Drag Correlation of Drop Motion on Fibers

The objective of this article is to correlate a drag coefficient to the Reynolds number for axial motion of barrel drops on fibers. This work includes effects of vibration-induced motion of droplets and coalescence. The study of motion of drops is important to understand the drainage behavior of droplets. Drainage of liquid helps to eliminate moisture from media samples before applying thermal energy and hence reducing the drying cost. A significant amount of literature describes the mechanisms of droplet capture, coalescence, and drainage from filter media and models are developed at a scale that accounts for the liquid held in the filter through averaged parameters such as saturation. Few papers discuss the motion of individual drops attached to fibers.

The study of drop motion on fibers is of scientific and economic interest for many possible applications like printing, coatings, drug delivery and release, and filters to remove or neutralize harmful chemicals or particulates from air streams. Gas convection-induced drop motion in fibrous materials occurs in coalescing filters, clothes dryers, textile manufacturing, convection ovens, and dewatering of filter cakes. Droplet removal can significantly reduce drying costs by reducing the free moisture contained in fibrous materials prior to applying thermal drying techniques.

In this article, the experimental drag coefficient versus Reynolds number data are compared for 1-D and 3-D cylindrical drop models. The results show that 1-D models are inadequate to predict the drag coefficient but do show the same general trends.     

A case study of simulating submicron aerosol filtration via lightweight spun-bonded filter media

The most common method of filtration is via fibrous nonwoven media. Fibrous filters are generally characterized by their collection efficiency and pressure drop. Traditional computational studies in this area are typically based on unrealistic 2-D geometries with the fibers simply placed in a lattice (regular array) perpendicular to the flow. The traditional approaches however, do not permit studying the relation between the 3-D structure of a filter media and its performance. In this study, for the first time, a virtual 3-D web is generated based on the fiber orientation information obtained from analyzing microscopic images of lightweight spun-bonded filter media. Pressure drop and collection efficiency of our virtual filter are simulated and compared with the previous 2-D analytical and numerical models as well as experiment. Our pressure drop calculation, unlike the previous models, showed a perfect agreement with the predictions of the Davies’ empirical equation. The collection efficiencies obtained from simulating a thin spun-bonded filter media challenged with submicron particles having diameters ranging from 50 to 500 nm showed a similar trend as that of the previous 2-D models. For the solid volume fraction (SVF), filter thickness, and the fiber and particle diameters considered in this study, we found collection efficiencies higher than that of the above mentioned 2-D models with a relatively good agreement with experimental data obtained from a TSI 8130 filter tester.     

Experimental verification of the additivity between the barrel droplet's drag force and the fiber number

Research on the single fiber scale has an essential application value in the coalescence field. The study of the droplets' behavior on the fiber junctions can provide support data for optimizing the coalescer's drainage performance on the macroscopic scale. However, relevant research focusing on the force change of droplets during the transition from a single fiber to multifiber is relatively scarce. The droplet migration platform was built using the Lavision particle image velocimetry system, which can observe the behavior of droplets on fibers. The force and fiber number relationship were analyzed when the droplets were separated from the fiber junctions. Two detachment modes were observed during separation. Furthermore, the drag force satisfied the additivity theorem by increasing the number of fibers under the same detachment mode. In addition, the minimum Reynolds number prediction model was established under two separation forms, which had good prediction compared to the experimental data.     

Electric Field-Enhanced Coalescence of Liquid Drops

Abstract

A fundamental understanding of drop coalescence and growth is of importance to separations and materials processing. Under external driving forces, drops dispersed in an immiscible fluid collide and coalesce with each other due to their relative motion. As a result of drop coalescence, the average drop size in the dispersion increases over time, improving the separation process. Collision and coalescence of spherical, conducting drops bearing no net charge in dilute, homogeneous dispersions are considered theoretically under conditions where drop motion results from gravity settling and electric field-induced attraction. A trajectory analysis is used to follow the relative motion of two drops and predict pairwise collision rates. A population dynamics equation is then solved to predict the time evolution of the size distribution and the average size of drops. The results show that the rate of drop collision and growth can be increased significantly by applying an electric field, in accord with fundamental experiments and patents on electrocoalescence.     

