Dynamic fluid flow behaviour of a tank draining through a vertical tube

This paper describes the unsteady draining of a sealed tank partially filled with water. The water discharges via a vertical tube into an open tank at atmospheric conditions. The air inflow, compensating for the volume of the discharged liquid, enters the system in an oscillatory manner, much like the “gulping” seen in an upended beer bottle. A mathematical model, based closly on that derived by Dougall & Kathiresan [Chem. Engng Commun. 8, 289–304 (1981)], has been applied to predict the pressure fluctuations in the closed tank. The rate of water discharge from the tank has been predicted and gives a much closer agreement with experimental results than a prediction based on a steady counter-current flooding limitation approach. A drift flux model has been used to describe the two-phase flow effect in the tube and the Wallis flooding criterion has been modified for use in the slug flow regime to describe the boundary conditions at the bottom of the tube. The pressure fluctuations in the sealed tank have been measured and compared with results obtained from the mathematical prediction for a variety of tube diameters.     

Marangoni效应下气泡上升过程的FTM模拟

采用界面跟踪法FTM(Front-Tracking Method),并结合CSF(continuum surface force)模型,研究了在垂直方向上温度分布不均匀的对称流场中由Marangoni效应引起的气泡上升运动问题。模拟了在不同的M a数和Pr数下单气泡及同轴双气泡的运动。研究结果表明,在不同的M a数下气泡的运动差异较大,M a数越大,气泡运动至稳态时的速度越大,且气泡运动的最大速度值与M a数呈正相关关系;增大Pr数所造成的粘度增大或热扩散率减小将削弱气泡的迁移运动;Marangoni对流中双气泡的局部运动证实了温度梯度和气泡运动速度紧密相关。     

Fluid flow driven along microchannel by its upper stretching wall with electrokinetic effects

We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boundary condition, for instance, the zero electrostatic potential in the middle of the channel. Using the similarity transformation, we employ the homotopy analysis method (HAM) to get the analytical solution of the model. In our approach, the unknown pressure constant and the integral constant related to the electric potential are solved spontaneously by using the proper boundary conditions on the channel walls, which makes our model consistent with the commonly accepted models in the field of fluid mechanics. It is expected that our model can offer a general and proper way to study the flow phenomena in microchannels.     

Adiabatic and diabatic two-phase venting flow in a microchannel

The growth and advection of the vapor phase in two-phase microchannel heat exchangers increase the system pressure and cause flow instabilities. One solution is to locally vent the vapor formed by capping the microchannels with a porous, hydrophobic membrane. In this paper we visualize this venting process in a single 124 μm by 98 μm copper microchannel with a 65 μm thick, 220 nm pore diameter hydrophobic Teflon membrane wall to determine the impact of varying flow conditions on the flow structures and venting process during adiabatic and diabatic operation. We characterize liquid velocities of 0.14, 0.36 and 0.65 m/s with superficial air velocities varying from 0.3 to 8 m/s. Wavy-stratified and stratified flow dominated low liquid velocities while annular type flows dominated at the higher velocities. Gas/vapor venting can be improved by increasing the venting area, increasing the trans-membrane pressure or using thinner, high permeability membranes. Diabatic experiments with mass flux velocities of 140 and 340 kg/s/m² and exit qualities up to 20% found that stratified type flows dominate at lower mass fluxes while churn-annular flow became more prevalent at the higher mass-flux and quality. The diabatic flow regimes are believed to significantly influence the pressure-drop and heat transfer coefficient in vapor venting heat exchangers.     

Collision dynamics of bubble pairs moving through a perfect liquid

Equations are derived describing the inertial motion of a bubble pair through a perfect liquid. The relative bubble motion is driven by an interactional force induced by the centre of mass motion. This force can be derived from a potential that is proportional tos ⁿ (n3) and that depends on the bubble pair orientation. The path of two bubbles passing each other is investigated. The angle of deflection of the relative velocity in a two-bubble encounter is calculated numerically as a function of the impact parameter, the relative velocityg and the ratio of the centre of mass velocity componentsc ₂/c ₁. The specific conditions necessary for two bubbles to collide are determined. Ifc ₂/c ₁>1 there is a region with irregular behaviour of the deflection angle. The collision cross-section is calculated and depends smoothly ong, approximately proportional tog ^–1, and has a weak dependence onc ₂/c ₁.     

