Experimental and numerical analysis of droplet deformation in a complex flow generated by a rotor-stator device

The deformation behaviour of single drops suspended in a second immiscible liquid undergoing a complex laminar flow is analysed both experimentally and numerically. The flow is generated in a channel formed by two rotating concentric cylinders with teethed walls as a model for extruding flow. The transient drop deformation and position in the device is captured by a twin-camera system in which one camera captures the drop deformation and the other camera captures the position of the drop. Results from an experiment consist of the transient drop deformation and the particle track of the drop. In our data analysis we define a geometry-based apparent shear rate which we compare to time-averaged drop deformations. Results indicate that for small deformations the relation between the time-averaged drop deformation and time-averaged apparent shear rate can be described by Taylor's small deformation theory.Furthermore we have used the particle track data obtained from a number of experiments to numerically calculate the local flow experienced by the drop. The numerically calculated local flow is then used as input to a computational algorithm for simulating the transient drop deformation. Comparison between numerical calculations of the drop deformation and experimental results generally agree well although calculations predict a somewhat higher deformation than experimentally observed.     

简单剪切流动中液滴断裂机理

The experimental results of the deformation and breakup of a single drop immersed in a Newtonian liquid and subjected to a constant shear rate which generated by counter rotating Couette apparatus were presented in this paper. From experimental observations, the breakup occurred by three mechanisms, namely, necking, end pinching, and capillary instability. Quantitative results for the deformation and breakup of drop are presented. The maximum diameter and Sauter mean diameter of daughter drops and capillary thread radius are linearly related to the inverse shear rate and independent of the initial drop size, the dimensionless wavelength which is the wavelength divided by the thread width at breakup is independent of the shear rate and initial drop size, and the deformation of threads follows a pseudo-affine deformation for Cai/Cac larger than 2.     

Shear and elongational viscosities of a thermotropic liquid crystalline polymer and its blend with polycarbonate

The shear and elongational viscosities of a thermotropic liquid crystalline polymer (LCP), polycarbonate (PC), and their 20%LCP/80%PC blend, were studied using a capillary rheometer. The investigation focused on experimental studies using two sets of capillaries. The first set comprised capillaries having a converging entrance followed by a cylindrical section. The second set, “zero length” set, included capillaries having only the converging section. In the two sets various entrance angles were used. Experimental results have shown that shear viscosities and entrance pressures are practically independent of the entrance angles. The entrance pressure drop was small in the case of PC and reached 50% of the total pressure drop for LCP. The elongational viscosities of the LCP were found to be higher than those of the PC in the elongational-rate range studies, while shear viscosities of the LCP were higher in the lower shear rate region and lower in the higher shear rate region compared to those of PC. This was attributed to the orientability of LCP in elongational and shear flows.     

Drop impact and agglomeration under static powder bed conditions

The influence of impact conditions (reported in terms of Weber and Reynolds numbers) on nucleus formation was studied for single drops striking a static glass bead bed. Results from high speed images showed that the nucleation rate is not influenced by liquid physical properties (density, surface tension, viscosity) for drops that spread significantly (30 < We < 233). Results also showed that nucleus size is determined by how much liquid penetrates into the bed during drop spreading, so does depend on surface tension and liquid density. A corresponding analytical model, derived from first principles, predicts nucleus size to with 1.5% using only liquid physical and powder bed properties, plus the experimentally measured drop spreading behavior. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

High speed imaging of drop formation from low viscosity liquids and polymer melts in spinning disk atomization

An investigation of drop formation in a recently developed spinning disk atomization (SDA) technique is presented. In‐situ observations of drop formation at the disk rim, using a high speed imaging installation, are made. Atomizations covering two orders of magnitude in flow rate show that ligaments can also form at low flow rates. Sequences of pictures indicate that drops undergo a rotary motion as they detach from a ligament. In the direct drop regime, oscillating motions dominate. The effect of teeth shape at the disk rim on the resulting drops is compared. The effect on drop size and size distribution is found to decrease with increasing rotation rate and corresponding images are studied. Experiments with liquid viscosities ranging from 1 to 120 mPas reveal a fundamental difference in drop breakup, but a negligible change in drop size. Likewise, only a small effect of liquid density is detected. The surface tension's influence on the liquid spreading at the disk rim is described and the subsequent drop formation is qualitatively analyzed.     

