Liquid flow in molds with prelocated fiber mats

The mechanism associated with mold filling in the manufacture of structural RIM (SRIM) and resin transfer molding (RTM) composites is studied by means of flow visualization and pressure drop measurements. To facilitate this study, an acrylic mold with a variable cavity was constructed and the flow patterns of nonreactive fluid flowing through various layers, types, and combinations of preplaced glass fiber reinforcement mats were photographed for both evacuated and nonevacuated molds. The pressure drops in the flow through a single type of reinforcement (e.g., a continuous strand random fiber mat) and also a combination of reinforcement types (e.g., a stitched bidirectional mat in combination with a random fiber mat) were recorded at various flow rates to simulate high-speed feeding processes (e.g., SRIM) and low-speed feeding processes (e.g., RTM). By changing the amount of reinforcement placed into the mold, the permeabilities of the different types and combinations of glass fiber mats were obtained as a function of porosity. It is shown that partially evacuating the mold cavity decreases the size of bubbles or voids in the liquid, but ultimately increases the maximum pressure during filling. The results also show that glass fiber mats exhibit anisotropic permeabilities with the thickness permeability, K_z, being extremely important and often the determining factor in the pressure generated in the mold during filling.     

Mass transfer around prolate spheroidal drops in an extensional flow

Mass transfer in the continuous phase around a small eccentricity prolate spheroidal drop in an axisymmetric extensional creeping flow and at large Peclet numbers was investigated theoretically. The results show that, at very short times, the total quantity of solute transferred to or from the drop represents, at O(Ca¹), mass transfer by diffusion only around a sphere. For long times, or at steady‐state, the total quantity of solute transferred is, at O(Ca¹), slightly smaller than that of a spherical drop, and it decreases with an increase of the capillary number or the viscosity ratio. © 2012 Canadian Society for Chemical Engineering     

BUOYANCY-DRIVEN MOTION OF DROPS AND BUBBLES IN A PERIODICALLY CONSTRICTED CAPILLARY

Buoyancy-driven motion of viscous drops and air bubbles through a vertical capillary with periodic constrictions is studied. Experimental measurements of the average rise velocity of buoyant drops are reported for a range of drop sizes in a variety of two-phase systems. The instantaneous drop shapes at various axial positions within the capillary are also quantitatively characterized using digital image analysis. Periodic corrugations of the capillary wall are found to have a substantial retarding effect on the mobility of drops in comparison with previous experimental results in a straight cylindrical capillary. For systems characterized by small Bond numbers, drop deformations are found to be periodic. In large Bond number systems, however, drop breakup eventually occurs as the drop size is increased beyond a critical limit. The observed mode of breakup is a tail-pinching process similar to that observed by Oibricht and Leal (1983) for pressure-driven motion of low viscosity ratio drops through a sinusoidally constricted capillary. In contrast to their results, however, the same mode of breakup was also observed for systems with O (1) viscosity ratios,     

Motions of a fluid drop in linear and quadratic flows

A theoretical analysis is presented of the flow field near a spherical fluid drop immersed in an incompressible Newtonian fluid which, at large distances from the drop, is undergoing an undisturbed flow. The undisturbed flows considered here are relevant to studies of drop motions near a phase boundary, and to some aspects of the coalescence of liquid drops. Exacl solutions in closed form have been found using the harmonic function expansion in spherical coordinates. Calculation of the hydrodynamic force on the drop leads to a generalization of Faxen’s law to afluid particle in anarbitrary undisturbed creeping-flow. The solutions are then expressed in terms of she fundamental singularity solutions for Stokes flow in anticipation of future analysis of the drop coalescence. In addition, the deformed shapes are determined for a fluid drop freely suspended in an axisymmetric Poiseuillian flow.     

Experimental study on energy consumption characteristics of rotational–perforated static mixers

An ideal static mixer can achieve efficient mixing at low pressure drops. Owing to the excellent performance of the tridimensional rotational flow sieve tray (TRST) in a gas–liquid two-phase system, the TRST structure was modified into a rotational–perforated static mixer (RPSM) to enhance mixing in multicomponent liquid systems. The energy consumption characteristics of the RPSM were experimentally studied based on Reynolds numbers in the range of 986–7892, gap L = 0–80 mm, and relative angle γ = 0–45°. The effects of the element installation method, number, gap, relative angle, fluid Reynolds number, fluid properties, and other parameters on the RPSM pressure drop were also investigated. An interaction analysis of each factor was performed using the factorial design method and an empirical model of the RPSM Z-factor was established. Additionally, pressure drop in the RPSM was compared with those of other commonly used static mixers. Results show that, when the element is backward-installed, the pressure drop is higher than that in the forward direction because the fluid is constantly twisted. Moreover, the pressure drop increases with increasing element gap, and the average increase is 43.64% and 19.28% for the forward and backward installations, respectively. The influence of the relative angle on the pressure drop is mainly reflected when the gap L = 0. Subsequently, the degree of influence of each factor was determined, and the Z-factor was calculated and found to be consistent with the experimental values (relative error of less than 15%).     

