Two touching spherical drops in uniaxial extensional flow: analytic solution to the creeping flow problem

We solve the problem of the creeping motion of a uniaxial extensional flow past two touching spherical drops when the line of centers is parallel to the axis of symmetry of the flow, using tangent sphere coordinates. We apply this solution to the case of two equal size drops. It provides an exact result for the equal and opposite force acting on each drop along the line of centers. We also use it to determine the magnitude of the internal recirculating flow in the vicinity of the rear stagnation point, which can be used to evaluate the importance of this flow on the film drainage process for two (nearly) touching drops in a coalescence process for the limiting case, Ca < 1.     

Shaping of gelling biopolymer drops in an elongation flow

Shaping, defined as deformation in combination with gel formation of gelatine and kappa-carrageenan drops in an elongation flow, was studied. The focus was to investigate the possibility of shaping and fixating small drops in the diameter range 20 to 229 mum. In the shaping progress and the influence of experimental properties, the viscosity, temperature, and flow of the deforming fluid were examined on the final drop shape. In the experiments a hot emulsion of an aqueous biopolymer solution in silicone oil was injected into cold silicone oil where a deforming elongation flow field existed. After injection, a temperature decrease in the drops resulted in a gel formation of the biopolymer and a fixation of the deformed drop in the flow. The shape was measured and the effect on the drop aspect ratio was determined by image analysis. Over the total drop diameter range, kappa-carrageenan was more ellipsoid-shaped than gelatine, with a maximum aspect ratio of 6 compared to 4 for gelatine. For small drops, around 22 mum, it is possible to shape kappa-carrageenan, but for gelatine small drops tend to be unaffected. An increase in viscosity, temperature, and flow resulted in an increase in the final fixated shape of the drops. The differences in drop deformation between the biopolymers were explained by drop-viscosity/oil differences and differences in the kinetics of gel formation. The different gel formation kinetics resulted in a short, well-defined, shaping process for kappa-carrageenan, while for gelatine the process was more complex, with both deformation and relaxation present at different stages.     

Emulsification in turbulent flow 2. Breakage rate constants

Systematic experimental study of the effects of several factors on the breakage rate constant, k(BR), during emulsification in turbulent flow is performed. These factors are the drop size, interfacial tension, viscosity of the oil phase, and rate of energy dissipation in the flow. As starting oil-water premixes we use emulsions containing monodisperse oil drops, which have been generated by the method of membrane emulsification. By passing these premixes through a narrow-gap homogenizer, working in turbulent regime of emulsification, we study the evolution of the number concentration of the drops with given diameter, as a function of the emulsification time. The experimental data are analyzed by a kinetic scheme, which takes into account the generation of drops of a given size (as a result of breakage of larger drops) and their disappearance (as a result of their own breakage process). The experimental results for k(BR) are compared with theoretical expressions from the literature and their modifications. The results for all systems could be described reasonably well by an explicit expression, which is a product of: (a) the frequency of collisions between drops and turbulent eddies of similar size, and (b) the efficiency of drop breakage, which depends on the energy required for drop deformation. The drop deformation energy contains two contributions, originating from the drop surface extension and from the viscous dissipation inside the breaking drop. In the related subsequent paper, the size distribution of the daughter drops formed in the process of drop breakage is analyzed for the same experimental systems.     

Formation of shaped drops in a fast continuous flow process

Drop shaping, i.e., flow-induced deformation and fixation by gel formation, was studied under dynamic conditions in a fast continuous process for a water-in-oil system. The system consisted of sunflower oil with different surfactant concentrations (0.1-2% Admul Wol) and a 1.5% kappa-carrageenan solution with different Na(+) and K(+) concentrations. The continuous phase flowed in a 10-mm-wide straight channel into which the dispersed phase was injected via a thin needle. A subsequent shaping channel with a width of 1 or 2 mm deformed the drops. Gel formation was induced by a temperature gradient between the continuous and dispersed phase. Drop sizes in the range 220-roughly 1000 microm were produced at the needle tip by varying the ratio between the oil and carrageenan flow rate. A diffusion zone before the narrow channel allowed the surfactant to adsorb at the interface. In the elongation flow at the entrance of the shaping geometry, drops underwent initial elongation. In the narrow channel, the drops developed a parabolic shape within a residence time of 0.03-0.15 s. Choosing the correct parameter combinations made it possible to fix the deformation by gel formation within this time period. Shaped drops were shown to be functional. At a concentration of 25% in an emulsion, they increased the viscosity by about 15-20% compared to spherical drops even though 45% of the shaped drops had an aspect ratio of less than 1.2.     

