Stagnant Liquid Research Articles

Simplified generalised drift velocity correlation for elongated bubbles in liquid in pipes

Most of the existing drift velocity models have limitations, and sometimes low predictive capabilities, primarily because they are derived from experimental data which scarcely account for the combined effect of viscosity, surface tension and pipe inclination. Published data of drift velocity of elongated bubbles in pipes have been extracted from the open literature, and new data have been generated from Taylor bubble experiments conducted in a low pressure flow loop using nominal oil viscosities of 160cP and 1140cP in 0.099 m and 0.057 m internal diameter inclined pipes (1.0–7.5° from horizontal). These data have been processed and a simplified generalised drift velocity correlation established. The evaluation of some existing elongated bubble rise velocity has also been carried out. The prediction of the drift velocity of a single elongated gas bubble in liquid in pipes can sometimes be over-estimated by 20% or more, and sometimes be under-estimated by 20% or more. It is shown that the new proposed simplified generalised correlation has an improved predictive capability when used to estimate the drift velocity of a bubble in stagnant liquid in a pipe.

A novel numerical approach for investigation of the gas bubble characteristics in stagnant liquid using Young-Laplace equation

In the present study, the Young-Laplace equation was applied to simulate the adiabatic gas bubble growth from a submerged needle in stagnant liquid column. In order to solve the Young-Laplace equation the axisymmetric bubble height was used as input from experimental data. To increase the accuracy of Young-Laplace equations’ prediction during the bubble growth, the bubble was divided into four sections with the same height, and Young-Laplace equation was solved for each section individually. By dividing the bubble into four sections, the effects of viscosity and inertia forces within each section were reduced as compared to that of buoyancy and liquid-gas surface tension. Unlike the conventional Young-Laplace approach (one Young-Laplace equation for the entire bubble), the new approach was able to predict bubble characteristics reliably during the growth cycle. The bubble growth was investigated in a column of liquid with a triple contact line that fixed to the needle perimeter. To validate the numerical results, the bubble profiles that predicted by numerical simulation were compared with the experimental results. Experiments were performed by injection of air at constant gas flow rate of 600ml/h in the quiescent deionized water and SiO2 nanofluid. The nanoparticle concentrations were 0.05, 0.1 and 0.2wt%, and air flow injected from G14 and G17 standard needles. Eventually, evaluation of bubble characteristics, such as the bubble volume, the center of gravity, the instantaneous contact angle, and the bubble aspect ratio were investigated, and the effects of variation of liquid properties on the bubble characteristics were discussed. The results show that the present method can predict the bubble shape during 97.5% of growth time with mean absolute error of 6%. Furthermore, the results revealed that the bubble size decreased with increment of Bond number. Also, bubble instantaneous contact angle and bubble aspect ratio were almost irrelative to Bond number during the growth cycle.

Lift force acting on single bubbles in linear shear flows

Lift coefficients, CL, of single bubbles in linear shear flows are measured to investigate effects of the bubble shape, the liquid velocity gradient and the fluid property on CL. The range of the Morton number, M, tested is from logM = − 6.6 to − 3.2. The shapes of bubbles are spherical and ellipsoidal. A correlation of bubble aspect ratio for single bubbles in infinite stagnant liquids proposed in our previous study can give good evaluations for bubbles in the linear shear flows. The CL of spherical bubbles at low bubble Reynolds numbers, Re, depend on the dimensionless shear rate Sr and Re and decrease with increasing Re. These characteristics agree with the Legendre-Magnaudet correlation. The use of a single dimensionless group such as Re, the Eötvös number, the Weber number and the Capillary number cannot correlate CL of non-spherical bubbles. The trend of the critical Re for the reversal of the sign of CL is the same as that for the onset of oscillation of bubble motion, which supports the mechanism proposed by Adoua et al., at least within the range of −6.6 ≤ logM ≤ −3.2. An experimental database of CL is provided for validation of available CL models and CFD.

Rising behavior of single bubble in infinite stagnant non-Newtonian liquids

This work is an experimental study of the rising behavior of single air bubbles in infinite stagnant non-Newtonian liquids. Aqueous solutions of carboxymethyl cellulose (CMC) are selected to study the effect of rheological properties. The high speed photography is employed to record the bubble motion in CMC solutions. The bubble size, rising trajectory, bubble shape and velocities are determined by digital image processing technique. As expected, the rheological properties have great influence on the rising behavior of single bubble. In the less concentrated CMC solutions, the bubble rising process can be divided into three stages according to spatial evolution of bubble shape. The deformation changes the trajectories of rising bubbles and bubble hydrodynamics. As the solution concentration increases, the transitional stage gradually disappears. In the most concentrated CMC solution, the first continuous shape flattening stage is directly followed by a rising process with bubble shape basically constant, the rectilinear path and constant rising velocity. Dimensional analysis is performed to formulate a general dimensionless correlation for the deformation and motion of bubbles in infinite liquids by considering the rheological properties.