Experimental investigation of flow-induced microvoids during impregnation of unidirectional stitched fiberglass mat

The complexity of the resin injection step in liquid composite molding (LCM) processes, such as resin transfer molding (RTM) and structural reaction injection molding (SRIM), often results in flow-induced defects such as poor fiber wetting and void formation. These defects have a deleterious effect on the mechanical properties of composites. In this work, high resolution video-assisted microscopy was used for in situ observation of flow-induced interstitial voids or microvoids formed inside the fiber tows during mold filling. Flow visualization experiments were carried out with different liquids to better understand the microscale flow behavior that led to the formation of microvoids for flow both along and normal to the fiber tows. Microvoid formation was correlated to the modified capillary number, Ca#* = μν/γcos(θ). The study revealed that for axial flow, microvoids were formed at Ca#* > 10⁻³. For transverse flow, microvoids were formed at an even lower capillary number. ∼ 10⁻⁴. Once formed, microvoids were difficult to purge and remained trapped even after bleeding the liquid at much higher flow rates than those at which they were formed.     

Numerical analysis of injection molding of glass fiber reinforced thermoplastics. Part 1: Injection pressures and flow

Numerical calculations of flow and injection pressures during injection molding of fiber-filled thermoplastics are compared to experimental measurements. The flow is modeled as a 2–D, nonisothermal, free-surface flow with a new viscosity model dependent upon temperature, pressure, and fiber concentration. The steady-state viscosity model is developed to account for the fiber-concentration and shear-thinning viscosities of the polymer based upon combining the Dinh-Armstrong fiber model with the Carreau viscosity model. The new model has four parameters, three from the Carreau model and one from Dinh-Armstrong for fiber concentrations. The new model calculates reasonably well the steady-state viscosity of fiber-filled polypropylene over the shear rate range of 0.01 s^?1to 20 s^?1. The numerical work successfully describes the flow of fiber-filled polymers during injection molding using finite-difference solutions for the transport equations and marker particles to track the flow front. The comparisons between the calculated and measured pressure drops for an injection molded part were reasonable for the unfilled and fiber-filled polypropylene materials. The pressure drop comparison is very good for slow fill of a base case resin, Himont polypropylene, but not as good for fast fill of the resin. The pressure drop comparison is very good for fast fill of glass-filled resin, DSM polypropylene with 10% and 20% short fibers, but not as good for slow fill of the resin and resin plus fibers.     

Inducing arbitrary vapor pressures,and quantifying leakages

We generalize the Maxwell drop evaporation equation to cover the range from closed system to open system through semiclosed system where the evaporation is restricted to an arbitrary degree which we show how to characterize. We first consider a suspended drop, and then a drop contacting a surface where the surface's vicinity restricts the evaporation paths. We show how to use these results to obtain arbitrary values of vapor pressure by simple manipulations of the numbers and sizes of droplets added to the system for a constant leak size, or, alternatively, control the leak size with a valve for given sizes of drops. We further show how to use this result to quantify a leakage in a system. Such a leakage is characterized using a single parameter (leakage length) which the described method calibrates. The calibrated leakage length can be used for systematic control of vapor concentrations within the chamber. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4548–4553, 2016     

Cover Chem. Eng. Technol. 10/2013

Pilot Setup for Dynamically Enhanced Membrane Emulsification This setup allows the production of emulsions with narrow drop size distributions. A disperse liquid phase is pushed through a porous membrane into another immiscible fluid phase. A rotor above the membrane induces laminar shear flow, which detaches the drops from the membrane pores. A narrow shear gap and micro engineered membranes help to maintain good control over drop detachment. The sub pictures show drops detaching from membrane pores (top) at different shear flow conditions acquired in a separate visualization setup. The bottom picture shows a cut through a micro engineered silicon membrane, which was specifically designed and fabricated at ETH Zurich for the emulsification setup. The apparatus was designed and built by the Bühler AG, Uzwil, Switzerland in close collaboration with the ETH Zurich, Switzerland. DOI: 10.1002/ceat.201300256 Drop Detachment from a Micro‐Engineered Membrane Surface in a Dynamic Membrane Emulsification Process S. Holzapfel*, E. Rondeau, P. Mühlich, E. J. Windhab* Chem. Eng. Technol. 2013 , 36 (10), 1785–1794     

Surface remobilization of buoyancy-driven surfactant-laden drops at low reynolds and capillary numbers