Continuum Model Evaluation of the Effect of Saturation on Coalescence Filtration

Abstract

Coalescing filters are widely used throughout industry for removal of liquid aerosols from gases or the separation of liquid droplets from emulsions. Typical filters are constructed of non-woven fibers. Fibrous filters are capable of efficient removal of micron and submicron sized droplets and particles. The filtration process is highly complex due to variability in fiber sizes, particle sizes, mixtures of particles and droplets, mixture of types of droplets (oil, water, etc.), and effects of viscosity, surface tension, and chemical reactions between components or with the filter fibers. Prediction of filter performance under such complex conditions is difficult.

Performance of a filter depends on many factors like particle and fiber sizes, flow rate, surface properties of the fibers etc. One of those parameters is the saturation of the filter medium. Saturation is a measure of the amount of liquid present in the void space. Prior models assume that the saturation is uniform along the depth of the medium. In real media, the liquid holdup at steady state need not be uniform with position. Local velocity increases when the saturation is high.

In this paper, a steady state model for a coalescing filter is used to evaluate the effects of saturation on void fraction and its subsequent effect on filter performance. Single fiber mechanisms of direct interception and diffusion deposition are used to model droplet capture efficiencies and drag forces. These mechanisms are applied to volume averaged continuum equations in which the saturation is varied linearly with position in the filter. The results show the minimum pressure drop and largest quality factor occurs with a uniform saturation profile and that variation in average saturation has a greater effect on filter performance than does the slope of the linear saturation profile. The model predicts that uniform saturation profile performs better than the other profiles.     

Comparative performance of philic and phobic oil‐mist filters

The evolution of pressure drop, drainage rate, saturation, and efficiency of combined philic, and phobic oil mist filters in real‐time are examined. The experiments used four different filter configurations, with a combination of oleophobic and oleophilic fibrous filter media, and one oleophilic only reference. The effect of separating filter materials of differing wettability, with a mesh, was also explored. It was found that inclusion of a mesh between layers promoted increased drainage rates and resulted in a significantly lower pressure drop across the filter. The overall mass‐based filtration efficiency was also slightly higher for the configurations containing the mesh. Conversely, re‐entrainment of droplets from the rear face of the filter was only observed in filter configurations without the central mesh. Filters with oleophobic initial layers did not display a classical “depth filtration” pressure drop curve. The oleophobic media was found to possess lower steady‐state saturation than oleophilic media. Additionally, the steady‐state saturation of the oleophilic filter media, when placed at the rear of the filter, was lower when the central mesh was present. The saturation values were compared with recently published theory. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2976–2984, 2014     

CFD modeling of a pilot-scale countercurrent spray drying tower for the manufacture of detergent powder

A steady-state, three-dimensional, multiphase computational fluid dynamics (CFD) modeling of a pilot-plant countercurrent spray drying tower is carried out to study the drying behavior of detergent slurry droplets. The software package ANSYS Fluent is employed to solve the heat, mass, and momentum transfer between the hot gas and the polydispersed droplets/particles using the Eulerian–Lagrangian approach. The continuous-phase turbulence is modeled using the differential Reynolds stress model. The drying kinetics is modeled using a single-droplet drying model, which is incorporated into the CFD code using user-defined functions (UDFs). Heat loss from the insulated tower wall to the surrounding is modeled by considering thermal resistances due to deposits on the inside surface, wall, insulation, and outside convective film. For the particle–wall interaction, the restitution coefficient is specified as a constant value as well as a function of particle moisture content. It is found that the variation in the value of restitution coefficient with moisture causes significant changes in the velocity, temperature, and moisture profiles of the gas as well as the particles. Overall, a reasonably good agreement is obtained between the measured and predicted powder temperature, moisture content, and gas temperature at the bottom and top outlets of the tower; considering the complexity of the spray drying process, simplifying assumptions made in both the CFD and droplet drying models and the errors associated with the measurements.     