Numerical simulation of superheated vapor bubble rising in stagnant liquid

In present study, the rising of superheated vapor bubble in saturated liquid is simulated using volume of fluid method in OpenFOAM cfd package. The surface tension between vapor–liquid phases is considered using continuous surface force method. In order to reduce spurious current near interface, Lafaurie smoothing filter is applied to improve curvature calculation. Phase change is considered using Tanasawa mass transfer model. The variation of saturation temperature in vapor bubble with local pressure is considered with simplified Clausius–Clapeyron relation. The couple velocity–pressure equation is solved using PISO algorithm. The numerical model is validated with: (1) isothermal bubble rising and (2) one-dimensional horizontal film condensation. Then, the shape and life time history of single superheated vapor bubble are investigated. The present numerical study shows vapor bubble in saturated liquid undergoes boiling and condensation. It indicates bubble life time is nearly linear proportional with bubble size and superheat temperature.

Modelling and experimental investigation of horizontal buoyant gas jets injected into stagnant uniform ambient liquid

In this article, an experimental and theoretical study on the buoyant non-condensable gas jet that is injected horizontally into a high-density liquid ambient at different initial conditions is performed. Direct and instantaneous global measurements of the interface were performed using a high-speed photography. The position and motion of the entire gas jet were captured by a high-velocity camera and the images were processed, averaged and analyzed to extract the jet parameters and interface position. In the mathematical model, the rate of entrainment is assumed to be a function of the jet centerline velocity, the ratio of the mean jet and the ambient densities, while the entrainment coefficient depends on the local Froude number at the jet region. An interfacial shear stress acting at the interface between the jet flow and the water ambient in the opposed direction to the main jet momentum flux is considered. The results showed that the model is able to accurately predict the jet parameters: trajectory, spread, jet angles and penetration lengths as well as the jet regimes. An overall good agreement was obtained between the simulation and experimental results over a large range of Froude numbers and jet diameters. The developed model has proven to be an adequate tool to predict the different jet parameters.

Experimental and numerical 3D study of a Taylor drop rising in a stagnant heavier liquid

The present work concerns 3D numerical simulations and experiments on the rise of individual liquid Taylor drops through vertical columns of stagnant heavier liquids. Asymmetric effects are assessed for different conditions, following the observations in a previous work. Furthermore, the disturbances in the continuous phase due to the Taylor drop are studied. Experiments were performed with pairs of liquids in ranges not studied in the literature. Simulations targeted a broad range of dimensionless numbers and were done in a commercial code, using its implementation of the volume of fluid method in a three-dimensional domain. Results were processed according to relevant dimensionless numbers. Different behaviors are found concerning the existence or not of flow and drop shape asymmetries. Depending on the viscosity ratio, three ranges with different characteristics were identified. Relevant results are also reported concerning drop velocity when compared to the literature two-dimensional model. Drop influence in the surrounding continuous phase is also reported.

Molecular mechanism for liquid–liquid extraction: Two‐film theory revisited

We investigate here the molecular mechanism for liquid‐liquid extraction and revisit the classical two‐film theory. With equilibrium and non‐equilibrium molecular dynamics simulations, we illustrate the kinetics of solute crossing the interface and in particular the structure of the interface at which two stagnant liquid films adhere. Our simulation results show that beyond the two‐film theory, the interface is well structured and plays an essential role in solute transfer. We found that at the well‐developed interface region the overall density profile exhibits a dip, while the solute concentration shows a significant maximum. Free energy analysis demonstrates the interfacial enrichment of solute molecules serving as a potential well for solute adsorption. Thus, different from the assumption of the two‐film theory, our simulations show that there exists a resistance for solute molecules crossing the interface, which could be overcome only at high interface concentration of solute caused by interfacial enrichment. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2464–2470, 2017