It is well known that the terminal velocity of a drop settling in a viscous fluid is impacted by surface tension gradients. These gradients can develop because of nonuniform accumulation of surfactant on the surface as a result of a number of transport mechanisms. Here, a surfactant transport model based on a sorption-limited Frumkin framework is used to describe surfactant transport in the presence of both surface convection and diffusion at low Reynolds and capillary numbers. Constants characterizing surfactant transport in the Frumkin framework are experimentally determined and used to predict aqueous drop velocities with varying surfactant concentrations and volumes. Computation is carried out by satisfying equations governing mass, momentum, and interface species conservation. Experiments demonstrate qualitative and quantitative agreement between predicted and measured drop velocities. It is shown that surface remobilization explains some observed trends in measured velocity as the drop size decreases. © 2018 American Institute of Chemical Engineers AIChE J, 65: 294–304, 2019     

ON THE EFFECTIVE CONDUCTIVITY OF A DILUTE SUSPENSION OF SPHERICAL DROPS IN THE LIMIT OF LOW PARTICLE PECLET NUMBER

In this paper we consider the effective conductivity of a dilute suspension of neutrally bouyant spherical drops which is undergoing a simple shear flow. The thermal conductivity, viscosity and specific heat capacity of the drops are assumed to be different from those of the suspending fluid, though it is assumed that the local Peclet and Reynolds numbers are small both inside and outside the drop. The analysis consists of three parts: a derivation of the relationship between bulk heat flux on the one hand and the thermal and momentum fields at the microscale of the suspended particles on the other; a calculation of the local temperature field near a single neutrally buoyant spherical drop in shear flow with an imposed transverse temperature gradient at large distances; and a synthesis of the general relationship for bulk heat flux and the calculated local temperature field to determine an effective conductivity for a dilute suspension of spherical drops.     

Drop volumes and terminal velocities in aqueous two phase systems

The terminal velocities and sizes of drops in aqueous two-phase systems formed by PEG (4000)-sodium sulphate-water, PEG (6000)-sodium sulphate-water and PEG (4000)-dextran-water were measured. Nozzle sizes were varied from 1.0 to 2.5 mm and the drops were formed of both light and heavy phases. Based on video photographic analysis for drop formation, the shape of the drop during formation was found to have an important bearing on the drop volume. Therefore a generalised model was developed using the video photographic measurements. A correlation was developed for the terminal velocities of the drops in aqueous two phase systems, which covers Morton numbers from 0.00211 to 11050 and Eötvös numbers from 0.091 to 288.     

INFLUENCE OF THE DISTRIBUTOR PLATE AND OPERATING CONDITIONS ON THE FLUIDIZATION QUALITY OF A GAS FLUIDIZED BED

Experiments were carried out to examine the influence of both the type and the pressure drop of distributor plates on the fluidization quality of an atmospheric fluidized bed. Three different distributor types were used, perforated Perspex, metallic mesh, and porous ceramic, with pressure drops ranging from 0.05 to 350 kPa and superficial air velocities ranging from 0.1 to 2.3 m/s. Three sizes of silica Ballotini beads, 355–425, 600–710, and 850–1000 µm, were used as bed material. The static bed height was set to 300 mm and was divided into six horizontal 50 mm high slices. For each slice, pressure drop values were recorded for U₀/U_mf ratios from 20 to 1. In order to produce a reference for the pressure drop evolution, a modification of the two-phase theory was introduced, taking into consideration the increase in the average global porosity as well as the change in the ratio of flow through the bubbles versus the flow through the dense phase. This allowed assessment of the influence of the different operating conditions and setups on the quality of fluidization, Q?.     

Influence of normal stress difference on polymer drop deformation

Polypropylene drops of varying viscosity and elasticity were sheared in a polystyrene matrix. Two transparent, counter-rotating parallel disks provided simple shear flow. By adjusting the speed of one disk the drop center was fixed in the laboratory frame and deformation followed via high magnification video camera. It was found that with high matrix elasticity drops of the minor phase stretched perpendicular (x₃) to the flow direction (x₁). This is the first report of widening of drops in shear flow. An analytical relation was established between the second normal stress differences of the phases and degree of widening. The formation of sheets and the phenomena of widening results in a larger than affine area generation.     

DROP DISPERSION IN SUSPENSION POLYMERIZATION

Four models, two based on laminar shear and two based on turbulent flow, are proposed to describe drop dispersion in non-coalescing systems. The models predict the largest surviving drop size _dmax as a function of geometry, speed and physical property variables.

Laboratory data including suspension polymerization runs support the boundary layer laminar shear model for drops larger than approximately 200 microns. Smaller drops support a turbulence model.