Influence of fiber orientation distribution on performance of aerosol filtration media

This work is conducted to better our understanding of the influence of fibers’ in-plane and through-plane orientations on pressure drop and collection efficiency of fibrous media. The Stokes flow equations are numerically solved in virtual, 3-D, fibrous geometries with varying in-plane and/or through-plane orientations. Pressure drop and aerosol collection efficiency characteristics of such media are calculated and compared with available studies from the literature. Our results indicate that pressure drop and submicron particle capture efficiency of common fibrous filters with a fiber diameter of about 10 μm are independent of the in-plane orientation of the fibers, but decrease with increasing the fibers’ through-plane orientation. More interestingly, it was found that filters with higher through-plane fiber orientations have a higher figure of merit if challenged with nanoparticles. The figure of merit of these media, however, decreases as the particle size increases, reversing the effect of fibers’ through-plane orientation. It was also shown that when the diameter of the particles is comparable to that of the fibers, collection efficiency increases with decreasing the fibers’ in-plane orientation, while the pressure drop remains almost unchanged. This indicates that decreasing the fibers’ in-plane orientation increased the figure of merit of media made of nanofibers.     

Combined Wettable/Non‐wettable Filter for Mist Purification

Previous studies by Agranovski and Braddock [1] show that wettable filters are very efficient at collecting small liquid aerosols. However, a major problem associated with wettable filters is the breakthrough process associated with the destruction of film covering the fibres, and the removal of relatively large droplets by the carrier gas passing through the rear surface of the filter. A non‐wettable filter is relatively efficient at collecting large droplets and discarding them down its front face [2]. These two types of filters can be combined in layers to make use of these distinctive properties. The best arrangement is where the carrier gas passes first through the wettable filter, and then through the non‐wettable filter. Where there is a contact between the two filters, interface effects assist the filtration and filter system drainage. The filtration mechanisms are enhanced when the filter box is tilted so that gravity partially opposes the drag forces on the liquid in the filter. In the current paper, the results of experimental analysis of combined filtration systems are presented, and further steps towards industrial design are discussed.     

The dynamics of single air bubbles and alcohol drops in sunflower oil at various temperatures

Steady rises of a single air bubble, a methanol drop, and an ethanol drop in a vertical glass column of refined sunflower oil at temperatures of 25, 30, 40, and 50°C are investigated experimentally using photography. The Reynolds numbers obtained are 0.07–16, 0.02–13.43, and 0.017–11.18 for the air bubbles, methanol drops, and ethanol drops, respectively. Results for terminal velocity and drag coefficient are compared with the selected existing correlations for bubble and drop motions in immiscible liquids. Correlations by Rodrigue show good agreement for various bubble sizes and system temperatures. Experimental drag coefficients of methanol and ethanol drops show a systematic deviation from the Oliver and Chung and the Darton and Harrison correlations, respectively. Considering the effect of dissolution of alcohol in vegetable oil, which varies with temperature, on the drop dynamics, semiempirical correction factors are applied to the last two correlations to fit the experimental results. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Drop mixing in suspension polymerisation

In suspension polymerisation, monomer is suspended as liquid droplets in a continuous water phase by means of strong agitation and the presence of a suspending agent. As the suspension polymerisation proceeds, the viscosity of a monomer-polymer droplet increases with conversion. Hence, the physical behaviour of the droplet changes during the process. When new dispersible material is added to the existing suspension drops, the new material and existing drops can remain segregated for significant amounts of time. The aim of this project was to study the behaviour of drop mixing when new material is added to the existing suspension polymerisation. This study concentrated on the effect of the dispersed phase viscosity on drop mixing. The results show that viscosity affects drop size and that may then affect the rate of coalescence between drops. A critical drop size exists which determines the coalescence efficiency effect. Above the critical drop size, mixing rate increases as the drop viscosity decreases. While below the critical drop size, drop size of the dispersion determines the coalescence rate; as the drop size increases, coalescence rate also increases. The investigation of the effect of suspending agent shows that Tween 20 is more efficient in stabilising and protecting the drops, based on a weight basis, than PVA as the coalescence rate is lower with Tween 20.     

