillary electrospray

Cone-jet electrospray has been proposed for various applications due to its ability to produce monodisperse droplets. The stable operation of the electrospray process is extremely important for quality assurance purposes, particularly for applications that require long-term operations. Typically, both the spray current and liquid meniscus shape are used to monitor the working condition of an electrospray. In practice, various factors (operational and environmental) could affect the electrospray operation. Thus, a new spray current control system was developed to improve the stability of a single capillary electrospray operated in the cone-jet mode. The new spray current control system has two control loops: the primary loop for spray current control and the auxiliary loop for meniscus image control. A simple method to characterize the shape of the liquid meniscus and to identify the operational mode of an electrospray was proposed and the performance of the proposed spray current control system was investigated. It was shown that, with the new control strategy, a single capillary electrospray system was able to continuously operate when encountering a severe perturbation (without the over-shooting caused by the previous control strategies) (i.e., the electrospray converged to the target spray current and liquid meniscus shape even when challenged by step perturbation on the spray liquid feeding flow rate).

Microgravity Enabling Multirotors

This work establishes multirotor unmanned aerial vehicles (UAVs) as viable microgravity platforms. Towards this, a vertical microgravity enabling maneuver suitable for multirotors, control and automation strategies, and techniques to enhance the performance of multirotors as microgravity platforms are proposed. Successful microgravity enabling maneuvers are performed to show the proposed control and automation strategies’ effectiveness using two multirotor test vehicles. Further, this paper shows that all the existing multirotors can be microgravity platforms and provide a method to calculate the maximum microgravity duration a multirotor can provide. Finally, experiments are conducted onboard one of the multirotors executing a microgravity enabling maneuver to observe the effect of microgravity on liquid level in a capillary and liquid meniscus shape in a glass cuvette. These experiments and the microgravity enabling flight tests demonstrate that multirotors can be turned into microgravity platforms. To the best of the author’s knowledge, the two UAVs presented in this paper are the first multirotor UAVs to achieve microgravity and the first UAVs—fixed-wing or rotary—to conduct onboard experiments in microgravity.

Analysis of heat transfer performance and vapor–liquid meniscus shape of ultra-thin vapor chamber with supporting columns

Abstract Establishing the theoretical analysis model of vapor chamber is helpful to predict its heat transfer performance. It provides a valuable reference for heat transfer enhancement and structural design of ultra-thin vapor chamber (UTVC). In this paper, a theoretical analysis model of ultra-thin vapor chamber with supporting columns is established. This model considers the influence of supporting columns on vapor flow and the Marangoni effect on liquid flow and gives the analytical solution of temperature distribution and heat transfer limit of the UTVC. The accuracy of the model is verified by experiments. Compared with the experimental results, the maximum error of theoretical heat transfer limit is less than 10%. The meniscus shape under different heating power is displayed. The effects of key parameters such as the vapor space thickness, wick thickness, and the supporting columns arrangement on the heat transfer performance of the UTVC are analyzed. According to the theoretical analysis model, the critical thickness of vapor space is 0.3 mm. Thinning the wick thickness improves the uniformity of temperature. In addition, reducing the number of supporting columns on the flow section can effectively improve the heat transfer limit of UTVC.

Theoretical background for simulation of the interfacial layer “liquid-gas”

The study shows that macroscopic approach to the description of surface phenomena used to simulate the interfacial layer as a membrane using Laplace equation allows to calculate the shape of liquid meniscus regardless of the determination of height of liquid elevation in a capillary. The use of van der Waals statements to describe the state of the medium in the interfacial layer makes it possible to estimate the distribution of molecular pressure along the layer thickness. The tensor of interfacial stresses, represented by a set of ball and deviator parts, is determined based on continuous medium equilibrium conditions. The stresses that form the surface tension of the fluid are deviator components of the tensor. As a result, the study provides the expression linking the parameters of interfacial layer thickness and surface tension of liquid.

Influence of condensation enhancement effect on AFM image contrast inversion in hydrophilic nanocapillaries

We found that enhanced vapor condensation in nanopores and nanochannels on hydrophilic surfaces affects contrast and spatial resolution of the atomic force microscopy (AFM) imaging. It was demonstrated, that at ambient conditions the use of conventional Si probes may provide contrast inversion of the topography image of the hydrophilic samples with nano-sized surface features whereas use of the probes modified with hydrophilic Pt/C nanowires ensures adequate AFM imaging. The phenomenon of the AFM contrast inversion and the spatial resolution improvement effect obtained with the probes modified with the nanowires are discussed. The explanation of the phenomenon considering the shape of liquid meniscus in hydrophilic nanopores and nanochannels is proposed.