Viscosity measurement in a pipe flow using a numeric recursion approach for in-line quality control

The use of a pipe as a sensor for measuring viscosity and shear rate would require a separated flow rate instrument and would result in a more complicated mechanism for in-line quality control. In this study, a method of applying numeric recursion to the pipe pressure drop to directly calculate the viscosity and the shear rate is proposed. This viscosity sensor was verified by using it to measure the viscosity and shear rate for low-density polyethylene. The viscosity and shear rate obtained by this approach differ little from those obtained by using a standard off-line capillary rheometer. Therefore, this viscosity measurement method is applicable for in-line quality control.     

Determination of shear viscosity and shear rate from pressure drop and flow rate relationship in a rectangular channel

In this study, we present a unique approach to calculate the shear viscosity and shear rate with the pressure drop and flow rate data from a channel having a rectangular cross-section with a height-to-width ratio (H/W) of close to one. The derived equation was verified with experimental data from rectangular dies whose height-to-width ratio (H/W) ranges from 0.1 to 1. It was confirmed that the proposed approach is reliable for the calculation of the shear viscosity and shear rate from the flow data in a rectangular channel.     

Numerical study of drop spreading over saturated pores

Numerical study of the dual effect of pores in liquid spreading over porous surface (flat and spherical) whereby liquid movement is facilitated as well as restricted (visualised by Khanna and Nigam [Khanna and Nigam, Chem. Eng. Sci. 57, 3401–3405 (2002)]) is presented to improve the present understanding of wetting. Using the volume of fluid (VOF) method in a two‐dimensional solution domain, the influence of various parameters viz. drop volume, pore density, surface wettability and liquid properties on the liquid spreading over 2D pellets with saturated pores was numerically investigated. Simulation results were found to capture the key features of the liquid spreading over non‐porous and porous surfaces qualitatively. The variation of spread factor and the apex height of liquid film with time were in a good qualitative agreement with the concept of dual action of pores. The liquid spreading was observed to have a direct proportionality with the pore density, that is, higher the number of pores, better was the liquid spreading. It was also observed that the influence of the pores on the liquid spreading was reduced with decrease in the surface wettability. It is expected that this numerical analysis of the liquid droplet spreading over saturated porous surface will be useful for better understanding of the physics of drop and pore (saturated) interactions.     

Viscoelasticity and Kinetics of Wetting on Rubber

The kinetics of spreading of a liquid drop is usually controlled by conversion of capillary potential energy into viscous dissipation within the liquid when the solid is rigid. However, if the solid is soft, a “wetting ridge” near the solid/liquid/vapour triple line can also be a dissipative sink as the wetting front moves. As a consequence, the kinetics of wetting of rubber may be controlled essentially by viscoelastic losses in the polymer rather than by viscous losses in the liquid drops. Therefore, a direct analogy between the kinetics of wetting and adhesion, respectively, for a liquid and a solid on an elastomeric substrate has been recently proposed. In this paper, the superposition of viscoelastic braking and moderate rubber swelling in the drop spreading phenomenon is considered.     

Viscoelasticity and Kinetics of Wetting on Rubber

The kinetics of spreading of a liquid drop is usually controlled by conversion of capillary potential energy into viscous dissipation within the liquid when the solid is rigid. However, if the solid is soft, a “wetting ridge” near the solid/liquid/vapour triple line can also be a dissipative sink as the wetting front moves. As a consequence, the kinetics of wetting of rubber may be controlled essentially by viscoelastic losses in the polymer rather than by viscous losses in the liquid drops. Therefore, a direct analogy between the kinetics of wetting and adhesion, respectively, for a liquid and a solid on an elastomeric substrate has been recently proposed. In this paper, the superposition of viscoelastic braking and moderate rubber swelling in the drop spreading phenomenon is considered.     