Controllable preparation of nanoparticles by drops and plugs flow in a microchannel device

Well controlled two-liquid-phase flows in a T-junction microchannel device have been realized. The system of H2SO4 and BaCl2, respectively, in two phases to form BaSO4 nanoparticles was used as a probe to characterize the microscale two-phase flow and transport conditions of a system with interphase mass transfer and chemical reaction. Nanoparticles with narrow size and good dispersibility were produced through drops or plugs flow in the microdevice. As a novel work, the influence of mass transfer and chemical reaction on interfacial tension and flow patterns was discussed based on the experiments. At the same time, the effect of the two-phase flow patterns on the nanoparticle size was also discussed. It was found that the increase of the amount of mass transfer and chemical reaction could change the flow patterns from plugs flow to drops flow. The drop diameter or plug length could be changed in a wide range. Accordingly, a new parameter of mu(0)u(c)/gamma(0)/Q(d) was defined to distinguish the flow patterns. The prepared nanoparticles ranged in size from 10 to 40 nm. Apparently, the particle size decreased with the increase of the drop diameter or plug length. Reasons were discussed based on the mass transfer direction and speed in drops and plugs flow patterns.     

Emulsification in turbulent flow: 3. Daughter drop-size distribution

Systematic set of experiments is performed to clarify the effects of several factors on the size distribution of the daughter drops, which are formed as a result of drop breakage during emulsification in turbulent flow. The effects of oil viscosity, etaD, interfacial tension, sigma, and rate of energy dissipation in the turbulent flow, epsilon, are studied. As starting oil-water premixes we use emulsions containing monodisperse oil drops, which have been generated by membrane emulsification. By passing these premixes through a narrow-gap homogenizer, working in turbulent regime of emulsification, we monitor the changes in the drop-size distribution with the emulsification time. The experimental data are analyzed by using a new numerical procedure, which is based on the assumption (supported by the experimental data) that the probability for formation of daughter drops with diameter smaller than the maximum diameter of the stable drops, d相似文献   

Emulsion drops in external flow fields — The role of liquid interfaces

We review the flow of emulsion drops, focusing on recent work involving complex interfaces, which may include the presence of surfactants, particles, surface-active polymers, or solid-like membrane layers. En route, important phenomena in multiphase flow associated with emulsion rheology are considered, including drop coalescence and breakup, surfactant transport, or the mechanics of composite interfaces.     

Influence of peak inspiratory flow rates and pressure drops on inhalation performance of dry powder inhalers

The aim of this study was to reveal the relationship between human inspiratory flow patterns and the concomitant drops in pressure in different inhalation devices, and the influence of the devices on inhalation performance. As a model formulation for inhalers, a physically mixed dry powder composed of salbutamol sulfate and coarse lactose monohydrate was selected. The drops in pressure at 28.3?L/min of three inhalation devices, Single-type, Dual-type, and Reverse-type, was 1.0, 5.1, and 8.7?kPa, respectively. Measurements of human inspiratory patterns revealed that although the least resistant device (Single) had large inter- and intra-individual variation of peak flow rate (PFR), the coefficients of variation of PFR of the three devices were almost the same. In tests with a human inspiratory flow simulator in vitro, inhalation performance was higher, but the variation in inhalation performance in the range of human flow patterns was wider, for the more resistant device. To minimize the intra- and inter-individual variation in inhalation performance for the model formulation in this study, a formulation design that allows active pharmaceutical ingredient to detach from the carrier with a lower inhalation flow rate is needed.     

Investigations of flow field designs in direct methanol fuel cell

An experimental and simulation research had been performed to investigate the performance as well as the flow distribution in the cathode flow field in the case of direct methanol fuel cells (DMFCs). The gas was well distributed in serpentine flow field, whereas stagnation of the gas was observed in parallel flow field. These would contribute to the cell performance greatly due to mass transfer effect when the cells start operating. In addition, the durability test of DMFC was drastically affected in parallel flow field due to poor ability to drain flooded water produced electrochemically at cathode and crossover from anode. In addition, pressure drops of different flow fields were also investigated to evaluate their contribution and feasibility as an economic application for DMFC. DMFC with serpentine flow field featuring higher pressure difference resulted in a larger parasitic energy demand. However, the optimal flow field designs are needed to balance the performance and pressure loss to achieve a uniform fluid distribution and simultaneously minimize energy demand for mass transport. Consequently, flow field with grid pattern appears to be the optimal design for the DMFC cathode.     