Porous micropillar structures for retaining low surface tension liquids

The ability to manipulate fluid interfaces, e.g., to retain liquid behind or within porous structures, can be beneficial in multiple applications, including microfluidics, biochemical analysis, and the thermal management of electronic systems. While there are a variety of strategies for controlling the disposition of liquid water via capillarity, such as the use of chemically modified porous adhesive structures and capillary stop valves or surface geometric features, methods that work well for low surface tension liquids are far more difficult to implement. This study demonstrates the microfabrication of a silicon membrane that can retain exceptionally low surface tension fluorinated liquids against a significant pressure difference across the membrane via an array of porous micropillar structures. The membrane uses capillary forces along the triple phase contact line to maintain stable liquid menisci that yield positive working Laplace pressures. The micropillars have inner diameters and thicknesses of 1.5–3 μm and ∼1 μm, respectively, sustaining Laplace pressures up to 39 kPa for water and 9 kPa for Fluorinert™ (FC-40). A theoretical model for predicting the change in pressure as the liquid advances along the porous micropillar structure is derived based on a free energy analysis of the liquid meniscus with capped spherical geometry. The theoretical prediction was found to overestimate the burst pressure compared with the experimental measurements. To elucidate this deviation, transient numerical simulations based on the Volume of Fluid (VOF) were performed to explore the liquid pressure and evolution of meniscus shape under different flow rates (i.e., Capillary numbers). The results from VOF simulations reveal strong dynamic effects where the anisotropic expansion of liquid along the outer micropillar edge leads to an irregular meniscus shape before the liquid spills along the micropillar edge. These findings suggest that the analytical prediction of burst Laplace pressure obtained under quasi-static condition (i.e., equilibrium thermodynamic analysis under low capillary number) is not applicable to highly dynamic flow conditions, where the liquid meniscus shape deformation by flow perturbation cannot be restored by surface tension force instantaneously. Therefore, the critical burst pressure is dependent on the liquid velocity and viscosity under dynamic flow conditions. A numerical simulation using Surface Evolver also predicts that surface defects along the outer micropillar edge can yield up to 50% lower Laplace pressures than those predicted with ideal feature geometries. The liquid retention strategy developed here can facilitate the routing and phase management of dielectric working fluids for application in heat exchangers. Further improvements in the retention performance can be realized by optimizing the fabrication process to reduce surface defects.

Multiscale Modeling of the Three-Dimensional Meniscus Shape of a Wetting Liquid Film on Micro-/Nanostructured Surfaces.

The design of structured surfaces for increasing the heat flux dissipated during boiling and evaporation processes via enhanced liquid rewetting requires prediction of the liquid meniscus shape on these surfaces. In this study, a general continuum model is developed to predict the three-dimensional meniscus shape of liquid films on micro/nanostructured surfaces based on a minimization of the system free energy that includes solid-liquid van der Waals interaction energy, surface energy, and gravitational potential. The continuum model is validated at the nanoscale against molecular dynamics simulations of water films on gold surfaces with pyramidal indentations, and against experimental measurements of water films on silicon V-groove channels at the microscale. The validated model is used to investigate the effect of film thickness and surface structure depth on the meniscus shape. The meniscus is shown to become more conformal with the surface structure as the film thickness decreases and the structure depth increases. Assuming small interface slope and small variation in film thickness, the continuum model can be linearized to obtain an explicit expression for the meniscus shape. The error of this linearized model is quantitatively assessed and shown to increase with increasing structure depth and decreasing structure pitch. The model developed can be used for accurate prediction of three-dimensional meniscus shape on structured surfaces with micro/nano-scale features, which is necessary for determining the liquid delivery rate and heat flux dissipated during thin-film evaporation. The linearized model is useful for rapid prediction of meniscus shape when the structure depth is smaller than or comparable to the liquid film thickness.

Mathematical modelling of liquid meniscus shape in cylindrical micro-channel for normal and micro gravity conditions

Mathematical model of liquid meniscus shape in cylindrical micro-channel of the separator unit of condensing/separating system is presented. Moving liquid meniscus in the 10 μm cylindrical microchannel is used as a liquid lock to recover the liquid obtained by condensation from the separators. The main goal of the liquid locks to prevent penetration of a gas phase in the liquid line at the small flow rate of the condensate and because of pressure fluctuations in the vapor-gas-liquid loop. Calculation of the meniscus shape has been performed for liquid FC-72 at different values of pressure difference gas - liquid and under normal and micro gravity conditions.