Spreading of Polydimethylsiloxane Drops on Solid Horizontal Surfaces

Effect of the volume of drops, surface energy and roughness of substrate together with temperature and viscosity on the spreading velocity of polydimethylsiloxane (PDMS) drops on solid horizontal surfaces was studied. Spreading velocity was shown to grow with decreasing drop volume, the effect being more pronounced at high viscosities of polymer. The deviation of shape of the spreading drop from that of a spherical segment is more pronounced the higher the surface energy of substrate, the higher the polymer viscosity and the smaller the drop volume. Spreading on a rough surface is slower than on a smooth one owing to the energy barrier created by surface inhomogeneities: the barrier is to be overcome by the spreading liquid. Based on the experimental results a mechanism of spreading of polymer drops is proposed. Changes in potential energy of a drop and in the free surface energy of the system during spreading were compared, allowing a theoretical evaluation of the influence of gravity on the spreading velocity of drops. A theoretical analysis of spreading kinetics of viscous drops is given. The equation proposed agrees well with the experimental results at 90° > θ > 0°.     

阶梯环填料层流体力学和传质性能研究

本文研究了16 mm聚丙烯阶梯环填料层的压强降和液流的分布特性,研究了液相传质性能。获得了压强降填料因子、泛点填料因子,以及液相真实传质单元高度的关联式。结果表明,阶梯环填料对液体分布的保持性能好,分散常数C值比同尺寸的拉西环大23.4％;传质单元高度比同尺寸的拉西环低20～45％。     

不混溶液体表面上蒸发液滴的动力学特性

针对不混溶均匀受热液体表面上蒸发液滴的动力学过程，基于润滑理论推导出了无量纲方程组。采用数值模拟方法，探究了蒸发液滴的动力学特性。结果表明，蒸发液滴的演化过程分为两个阶段：由“铺展主导”的液滴前进阶段和由“蒸发主导”的持续脉动振荡的后退阶段。液滴在低黏度比下的流动性更强，导致铺展更加迅速，黏度比的增加会导致铺展和收缩速率的降低。蒸发通过影响液滴界面的温度分布进而影响界面张力以及液滴铺展。相较于固体表面液滴蒸发出现的钉扎现象，蒸发液滴在不混溶液体表面上的铺展是去钉扎的，并且伴有液体基底的明显变形。     

Three-dimensional numerical modelling of interactions between a gas–liquid jet and a fluidized bed

This paper presents the development of a novel mathematical model that describes spray injection and spreading into a fluidized bed of solid particles. The model also includes the gas–liquid flow through the nozzle followed by the gas-assisted atomization. An Eulerian approach that is independent of the nature of the continuous phase is adopted for all phases, which are gas (or bubbles), liquid (or droplets), and solid particles that may be covered with a liquid layer. Variation in sizes of bubbles and droplets is represented by the particle number density approach that takes into account both break-up and coalescence. The atomization is considered as a catastrophic phase inversion triggered by a critical local volume fraction. New relationships were obtained for liquid spreading due to wet particle collisions and for heat conduction between a solid particle and a surrounding liquid layer. The model is applied to simulate liquid injection into the fluidized bed for conditions that were previously experimentally studied and published. The comparison reveals a reasonable agreement in prediction of the cumulative liquid distribution for two experimental cases. In addition, we evaluated a jet penetration distance with the model to compare it with the one measured in another set of experiments. This comparison also yields a good qualitative agreement. Finally, we evaluated the influence of the fluidization velocity on liquid distribution in the bed.     