DRAG AND MASS TRANSFER IN SLOW NON-NEWTONIAN FLOWS OVER AN ENSEMBLE OF NEWTONIAN SPHERICAL DROPS OR BUBBLES

An approximate solution for the slow motion of an ensemble of spherical drops through a power law fluid is obtained using Happel's free-surface cell model. It is shown that the drag coefficient decreases with decrease of the flow index and that this reduction is more significant at low voidage and large viscosity ratio parameter. The effect of the pseudoplastic anomaly on the mass transfer rate is more pronounced at low voidage for large values of viscosity ratio parameter, unlike the case of a single spherical drop

The present analysis covers the whole range of values of viscosity ratio parameter from infinity (an assemblage of solid spheres) to zero (a swarm of bubbles) and reduces to the solutions for those cases already known

The results for the motion of an ensemble of spherical drops also provide the basis for proposing a tentative expression for the expansion of liquid-liquid fluidized bed at low Reynolds number.     

Development of a filter set for breathing filters

We have studied the filter materials in the most popular foreign breathing filters. We have established that the filter set for a bacterial/viral heat and moisture exchange (HME) filter consists of a primary filtering layer which provides highly efficient removal of bacteria and viruses from the air as a result of mechanical or electrostatic filtration; barrier layers, preventing migration of fibers and moisture droplets into the primary filtering layer; and a heat and moisture exchange layer, providing the needed humidity and temperature for the air inspired by the patient.     

Effect of drop coalescence on mass transfer rate

Disperse-phase-controlled mass transfer rates from individual liquid drops suspended in a second liquid phase are measured optically immediately after the drop has been formed by coalescence of two smaller droplets. The net effect on mass transfer of the act of coalescence is determined by comparison to similar measurements made on the initial droplets in the absence of coalescence. The transfer rates immediately after coalescence are high rapidly fall to zero, rebound to an intermediate value and finally decay to the level expected for an undisturbed drop. The net effect on total mass transferred is detrimental in a clean system subject to interfacial instability but appears to be beneficial for contaminated systems or where no surface movements are spontaneously generated.     

Saturation models of oleophilic coalescing filters

Fibrous coalescing filters are widely used in a series of processes such as compressed air purification, engine crankcase ventilation, processing and cutting, and are used to remove liquid aerosol particles in the airflow. Pressure drop and ef?ciency of coalescence filters are greatly affected by saturation. It is of importance to establish the relationship among saturation, filter media parameters and operating conditions, which is helpful to optimize the filter design. Coalescence ?lters composed of thin glass fibrous media with micron fiber diameters are widely used in industry, while the saturation of which cannot be accurately predicted by the existing saturation models. This work investigated the relationship between pressure drop and saturation of multi-layered filters with different oleophilic filter media. In this study, there was no sharp boundary between wetting and non-wetting regions within filter media, thus a filter was regarded as a whole capillary system. According to the Jump-and-Channel model and capillary theory, a saturation model was developed. Compared with a large number of published literature data, it is found that when the saturation value is greater than 0.2, the predicted value is in good agreement with the experimental results, and the relative deviation is ≤20%. With the decrease in saturation, the boundaries become more and more obvious between the wetting and non-wetting regions. In this case, there is no need to modify to the capillary radius in the developed model. However, the developed model was also limited by the need for the channel pressure drop measurement, which should be solved in further work.     