Experimental detection of bubble-wall interactions in a vertical gas–liquid flow

Abstract Bubble motions and bubble-wall interactions in stagnant liquid were experimentally investigated by high-speed CCD and PIV technique with the main feature parameters such as Eotvos numbers Eo = 0.98–1.10, Morton number Mo = 3.21 × 10 − 9 and Reynolds numbers Re = 180 ~ 190. The effect of bubble injecting frequency and the distance S between the gas injection nozzle and the wall on the statistical trajectory of bubbles, average velocity distribution of flow field and Reynolds shear stress were studied in detail. It was shown that the combination of bubble injecting frequency and the distance S caused different bubble motion forms and hydrodynamic characteristics. When the normalized initial distance was very little, like S ⁎ ≈ 1.2 (here S ⁎ = 2 S / d e , and d e is the bubble equivalent diameter), bubbles ascended in a zigzag trajectory with alternant structure of high and low speed flow field around the bubbles, and the distribution of positive and negative Reynolds shear stress looked like a blob. With the increase of distance S ⁎ , bubbles' trajectory would tend to be smooth and straight from the zigzag curve. Meanwhile, with the increase of bubble injecting frequency, the camber of bubble trajectory at 20 y S ⁎ ≈ 3.6, the low-frequency bubbles gradually moved away from the vertical plane wall in a straight trajectory and the high-frequency bubbles gradually moved close to the vertical wall in a similar straight trajectory after an unstable camber motion. Under the circumstances, high-speed fluid was mainly distributed in the region between the wall and the bubbles, while the relative large Reynolds shear stress mainly existed in the region far away from the wall.

A broadly-applicable unified closure relation for Taylor bubble rise velocity in pipes with stagnant liquid

Taylor bubble velocity in slug flow is a closure relation which significantly affects the prediction of liquid holdup (or void fraction) and pressure gradient in mechanistic models of slug flow for oil and gas pipe applications. In this work, we use a validated Computational Fluid Dynamics (CFD) approach to simulate the motion of Taylor bubbles in pipes; the interface is tracked with a Level-Set method implemented in a commercial code. A large numerical database is generated covering the most ample range of fluid properties and pipe inclination angles explored to date (Eo ∈ [10, 700], Mo∈[1×10−6,5×103], andθ ∈ [0°, 90°]). A unified Taylor bubble rise velocity correlation is extracted from that database. The new correlation predicts the numerical database with 8.6% absolute average relative error and a coefficient of determination R2=0.97, and other available experimental data with 13.0% absolute average relative error and R2=0.84 outperforming existing correlations and models.

Superhydrophilic coatings with intricate nanostructure based on biotic materials for antifogging and antibiofouling applications

Methods for creating unique superhydrophilic interfaces by means of layer-by-layer (LbL) assembly have been demonstrated, and such interfaces have been used extensively in a variety of practical applications. Further, fabricating multifunctional superhydrophilic coatings using low-cost, nontoxic, environment-friendly, and plentiful materials from biological resources is highly desirable. Herein, superhydrophilic coatings with a highly jagged surface morphology were synthesized based on the electrostatic-interaction- or hydrogen-bonding-based LbL assembly of the biotic materials chitosan (CHI) and rice husk ash (RHA) nanosilica, which are abundantly available in nature. The synthesized multilayered (CHI/RHA nanosilica)n films were highly transparent and resisted fogging, frosting, and biofouling. Specifically, given the water-absorbing capability of the films, they showed excellent antifogging and antifrosting properties even under aggressive fogging and frosting conditions. Further, the as-prepared superhydrophilic multilayered films, which had a rough surface structure at the micro- and nanoscale, showed potential in reducing the attachment of proteins and various microorganisms, significantly preventing the phenomenon of biofouling in stagnant liquids. Hence, this work provides a new route for assembling superwetting coatings from cost-effective natural materials for use in industrial applications.

Experimental study of the falling film of liquid around a Taylor bubble

The present work reports an experimental study of the falling liquid film around single Taylor bubbles rising in vertical tubes filled with stagnant liquids by using a pulse-echo ultrasonic technique. The experiments were carried out in acrylic tubes 2.0 m long, with inner diameters of 0.019, 0.024 and 0.034 m, with five water-glycerin mixtures, corresponding to inverse viscosity number ranging from 15 to 22422. The rising bubble and the falling liquid film were measured by using ultrasonic transducers located at the one side of the tube. The velocity and profile of the Taylor bubble, and the development length and equilibrium thickness of the falling liquid film around the bubble were obtained by the ultrasonic signals processing. Based on the experimental results of the present study, several correlations available to estimate the equilibrium thicknesses of liquid films falling around Taylor bubbles were evaluated and new correlations were proposed to estimate the dimensionless equilibrium film thickness and the film development length respectively.