The liquid spreading on porous solids: Dual action of pores

Experimental observation of the dual effect of pores in liquid spreading over porous substrates, whereby liquid movement is facilitated as well as restricted is presented based on spreading of micro-liter-sized liquid drops on substrates that have saturated (filled) millimeter-sized pores. The drops were put on porous and nonporous parts of solid substrate. The substrate was then rotated in vertical direction and the resulting motion of drops was recorded by a video camera. The analysis of the recorded images revealed that depending on whether the drop edge is moving toward the pore or away from the pore, the pore acts as accelerator or brake for the drop edge. This dual nature of the saturated pores can be ascribed to the attraction between the liquid in the drop and the liquid inside the pore. Qualitative changes in the morphology of the drop as it slides over saturated pores are also presented to highlight the process. This dual effect of pores is expected to play a major role in processes such as flow through a trickle bed of porous catalyst where it manifests itself in increased wetting efficiencies as well as pronounced hysteresis [Khanna, R., Nigam, K.D.P., 2002. Partial wetting in porous catalyst: wettability and wetting efficiency. Chemical Engineering Science 57, 3401-3405; Maiti et al., 2004. Enhanced liquid spreading due to porosity. Chemical Engineering Science 59, 2817-2820; 2005. Trickle-bed reactors: Porosity induced hysteresis. Industrial and Engineering Chemistry Research, in press.].     

Spray and mixing characteristics of liquid jet in a tubular gas–liquid atomization mixer

For the design and optimization of a tubular gas–liquid atomization mixer,the atomization and mixing characteristics of liquid jet breakup in the limited tube space is a key problem.In this study,the primary breakup process of liquid jet column was analyzed by high-speed camera,then the droplet size and velocity distribution of atomized droplets were measured by Phase-Doppler anemometry (PDA).The hydrodynamic characteristics of gas flow in tubular gas–liquid atomization mixer were analyzed by computational fluid dynamics (CFD) numerical simulation.The results indicate that the liquid flow rate has little effect on the atomization droplet size and atomization pressure drop,and the gas flow rate is the main influence parameter.Under all experimental gas flow conditions,the liquid jet column undergoes a primary breakup process,forming larger liquid blocks and droplets.When the gas flow rate (Q_g) is less than 127 m~3·h~(-1),the secondary breakup of large liquid blocks and droplets does not occur in venturi throat region.The Sauter mean diameter (SMD) of droplets measured at the outlet is more than 140μm,and the distribution is uneven.When Q_g127 m~3·h~(-1),the large liquid blocks and droplets have secondary breakup process at the throat region.The SMD of droplets measured at the outlet is less than 140μm,and the distribution is uniform.When 127Q_g162 m~3·h~(-1),the secondary breakup mode of droplets is bag breakup or pouch breakup.When 181Q_g216 m~3·h~(-1),the secondary breakup mode of droplets is shear breakup or catastrophic breakup.In order to ensure efficient atomization and mixing,the throat gas velocity of the tubular atomization mixer should be designed to be about 51 m·s~(-1)under the lowest operating flow rate.The pressure drop of the tubular atomization mixer increases linearly with the square of gas velocity,and the resistance coefficient is about 2.55 in single-phase flow condition and 2.73 in gas–liquid atomization condition.     

The Rheology of Wetting By Polymer Melts

Theoretically, the rate of capillary penetration of a polymer melt into a slit, a model for a surface irregularity, has been shown to depend on γcosθ/η) where γ refers to the surface tension of the liquid, η its viscosity and θ a time-dependent contact angle. Analytical expressions relating the depth of penetration with time have been experimentally verified by observations of the penetration of molten polyethylene and poly-(ethylene-vinyl acetate) into aluminum channels. Values of η, calculated from the observed data, agree closely with independent determinations of this material parameter. A theoretical treatment has also been developed which describes the velocity of spreading of a liquid drop over a flat surface. Flow equations for the flow of free films were adapted for this purpose. The spreading velocity is predicted to depend on the product of three factors (1) a scaling factor, (γ/η1R_o), where R_o is the initial radius of curvature, (2) cosθ_∞. (l-cosθ/cosθ_∞) where θ_∞ refers to the equilibrium value of θ, and (3) geometric terms. After demonstrating that a drop of molten polymer may be treated as a spherical cap, the predicted dependence of spreading rate on drop size, cosθ_∞ (nature of the substrate) and the scaling factor was experimentally verified. Some discrepancies noted at long times and high temperatures are discussed.     