The structure of water-air bubble grid turbulence in a square duct

Local measurements of void fraction and continuous phase velocity field in water-air bubble, grid turbulence were conducted in a channel of vertical, square test section. The measured statistics indicate that, due mainly to the interaction of mean shear with the dispersed phase, the turbulence structure of the flow is modified. The observed change is characterized by a strong spatial dependence of void fraction and liquid flow properties, and the emergence of two spatial regions controlled by different physical processes. Intensity measurements indicate significant departure from isotropy in the flow. Two distinct regimes corresponding to low and high values of void fraction have been also identified. The autocorrelation and spectra measurements indicate that for low void fraction the scales of turbulence decrease while for higher values of void fraction increase again and inverse cascade is observed.     

Downstream pressure and elastic wall reflection of droplet flow in a T-junction microchannel

This paper discusses pressure variation on a wall during the process of liquid flow and droplet formation in a T-junction microchannel. Relevant pressure in the chan-nel, deformation of the elastic wall, and responses of the droplet generation are analyzed using a numerical method. The pressure difference between the continuous and dis-persed phases can indicate the droplet-generation period. The pressure along the channel of the droplet flow is affected by the position of droplets, droplet-generation period, and droplet escape from the outlet. The varying pressures along the channel cause a nonuniform deformation of the wall when they are elastic. The deformation is a vibration and has the same period as the droplet generation arising from the process of droplet formation.     

Extensional flow of liquid jets formed by bubble collapse in oils under cavitation-generated pressure waves

We report a study of liquid jets which are formed by bubble collapse under cavitation-generated pressure waves. The results obtained for jets formed from samples of a multigrade motor oil provide the first evidence that such jets experience a significant degree of extensional deformation, at high rates of extension. The results support the conclusion that the reduced velocity and final length of such jets, relative to their Newtonian counterparts, is due to an increased resistance to extensional flow. Insofar as the multigrade oils studied here are made viscoelastic by polymer additives and evidently possess significant levels of resistance to extension, the results provide evidence in support of a mitigating effect of viscoelasticity on a cavitation damage mechanism, as mooted by Berker et al. (J Non Newton Fluid Mech 56:333, 1995).     

Two-phase annular flow and evaporative heat transfer in a microchannel

A physical and mathematical model has been developed to predict the two-phase flow and heat transfer in a microchannel with evaporative heat transfer. Sample solutions to the model were obtained for both constant wall temperature and constant wall heat flux conditions. Results are provided for evaporation rate, liquid film thickness, liquid and vapor phase pressure and temperature distributions. In addition to the sample calculations that were used to illustrate the transport characteristics, computations based on the current model were performed to generate results for comparisons with the experimental results of Qu and Mudawar (2004) where two different mass flow rates of the working fluid were used in the experiment. The comparisons of total pressure drops with the experimental data of Qu and Mudawar (2004) cover the wall heat flux range of 142.71-240 W/cm² with a total channel mass flux of 400.1 kg/m² s and also the wall heat flu range of 99.54-204.39 W/cm² with total channel mass flux of 401.9 kg/m² s. The calculated results from the current model match closely with those of Qu and Mudawar (2004).     

The Motion of Long Bubbles in a Network of Tubes

The motion and interaction of discrete bubbles in porous materials is studied numerically using a network model. The goal is to extend analytical results for the motion of bubbles through a single straight tube to a more realistic geometry for porous materials, modeled here as a planar network of straight tubes of different radii. The problem is characterized by two dimensionless parameters, the capillary number (Ca) and the volume fraction of bubbles (); results are characterized by determining the effective permeability of the network and the mean residence time of bubbles in the material. The simulations indicate that at low volume fraction most of the bubbles follow a limited number of high-flow pathways through the network. In this case the predictions of our simulations can be approximated by a simple analytical model. Bubbles interact with each other because their presence changes the local resistance to flow in individual tubes. As increases, interactions between individual bubbles become important resulting in a wider range of residence times in the porous material.     

Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel

By method of the Laplace transform, this article presents semi-analytical solutions for transient electroosmotic and pressure-driven flows (EOF/PDF) of two-layer fluids between microparallel plates. The linearized Poisson-Boltzmann equation and the Cauchy momentum equation have been solved in this article. At the interface, the Maxwell stress is included as the boundary condition. By numerical computations of the inverse Laplace transform, the effects of dielectric constant ratio ε , density ratio ρ , pressure ratio p, viscosity ratio μ of layer II to layer I, interface zeta potential difference △ψ, interface charge density jump Q, the ratios of maximum electro-osmotic velocity to pressure velocity α , and the normalized pressure gradient B on transient velocity amplitude are presented.We find the velocity amplitude becomes large with the interface zeta potential difference and becomes small with the increase of the viscosity. The velocity will be large with the increases of dielectric constant ratio; the density ratio almost does not influence the EOF velocity. Larger interface charge density jump leads to a strong jump of velocity at the interface. Additionally, the effects of the thickness of fluid layers (h1 and h2 ) and pressure gradient on the velocity are also investigated.     

Estimates of Barometric Pumping of Moisture Through Unsaturated Fractured Rock

We present a theory for the motion of water vapor at depth in a discretely fractured permeable medium induced by atmospheric barometric pressure fluctuations, or barometric pumping. The theory involves multiphase mass and energy transport in a fracture/matrix system, with discrete representation of the fracture system. The barometric pressure fluctuations are approximated as periodic in time, with amplitude corresponding to measured values. To simplify the analysis, a single-horizon approximation is applied in which the time-mean gradient is used to evaluate the vertical advective flux in the fractures. Time-periodic solutions are obtained numerically, enabling the calculation of the net efflux of moisture per cycle. The model is applied to material representative of the Yucca Mountain region of southwestern Nevada. The results indicate that the efflux of moisture carried upward from significant depths by barometric pumping is much less than the near surface efflux that is commonly estimated by assuming that air enters the medium dry and is returned to the atmosphere fully saturated with water vapor. This near surface efflux consists primarily of moisture discharged from the upper layer which is frequently replenished by precipitation. Of greater interest to nuclear waste repository design and estimations of net infiltration in arid regions is the fraction of the total moisture efflux that comes from significant depths. This deep transport is quantified by the fracture/matrix transport model described here. Although the transport by barometric pumping from depth is small compared to the total moisture expelled from the surface layer, it is an order of magnitude greater than the vertical moisture flux carried from depth by diffusion.     

Symmetric mode instability of the slipflow model for flows in a microchannel with a vanishing Reynolds number

The slipflow model is usually used to study microflows when the Knudsen number lies between 0.01 and 0.1. The instability due to microscale effect seems to have never been studied before. In this paper we present preliminary results for the instability (not physical instability) of this model when applied to microchannel flow with a vanishing Reynolds number. The present paper is restricted to symmetrical mode. Both first-order and second-order slip boundary conditions will be considered. The project supported by the National Natural Science Foundation of China (10025210) and Tsinghua Project for Basic Research (2002)     

Void fraction measurement of bubble and slug flow in a small channel using the multivision technique

Using the multivision technique, a new void fraction measurement method was developed for bubble and slug flow in a small channel. The multivision system was developed to obtain images of the two-phase flow in two perpendicular directions. The obtained images were processed—using image segmentation, image subtraction, Canny edge detection, binarization, and hole filling—to extract the phase boundaries and information about the bubble or slug parameters. With the extracted information, a new void fraction measurement model was developed and used to determine the void fraction of the two-phase flow. The proposed method was validated experimentally in horizontal and vertical channels with different inner diameters of 2.1, 2.9, and 4.0 mm. The proposed method of measuring the void fraction has better performance than the methods that use images acquired in only one direction, with a maximum absolute difference between the measured and reference values of less than 6%.     