The influence of a magnetic field on the mechanical behavior of a fluid interface

This work focuses on a theoretical investigation of the shape and equilibrium height of a magnetic liquid–liquid interface formed between two vertical flat plates in response to vertical magnetic fields. The formulation is based on an extension of the so called Young–Laplace equation for an incompressible magnetic fluid forming a two-dimensional free interface. A first order dependence of the fluid susceptibility with respect to the magnetic field is considered. The formulation results in a hydrodynamic-magnetic coupled problem governed by a nonlinear second order differential equation that describes the liquid–liquid meniscus shape. According to this formulation, five relevant physical parameters are revealed in this fluid static problem. The standard gravitational Bond number, the contact angle and three new parameters related to magnetic effects in the present study: the magnetic Bond number, the magnetic susceptibility and its derivative with respect to the field. The nonlinear governing equation is integrated numerically using a fourth order Runge-Kutta method with a Newton–Raphson scheme, in order to accelerate the convergence of the solution. The influence of the relevant parameters on the rise and shape of the liquid–liquid interface is examined. The interface shape response in the presence of a magnetic field varying with characteristic wavenumbers is also explored. The numerical results are compared with asymptotic predictions also derived here for small values of the magnetic Bond number and constant susceptibility. A very good agreement is observed. In addition, all the parameters are varied in order to understand how the scales influence the meniscus shape. Finally, we discuss how to control the shape of the meniscus by applying a magnetic field.

Evaporative heat and mass transfer from the free surface of a liquid wicked into a bed of spheres

Evaporation of ethanol from square packed arrays of 3.95 mm diameter copper spheres in a transparent, enclosed chamber is investigated. The enclosure ensures that relatively saturated vapor conditions exist near the free surface. The desired heat flux is imposed on the copper substrate upon which the copper spheres are mounted, and the liquid level in the bed is maintained by wicking from a continuous supply of liquid provided by a syringe pump. Transparent windows in the enclosure allow for visualization of the evaporating liquid meniscus shape, which is recorded for different liquid feeding rates and heat fluxes. Experimentally measured meniscus profiles are compared to analytical results based on surface-energy minimization. A meniscus microregion is defined from the contact line to the length where the liquid thickness reaches 10 μm. An approximate kinetic theory-based analysis estimates that up to ∼55% of the total meniscus mass transfer occurs in this microregion.

A microscale model for thin-film evaporation in capillary wick structures

A numerical model is developed for the evaporating liquid meniscus in wick microstructures under saturated vapor conditions. Four different wick geometries representing common wicks used in heat pipes, viz., wire mesh, rectangular grooves, sintered wicks and vertical microwires, are modeled and compared for evaporative performance. The solid–liquid combination considered is copper–water. Steady evaporation is modeled and the liquid–vapor interface shape is assumed to be static during evaporation. Liquid–vapor interface shapes in different geometries are obtained by solving the Young–Laplace equation using Surface Evolver. Mass, momentum and energy equations are solved numerically in the liquid domain, with the vapor assumed to be saturated. Evaporation at the interface is modeled by using heat and mass transfer rates obtained from kinetic theory. Thermocapillary convection due to non-isothermal conditions at the interface is modeled for all geometries and its role in heat transfer enhancement from the interface is quantified for both low and high superheats. More than 80% of the evaporation heat transfer is noted to occur from the thin-film region of the liquid meniscus. The very small Capillary and Weber numbers resulting from the small fluid velocities near the interface for low superheats validate the assumption of a static liquid meniscus shape during evaporation. Solid–liquid contact angle, wick porosity, solid–vapor superheat and liquid level in the wick pore are varied to study their effects on evaporation from the liquid meniscus.

Evolution of Liquid Meniscus Shape in a Capillary Tube

There are still many unanswered questions related to the problem of a capillary surface rising in a tube. One of the major questions is the evolution of the liquid meniscus shape. In this paper, a simple geometry method is proposed to solve the force balance equation on the liquid meniscus. Based on a proper model for the macroscopic dynamic contact angle, the evolution of the liquid meniscus, including the moving speed and the shape, is obtained. The wall condition of zero dynamic contact angle is allowed. The resulting slipping velocity at the contact line resolves the stress singularity successfully. Performance of the present method is examined through six well-documented capillary-rise examples. Good agreements between the predictions and the measurements are observable if a reliable model for the dynamic contact angle is available. Although only the capillary-rise problem is demonstrated in this paper, the concept of this method is equally applicable to free surface flow in the vicinity of a contact line where the capillary force dominates the flow.