亲油型聚结滤芯饱和度预测模型研究

纤维聚结滤芯广泛用于压缩空气净化、发动机曲轴箱通风、加工和切割等一系列工艺过程中,用于除去气流中的液体气溶胶颗粒。由于聚结滤芯饱和度对于过滤效率及阻力具有重要影响,因此建立饱和度与滤材参数及操作条件之间的关系将有助于优化滤芯结构并提高过滤性能。目前实际工业用聚结滤芯通常由多层微米级玻璃纤维材料组成,然而现有计算模型无法用于此类滤芯的饱和度预测。因此,本文基于多种常用亲油型聚结滤芯压降及饱和度实验测试结果,根据"跳跃-通道"模型及毛细管理论建立了新的饱和度预测模型。通过与大量已发表文献数据对比发现,当饱和值大于0.2时,预测值与实验结果吻合度较好,相对偏差≤20%。随着饱和度的降低,滤芯润湿区域和非润湿区域之间界限逐渐明显,此时无需对毛细管半径进行修正。然而,新模型仍然要依靠压降测量值进行计算,这一问题需在后续工作中加以解决。     

Performance of fibrous filters during nanoparticle cake formation

Fibrous filters are highly efficient in removing micrometer particles, but their performance in the nanometer particle range is still little known. The aim of this study was to evaluate pressure drop and collection efficiency during nanoparticles cake formation using commercial fibrous filters. The filter media used were High Efficiency Particulate Air (HEPA) and polyester filters. The aerosols were generated by a commercial inhaler using a 5 g/L solution of NaCl and the particles produced were in the size range from 6 to 800 nm, with a peak at around 40 nm. A superficial velocity (v_s) of 0.06 m/s was employed. During the filtration, the maximum pressure drop established was ?P ₌ ?P_f +980Pa, where ?P_f is the initial pressure drop of the filter. The collection efficiency was determined for a clean filter and for intermediate pressure drops. The filtration curves obtained showed that the HEPA filter provided greater surface filtration, compared to the polyester filter. Comparison of the collection efficiencies for clean filters revealed that the HEPA filter was highly efficient, even in the absence of cake, while the polyester filter showed initial collection efficiencies of between 20 and 40% for particles in the size range from 100 nm to 1000 nm. However, after formation of the filter cake, the collection efficiencies of both filters were almost 100% during the final stage of filtration. This shows that the fibrous filter can be applied in several industrial processes with highly efficient nanoparticle separation, after the formation of a thin layer cake filtration.     

Transient rise velocity and mass transfer of a single drop with interfacial instabilities - experimental investigations

An experimental study of transient drop rise velocities and mass transfer rates was carried out in the system toluene/acetone/water which is known to show interfacial instabilities. The rise velocity of toluene drops was studied without added solute (acetone) in the diameter range 1-3 mm and with added solute for 2 mm drops. The initial concentration of the transferred solute was varied from 0 to 30 g/L. The transient drop rise velocities were used to quantify the Marangoni effect since the drag coefficient depends on the strength of the Marangoni convection patterns caused by interfacial tension gradients. In addition, mass transfer measurements were carried out in order to determine the modification of the mass transfer rate due to Marangoni convection. Velocity and mass transfer measurements were then correlated via the contact time. Results reveal the existence of a range in which a critical value for the solute concentration can be defined for Marangoni convection.     

On the pressure drop prediction of filter media composed of fibers with bimodal diameter distributions

In addition to collection efficiency, pressure drop is the most important characteristic of a filter medium. While there are numerous analytical expressions available for predicting the pressure drop of the filters made up of fibers with a unimodal fiber diameter distribution, there are not enough studies dedicated to filters composed of fibers with a bimodal (or multimodal) fiber diameter distribution. In this work, the pressure drop per unit thickness of filters made of bimodal fiber diameters is calculated by solving the Navier-Stokes equations in a series of 2-D geometries. These results are used to find the unimodal equivalent diameters of each bimodal filter that could be used in the existing expressions for calculating pressure drop. In agreement with the work of Brown and Thorpe [Brown, R.C., Thorpe, A., Glass-fiber filters with bimodal fiber size distributions. Powder Technology 118 (2001) 3-9.], it was found that the area-weighted averaging of the fiber diameters in a bimodal filter provides a relatively good estimation of its equivalent unimodal fiber diameter. We, however, noticed that in such an averaging the error percentage in the pressure drop prediction is sensitive to the fiber diameter ratios as well as the fraction of each fiber diameter in the bimodal filter. We, therefore, obtained a correction factor for the estimation of the unimodal equivalent diameters as a function of fiber diameter ratio and their number fractions.