The boundary layer shear model was confirmed in scale-up suspension polymerization runs aimed at producing 1000 micron maximum bead sizes. Five approximately geometrically similar polymerizers were used, varying in size from 7.5 to 15000 liters.     

TWO DROP MASS TRANSFER WITH CHEMICAL REACTION-ASYMPTOTIC CASE STUDIES

Mass transfer at very low and moderately high Peclet numbers has been analyzed for two interacting solid spheres and for drops in tandem. In the first case study, where the Peclet and Reynolds numbers approach zero, interactions between two drops with liquid phase chemical reaction affect the mass flux more drastically for gas resistance controlling cases than for liquid resistance controlling cases. The effects of drop size, spacing, and reaction rate on the Sherwood numbers have been considered and the various regimes of gas and liquid side control have been numerically established. The asymptotic value of the average Sherwood number as the interdrop distance approaches infinity is lower for the case of two drops than for two solid spheres, i.e. it was found that ¯Sh² _drops = ¯0.5Sh² _solidspheres, as (dAB/a)→∞

For the case of mass transfer at moderately high Peclet numbers potential flow, i.e. Re→∞, was assumed. This limited analysis indicates that there is no significant difference between the single drop and the two drop cases.     

Computational evaluation of effective transport properties of differential microcellular structures

This study presents a combined implementation of three-dimensional (3D) advanced imaging and computational fluid dynamics (CFD) modeling and simulation techniques to interpret the effective transport properties of single and stacked samples of differential microcellular structures. 3D morphological analysis software (ScanIP) was used to create representative elemental volumes via high-resolution tomography data for samples of tetrakaidekahedron-shaped Inconel and bottleneck-type aluminum foams. Pore-structure-related information for single and stacked differential samples were obtained with the aid of image analysis software, while their effective transport properties were attained by computationally resolving the pressure drop developed across these materials for superficial fluid velocities in the range from 0 to 6 m s⁻¹. Model validation was demonstrated by tolerable agreement between resulting CFD predicted results and experimentally measured values of flow properties. With these techniques, contributory effects were identified for pore-structure-related properties, pore density, and flow entrance on the flow dynamics of microcellular structures. This approach could prove useful in the design of highly efficient porous metallic components for applications specific to fluid transport.     

Forced Oscillations of Pendant Drops

Abstract

The efficiency of droplet/bubble breakup in multiphase contactors can be increased by applying external fields at resonance frequencies of the drops/bubbles. Experimental and theoretical techniques, developed for the study of forced oscillation of pendant drops on nozzles, are used to gain a fundamental understanding of drop response as a function of forcing frequency. Preliminary results of drop oscillations caused by electrical and flow perturbation techniques indicate that the relationship of resonance frequency to drop size for a given fluid system is not affected by the means of excitation. Computational techniques may be used to gain insight into phenomena which are difficult to probe by experiment, such as internal flow fields. The understanding gained by use of these techniques will be indispensable in design and operation of future multiphase contacting devices.     

Mass transfer around bubbles,drops, and particles in uniaxial and biaxial nonlinear extensional flows

Mass transfer around spherical bubbles, drops, and solid particles in uniaxial and biaxial nonlinear extensional creeping flows at large Peclet numbers is the subject of this theoretical report. The fluid mechanics problem is governed by the viscosity ratio (λ) and the nonlinear intensity of the flow (E). The flow outside such bodies reveals a different picture than the linear case (E = 0) such as separating surfaces or closed circulations. There is a range: −1.04 < E < 0 (bubbles and drops) and −0.490 < E < 0 (particles) where the mass transfer rate is lower than the linear case. Outside these ranges, the mass transfer rate is higher than the linear case and in general it increases as |E| increases. Same mass transfer rates are expected in uniaxial and biaxial flows, except in the presence of external closed circulations where the biaxial flow overcomes the uniaxial flow. © 2018 American Institute of Chemical Engineers AIChE J, 65: 398–408, 2019     

Study of an Annular Photoreactor with Tangential Inlet and Outlet: I. Fluid Dynamics

Photochemical reactors tend to exhibit turbulent flow even with low Reynolds numbers. The k‐? model is not always appropriate in this situation. An annular photoreactor was designed with tangential inlet and outlet tubes to investigate this. The fluid flow was characterized by residence time distribution (RTD) experiments, which were reproduced by computational fluid dynamics considering four relevant turbulence models: the k‐?, the k‐ω, the shear stress transport, and the Reynolds stress models. Inlet effects induced helical flow throughout the reactor, switching to plug flow depending on the flow rate and the turbulence model. The k‐ω model properly deals with viscous effects and reproduces the experimental RTD curves with correlation coefficients greater than 0.9566, against 0.8705 from the k‐? model.