Packing effect on mass transfer and hydrodynamics of rising toluene drops in stagnant liquid

Terminal velocity and mass transfer of rising drops in a stagnant liquid were experimentally measured. The chemical system included the toluene drops whose acetic acid content was transferred to the surrounding water. Three sets of structured packing were used in the column to investigate the impact of packing at different heights of 10, 25 and 40cm. The effects of flow rate (Q), drop size (d), inverse viscosity (Nf), Eötvös number (Eo), and Reynolds number (Re) on terminal velocity, ut, and Froude number, Fr, were investigated. The critical points of d=3.4mm, Eo=0.5 and Nf=200 were found at which two regions of circulating and oscillating drops were separated, and the Fr was constant within each region. The effect of packing height on Fr and Sherwood number against Reynolds number was also investigated. Compared to the non-packed column it was revealed that a 30% increase in Sherwood number could be achieved using a packing with 40cm in height. Moreover, it was found that simultaneous increase of packing height and the flow rate consistently enhanced the mass transfer coefficient. Finally, a correlation was proposed which permitted the prediction of Sherwood number versus the dimensionless numbers of Reynolds, Weber and the packing height ratio.

Wall effects on the thermocapillary migration of single gas bubbles in stagnant liquids

In this paper, the governing continuum conservation equations for two-phase flow are solved using the commercial software package (Ansys-Fluent 1) to investigate the thermocapillary movement of a single bubble in stagnant liquid under zero-gravity condition. The current results show that different temperature gradients lead to different bubble migration velocities, and bubble migration velocity varies linearly with the temperature gradient for the given conditions. Furthermore the inside column diameter was found to have a significant influence on the thermocapillary migration of the bubble. Calculation were made in columns with inside diameters Dr 15, 20, 30, 40, 60, 80, 100 and 120 mm. Reduction on bubble migration velocity only occurred when the ratio of the bubble diameter to the column diameter, db/Dr, is greater than 0.267 due to column wall effect. On the other hand, the influence of the column diameter on the rise velocity is negligible when db/Dr is equal to or smaller than 0.267. No bubble shape deformation were observed and the bubble were spherical in shape for all column width. Present investigation of the shape and trajectory of bubble motion driven by surface tension-gradient in different column width is a new area of study and aims to support research into space applications which can help to determine the new migration time and speed.

Fiber-based monolithic columns for liquid chromatography.

Fiber-based monoliths for use in liquid chromatographic separations are defined by columns packed with aligned fibers, woven matrices, or contiguous fiber structures capable of achieving rapid separations of proteins, macromolecules, and low molecular weight components. A common denominator and motivating driver for this approach, first initiated 25years ago, was reducing the cost of bioseparations in a manner that also reduced residence time of retained components while achieving a high ratio of mass to momentum transfer. This type of medium, when packed into a liquid chromatography column, minimized the fraction of stagnant liquid and resulted in a constant plate height for non-adsorbing species. The uncoupling of dispersion from eluent flow rate enabled the surface chemistry of the stationary phase to be considered separately from fluid transport phenomena and pointed to new ways to apply chemistry for the engineering of rapid bioseparations. This paper addresses developments and current research on fiber-based monoliths and explains how the various forms of this type of chromatographic stationary phase have potential to provide new tools for analytical and preparative scale separations. The different stationary phases are discussed, and a model that captures the observed constant plate height as a function of mobile phase velocity is reviewed. Methods that enable hydrodynamically stable fiber columns to be packed and operated over a range of mobile phase flow rates, together with the development of new fiber chemistries, are shown to provide columns that extend the versatility of liquid chromatography using monoliths, particularly at the preparative scale. Graphical Abstract Schematic representation of a sample mixture being separated by a rolled-stationary phase column, resulting separated peaks shown in the chromatogram.

Facilitating conceptual change in students’ understanding of concepts related to pressure

The aim of this research was to explore the effects of three different types of methods of learning physics (conceptual change-based, real life context-based and traditional learning) on high school physics students in the 11th grade in terms of conceptual change they achieved in learning about the various topics (pressure exerted by solids, pressure in stagnant liquids and gases, buoyancy, Bernoulli’s principle). In this study, a pre-test/post-test quasi-experimental method with nonequivalent control group, involving a 3 (group) × 2 (time) factorial design was used. Study group 1 were given the conceptual change texts on the mentioned subjects, study group 2 were offered a teaching approach based on real life context-based learning, whereas the control group was taught in the traditional style. Data for the research were collected with the ‘pressure conceptual test’. As a result of research, the number of misconceptions had been reduced or shifted altogether in all three groups. After the instruction, it was seen that none of the students formed new misconceptions. It was found that the most positive change could be seen in the conceptual change text group followed by context-based and lastly traditional. The fact that none of the students formed new misconceptions is important, particularly since research such as the following shows that conceptual change is tenuous and inconsistent, taking time to shift in a sustained manner.