DROP PRODUCTION IN COUETTE AND MEDIA MILL DEVICES

The media mill is a device used in the paint and pigment industry for mixing and dispersing solid/liquid mixtures. The media consists of spheres which are agitated in a vessel and the hydrodynamic interactions between these media spheres cause the fine-scale dispersion. The details of the flow are very complex. A technique to characterize the dispersion efficiency of a media mill is presented which involves monitoring the maximum drop diameters of a dispersed organic phase in an aqueous continuous phase. The largest surviving drops reflect the maximum shear and elongation fields that exist in the flow. The maximum drop size scales as impeller speed to the -0·82 power. This dependence is much lower than the dependence for a Rushton turbine in a tank, which would be -1·38. The mechanism of breakup is clarified by experiments in a Couette geometry for large drop size to gap ratios, where the dependence of drop size on shear rate also scales to the -0·82 power. An analysis of the hydrodynamics involved in two approaching spheres explains the similarity between drop formation in a media mill and the narrow gap Couette cell; drop-solid surface interactions strongly influence breakup in both geometries.     

Droplets sliding over shearing surfaces studied by molecular dynamics

Through molecular dynamics, the sliding motion of a liquid drop embedded in another liquid over a substrate as a result of a shear flow is studied. The two immiscible Lennard‐Jones liquids have the same density and viscosity. The system is isothermal. Viscosity, surface tension, and static contact angles follow from calibration simulations. Sliding speeds and drop deformations (in terms of dynamic contact angles) are determined as a function of the shear rate. The latter is nondimensionalized as a capillary number (Ca) that has been varied in the range 0.02–0.64. For Ca up to 0.32, sliding speeds are approximately linear in Ca. For larger Ca, very strong droplet deformations are observed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4020–4027, 2015     

Experimental study and CFD modelling of a two-phase slug flow for an airlift tubular membrane

The aim of the present study was to develop a computational fluid dynamics (CFD) model to study the effect of slug flow on the surface shear stress in a vertical tubular membrane. The model was validated using: (1) surface shear stresses, measured using an electrochemical shear probe and (2) gas slug (Taylor bubble) rising velocities, measured using a high speed camera. The length of the gas slugs and, therefore, the duration of a shear event, was observed to vary substantially due to the coalescing of gas slugs as they travelled up the tube. However, the magnitude of the peak surface shear stress during a shear event was not observed to vary significantly. The experimental conditions significantly affected the extent to which the gas slugs coalesced. More coalescing between gas slugs was typically observed for the experiments performed with higher gas flow rates and lower liquid flow rates. Therefore, the results imply that the frequency of shear events decreases at higher gas flow rates and lower liquid flow rates.Shear stress histograms (SSH) were used as a simple approach to compare the different experimental conditions investigated. All conditions resulted in bi-modal distributions: a positive surface shear peak, caused by the liquid slug, and a negative shear peak caused by the gas slugs. At high gas flow rates and at low liquid flow rates, the frequency of the shear stresses in both the negative and positive peaks were more evenly distributed. For all cases, increasing the liquid flow rate and decreasing the gas flow rate tends to result in a predominant positive peak. These results are of importance since conditions that promote evenly distributed positive and negative peaks, are likely to promote better fouling control in membrane system. At high liquid and low gas flow rates, the frequencies obtained numerically and experimentally were found to be similar, deviating by less than approximately 10%. However, at high gas and low liquid flow rates, the differences were slightly higher, exceeding 20%. Under these conditions, the CFD model simulations over predicted the shear stresses induced by gas slugs. Nonetheless, the results indicate that the CFD model was able to accurately simulate shear stresses induced by gas slugs for conditions of high liquid and low gas flow rates.