Groovy drops: effect of groove curvature on spontaneous capillary flow

Spontaneous capillary flow (SCF) of a drop in a groove with an ideally sharp corner is possible when the Concus-Fin (CF) condition is fulfilled. However, since ideally sharp corners do not exist in reality, it is important to understand the effect of finite corner curvature on SCF. This effect is analytically studied for long drops in a V-shaped groove with a curved corner, leading to a generalization of the CF condition for such drops. The generalized condition implies that SCF depends on the geometry of the corner as well as on the dimensionless length of the drop, in addition to its dependence on the opening angle and contact angle that is covered by the CF condition. Specific calculations are presented for rounded corners. In addition, this effect is numerically calculated for short drops in V-shaped grooves with rounded corners, using the Surface Evolver software. The results of both types of calculations show that even a relatively small corner radius strongly affects the possibility of SCF: when the corner is not ideally sharp, SCF requires conditions that are more difficult to achieve than predicted by the CF condition; also, the spreading of the drop stops at a finite length and does not proceed indefinitely.     

Continuous flow structuring of anisotropic biopolymer particles

We review concepts and provide examples for the controlled structuring of biopolymer particles in hydrodynamic flow fields. The structuring concepts are grouped by the physical mechanisms governing drop deformation and shaping: (i) capillary structuring, (ii) shear and elongational structuring and (iii) confined flow methods. Non-spherical drops can be permanently structured if a solidification process, such as gelation or glass formation in the bulk or at the interface, is superimposed to the flow field. The physical and engineering properties of these processes critically depend on an elaborate balance between capillary phenomena, rheology, gel or glass formation kinetics, and bulk heat, mass and momentum transfer in multiphase fluids. This overview is motivated by the potential of non-spherical suspension particles, in particular those formed from ‘natural’ and ‘sustainable’ biopolymers, as rheology modifiers in food materials, consumer products, cosmetics or pharmaceuticals.     

Controlled production of hierarchically organized large emulsions and particles using assemblies on line of co-axial flow devices

We describe a continuous flow scheme to conceive and produce hierarchically organized large emulsions and particles with very good control over size, shape and internal structure. By assembling together elementary co-axial flow modules and integrating their corresponding functions, modular set-ups can be designed “on demand” to engineer complex architectures in characteristic sizes ranging from 50 μm up to a few millimeters. The high potentiality of this approach stems from the continuous production of drops and the ability to manipulate and functionalize each one independently “on line”. Its great versatility is limited only by the number of combinations possible using the modular toolbox and one's imagination. We illustrate this through the encapsulation of droplets or solid particles of various shapes, composition and size, in liquid or solidified drops as well as the formation of large organic or inorganic cylindrical particles.     

On the effect of marangoni flow on evaporation rates of heated water drops

In this letter we show that the Marangoni flow contribution to the evaporation rate of small heated water droplets resting on hot substrates is negligible. We compare data of evaporating droplet experiments with numerical results and assess the effect of Marangoni flow and its contribution to the evaporation process. We demonstrate that heat conduction inside these water droplets is sufficient to give an accurate estimate of evaporation rates. Although convection in evaporating water droplets remains an open problem, our aim in this study is to demonstrate that these effects can be neglected in the investigation of evaporation rate evaluation. It is worth noting that the presented results apply to volatile heated drops which might differ from spontaneously evaporating cases.     

Electroosmotic flow with Joule heating effects

Electroosmotic flow with Joule heating effects was examined numerically and experimentally in this work. We used a fluorescence-based thermometry technique to measure the liquid temperature variation caused by Joule heating along a micro capillary. We used a caged-fluorescent dye-based microfluidic visualization technique to measure the electroosmotic velocity profile along the capillary. Sharp temperature drops close to the two ends and a high-temperature plateau in the middle of the capillary were observed. Correspondingly, concave-convex-concave velocity profiles were observed in the inlet-middle-outlet regions of a homogeneous capillary. These velocity perturbations were due to the induced pressure gradients resulting from axial variations of temperature. The measured liquid temperature distribution and the electroosmotic velocity profile along the capillary agree well with the predictions of a theoretical model developed in this paper.     

Intrusion pressure to initiate flow through pores between spheres

In this work, clusters of three or four spheres were used to examine intrusion pressure. Polytetrafluoroethylene (PTFE) or polyamide 66 (PA66) spheres were arranged horizontally to create a single pore. Liquid drops of water or ethylene glycol were gently introduced from above. If the spheres were too large, drops flowed through as soon as they were deposited. If the spheres were too small, liquid was suspended in the neck of the pore and could not pass through; drops became unstable and fell to one side. Alternatively, if spheres of a certain size were chosen, then capillary forces initially prevented drops of lesser stature from breaking though. However, as these drops grew taller, they eventually reached a height where the gravitational force exceeded the capillary force and the liquid flowed through the pore. A simple model for intrusion pressure was derived. Estimates from the model agreed well with experimentally measured values.     