Numerical investigation of interaction between rising bubbles in a viscous liquid

The rising behavior of bubbles undergoing bubble-bubble interaction in a viscous liquid is studied using a two-dimensional direct numerical simulation. Level contour reconstruction method (LCRM), one of the connectivity-free front tracking methods, is applied to describe a moving interface accurately under highly deformable conditions. This work focuses on the effects of bubble size on the interaction of two bubbles rising side-by-side in a stagnant liquid. Several characteristics of bubble-bubble interaction are analyzed quantitatively as supported by energy analysis. The results showed clear differences between small and large bubbles with respect to their interaction behavior in terms of lateral movement, vortex intensity, suppression of surface deformation, and viscous dissipation rate. Distributions of vorticity and viscous dissipation rate near the bubble interfaces also differed depending on the size of the bubbles. Strong vortices from large bubbles triggered oscillation in bubble-bubble interaction and played a dominant role in the interaction process as the size of bubbles increases.

Phase-field model-based simulation of two-phase fluid motion on partially wetted and textured solid surface

The applicability of a numerical method is preliminarily examined to determine its suitability for simulations of microscopic immiscible liquid-liquid motion on solid walls, which is used for evaluating fluidic devices with heterogeneously wettable and textured surfaces. The method adopts a conservation-modified Allen-Cahn equation for calculations of diffuse-interface advection and formation based on a phase-field model, and a lattice-Boltzmann method is employed as numerical scheme for solving the two-phase fluid-dynamics equations. The simulations demonstrate the ability of the method to successfully capture the shape and motion of a droplet, not only on flat and grooved surfaces in a stagnant liquid under an external force, but also in a liquid flow inside a rectangular microchannel.

Numerical study on the wettability dependent interaction of a rising bubble with a periodic open cellular structure

A phase-field method for interface resolving numerical simulations of two-phase flows with OpenFOAM® is validated for the buoyancy-driven rise of a single air bubble through a viscous stagnant liquid using experimental data from literature. The validation encompasses the terminal bubble rise velocity and the instantaneous cutting of the bubble by a solid horizontal cylinder. In the latter process, the numerical method takes into account the equilibrium contact angle of the three-phase system. The numerical method is then used to study the behavior of a single air bubble rising through a representative subdomain of a periodic open cellular structure (POCS) with cubic cell geometry filled with stagnant water. The results indicate that the bubble shape and path do significantly depend on the structure wettability. In the industrial application of POCS for enhancing mass transfer and as catalytic supports, the utilization of structures with high wettability (low contact angles) is expected to be beneficial.

Thermocapillary migration of an isolated droplet and interaction of two droplets in zero gravity

Fluid transfer within a stagnant liquid presents a significant challenge in zero-gravity conditions due to the lack of buoyancy effects. This challenge can be overcome by the utilisation of the Marangoni effect, or more specifically thermocapillary migration. The thermocapillary migration of droplets is driven by temperature gradients within the multiphase system which bring about a surface tension gradient driving the flow from the cold to the hot region. The migration speed of the droplet is significantly impacted by the heat transfer both inside the droplet and in its surroundings.This paper presents the analysis of drop movement in a stagnant liquid using computational fluid dynamics (CFD). The commercial software package Ansys-Fluent v.13 [1] is used to solve the governing continuum conservation equations for two-phase flow using the Volume of Fluid (VOF) method to track the liquid/liquid interface in 2D domain. This approach has been shown to be a valuable tool for studying the phenomena of liquid–liquid interaction. A strong agreement has been found with experimental observations conducted in microgravity.The inherent velocity of drops has been found to decrease with increasing Marangoni number. This finding is in line with the previous space experiments of Xie et al. (2005) [2] and in contrast to the numerical results of Ma (1999) [3] using the same liquid for the droplet and the host liquid.Data obtained in the present numerical study has been used to derive an expression predicting the scaled droplet velocity as a function of Marangoni number. A numerical study of the interaction of two spherical droplets undergoing thermocapillary migration in microgravity is also presented. The temperature thrust from the leading droplet towards the trailing droplet was found to disturb its migration velocity, but the trailing droplet was found to have no influence on the migration of the leading droplet.