A physically based correlation for the effects of power law rheology and inclination on slug bubble rise velocity

A study has been made of the motion of long bubbles in inclined pipes containing viscous Newtonian and non-Newtonian liquids. A semi-theoretical expression for the rise velocity of air bubbles in water is derived on the hypothesis that the dominant factor is the momentum exchange of the bubble underflow, i.e. the bubble nose shape. The correlation calls on empirical inputs from established literature on bubble rise speeds at high Reynolds number. The effects of increasing Newtonian viscosity are analysed with reference to the momentum exchange and it is shown how viscosity reduces the inclination dependence of the bubble Froude number. Results from an experimental survey in seven different non-Newtonian liquids in three different diameter pipes are presented. These data are correlated so as to decouple the effects of surface tension and viscosity. An empirical relation is proposed for the effective shear rate in the fluid travelling around the bubble nose. Our correlation is compared to literature data from a broad range of Reynolds numbers with excellent agreement except at shallow angles.     

Creation, transportation, and coalescence of liquid drops by means of a light beam

A novel principle of manipulation of discrete drops using concentration-capillary forces controlled by the thermal action of a light beam is proposed. The drops are created by the light beam in a thin layer of absorbing solution and in a film of that solution beneath an air bubble in the cell. The possibility of transporting both a single drop and a drop in an air bubble by means of a light beam is demonstrated. For the first time two drops are made to coalesce on a solid substrate by bringing them into contact by means of a light beam.     

An experimental investigation of outflow of liquids from single-outlet vessels

This paper considers the outflow of a liquid from a single outlet vessel, i.e. a vessel in which the outflowing liquid is displaced by another fluid which enters the vessel through the same opening. The simplest possible arrangement is investigated: a sealed axisymmetric cylindrical vessel with an outlet in its base, in which water is displaced by air.

It is shown experimentally that the average liquid discharge velocity is independent of the liquid level in the vessel and the shape of the outlet for the range of outlets employed; it increases weakly with both the diameter of the vessel and the diameter of the outlet.     

Oscillation and breakup of a bubble under forced vibration

Coupled shape oscillations and translational motion of an incompressible gas bubble in a vibrating liquid container is studied numerically. The bubble oscillation characteristics are mapped based on the bubble Bond number (Bo) and the ratio of the vibration amplitude of the container to the bubble diameter (A/D). At small Bo and A/D, the bubble oscillation is found to be linear with small amplitudes, and at large Bo and A/D, it is nonlinear and chaotic. This chaotic bubble oscillation is similar to those observed in two coupled nonlinear systems, here being the gas inside the bubble and its surrounding liquid. Further increases in the forcing, results in the bubble breakup due to large liquid inertia.     

表面应力调制的微流控技术的驱动原理

发展和优化对薄膜、液滴和气泡进行流动控制操作的多功能装置, 要求深入了解界面现象和微流体动力学流动.表面积/ 体积的大比值和低雷诺数流动是此类系统的特点.毛细数和Bond数强烈地受边界效应影响, 因而可以通过各种表面处理和表面力 来进行控制.本文综述了运用调制法向或切向应力, 对均匀的、带化学处理条纹及拓扑结构纹理表面上的微滴和液膜进行驱动 的常用技术的基本原理.     

Joule heating effect of electroosmosis in a finite-length microchannel made of different materials

This paper presents a numerical analysis of Joule heating effect of electroosmo- sis in a finite-length microchannel made of the glass and polydimethylsiloxane （PDMS） polymer. The Poisson-Boltzmann equation of electric double layer, the Navier-Stokes equation of liquid flow, and the liquid-solid coupled heat transfer equation are solved to investigate temperature behaviors of electroosmosis in a two-dimensional microchannel. The feedback effect of temperature variation on liquid properties （dielectric constant, vis- cosity, and thermal and electric conductivities） is taken into account. Numerical results indicate that there exists a heat developing length near the channel inlet where the flow velocity, temperature, pressure, and electric field rapidly vary and then approach to a steady state after the heat developing length, which may occupy a considerable portion of the microchannel in cases of thick chip and high electric field. The liquid temperature of steady state increases with the increase of the applied electric field, channel width, and chip thickness. The temperature on a PDMS wall is higher than that on a glass wall due to the difference of heat conductivities of materials. Temperature variations are found in the both longitudinal and transverse directions of the microchannel. The increase of the temperature on the wall decreases the charge density of the electric double layer. The longitudinal temperature variation induces a pressure gradient and changes the behavior of the electric field in the microchannel. The inflow liquid temperature does not change the liquid temperature of steady state and the heat developing length.