Dynamic protein adsorption in microchannels by "stop-flow" and continuous flow

This work addresses two ways of loading proteins on microchannel surfaces for immunoassay applications: the "stop-flow" and the continuous flow processes. The "stop-flow" method consists of successive static incubation periods where the bulk solution depletes upon the adsorption process. In the present paper, a multi-step "stop-flow" protein coating is studied and compared to a coating under continuous flow conditions. For the "stop-flow", a non-dimensional parameter is here introduced, indicating the adsorbing capacity of the system, by which it is possible to calculate the number of loads necessary to reach the optimum coverage. For the continuous flow, the effects on the adsorption of the kinetic rates, flow velocity and wall capacity have been considered. This study shows the importance of a careful choice of the fluid velocity to minimise the sample waste. For diffusion controlled and kinetics controlled processes, two flow velocity criteria are provided in order to obtain the best possible coverage, with the same amount of sample as with the "stop-flow".     

Mass and momentum transport in extra-luminal flow (ELF) membrane devices for blood oxygenation

In this paper, we report on the characterisation of transport in membrane modules for blood oxygenation where blood is circulated outside hollow fibre membranes arranged in double layer cross-laid mats at an angle with respect to the main direction of blood flow. The effect of design and operating variables on module performance was investigated with respect to oxygen transfer into water, as gaseous oxygen and water are circulated counter-currently, respectively inside the membrane lumen and through the membrane assembly.Increasing water flow rates and membrane angles enhanced oxygen transfer across the membrane and resulted in robust operation but also in high pressure drops.Module pressure drop and oxygen transfer rate were correlated to module geometry, fibre packing density, water flow rate and membrane angle with respect to the main direction of the liquid flow in non-dimensional equations that can be used by membrane module manufacturers for the design of optimal ELF blood oxygenators. The results suggest that an optimum membrane angle exists, beyond which module operation is not convenient in terms of energy.     

Particle motions in sheared suspensions

The effects of diffusion out of and into drops undergoing equatorial collision in laminar shear flow were studied. With an electric field perpendicular to the direction of flow, diffusion into undeformed drops enhanced coalescence, while diffusion from the drops inhibited it. With marked outward diffusion, drops having a collision angle greater than 83° assumed a stable alignment in opposition to the velocity gradient for several minutes and then rotated to become a permanent head-on collision doublet. With inward diffusion the separation of drop centers increased along the paths of approach and the apparent angle of collision decreased. The phenomena were explained qualitatively on the basis of surface flow arising from concentration gradients at the drop surfaces. Stable multiplets were formed on collision of highly deformed drops as a result of hydrodynamic forces both with and without diffusion.     

Experimental study on flow characteristics of tetrahydrofuran hydrate slurry in pipelines

Tetrahydrofuran (THF) was selected as the substitute to study the flow behaviors and the mechanism of the hydrates blockage in pipelines. The slurrylike hydrates and slushlike hydrates are observed with the formation of hydrates in pipeline. There is a critical hydrate volume concentration of 50.6% for THF slurries and pipeline will be free of hydrate blockage while the hydrate volume concentration is lower than the critical volume concentration; otherwise, pipeline will be easy to be blocked. Fully turbulent flow occurs and friction factors tend to be constant when the velocity reaches 1.5 m/s. And then, constant values of friction factors that depend on the volume concentrations in the slurry were regressed to estimate the pressure drops of THF hydrate slurry at large mean velocity. Finally, a safe region, defined according to the critical hydrate volume concentration, was proposed for THF hydrate slurry, which may provide some insight for further studying the natural gas hydrate slurries and judge whether the pipeline can be run safely or not.     

Linear voltage profiles and flow homogeneity in pressurized planar electrochromatography

Planar electrochromatography (PEC) is an emerging technique for thin-layer chromatography (TLC) where electroosmosis is the driving force for the solvent, not capillary action. This allows for much faster and constant flow rates in turn yielding increased zone capacities and efficiencies. Instrumental designs have changed greatly over the last few years solving many of the initial instrumentation challenges. We have previously shown that low applied pressure (or no applied pressure) PEC instruments do not give linear voltage drops across the separation path length of a TLC plate, which in turn results in non-stable electroosmotic flow (EOF). By the use of our unique reader electrode grid we have the ability to monitor the potential at eight discrete positions throughout the 10-cm separation path length. We now show that high-pressure PEC instruments, most commonly referred to as pressurized planar electrochromatography (PPEC) do show a linear voltage drop and constant EOF. We compare plate equilibration times of PPEC and low-pressure PEC, use of increased field strengths, as well as sample application designs. In addition, we discuss the use of rhodamine B as a visual marker for reproducible migration and calculation of theoretical plates.