Slit Flow Research Articles

Gas-focused liquid microjets from a slit

We report an experimental study on a new arrangement of flow focusing that uses a slit aperture. The slit can achieve similar flow chocking function as a classic circular aperture to established gas flow pressure drop. Fundamentally, the jetting mechanism and quantitative behavior of slit flow focusing are very similar to the classic flow focusing because of the singularity nature of the jet despite the drastically different aperture shapes. After re-scaling the jet shape, the axial coordinate with the hydraulic diameter of the slit, the experimental data follow closely with the universal jet profile derived in Gañán-Calvo, Ferrera, and Montanero [“Universal size and shape of viscous capillary jets: Application to gas-focused microjets,” J. Fluid Mech. 670, 427-438 (2011)] based on circular aperture. Practically, the slit configuration expands the possibility of manipulating the jets. The two thin plates that form the slit aperture can also be used as electrodes to apply electrohydrodynamic excitation to the jet for controlled jet breakup with narrower droplet size distribution. In addition, the modest throughput of a single flow focused jet can be increased by operating a linear array of jets focused and excited by the same slit.

Slip heating in die drool

When molten plastic is extruded from a die, it can collect on the open die face. Called die drool, this phenomenon costs plastics manufacturers by requiring shutdown for die cleaning. This has been attributed to cohesive failure within the fluid at an internal surface, where the fluid slips on itself; the corresponding isothermal analysis led to an analytical solution for the drool rate (Schmalzer and Giacomin, J. Polym. Eng. 2013, 33, 1). In this paper, we account for the frictional heating at the cohesive slip interface, which we call slip heating. We focus on slit flow, which is used in film casting, sheet extrusion, curtain coating, and in many other chemical engineering unit operations. In slit flow, the magnitude of the heat flux from the slipping interface is the product of the shear stress and the slip speed. We present the solution for the temperature rise in pressure‐driven slit flow subject to constant heat generation at the cohesive slip interface. We solve the energy equation in Cartesian coordinates for the temperature rise, for both the transient and steady temperature profiles, in both the drool layer and the bulk polymer. We then evaluate the effect of this temperature rise on the rate of die drool. For this simplest relevant non‐isothermal problem, we neglect viscous dissipation and convective heat transfer in the melt and we model viscosity as an Arrhenius function of temperature. We conclude with three worked examples showing the relevance of slip heating in determining die drool flow rates. We find that slip heating diminishes die drool. We arrive at two sufficient dimensionless conditions for the accurate use of our results: Br ≪1 or Gi ≪1.

Velocimetry in microchannels using photobleached molecular tracers: a tool to discriminate solvent velocity in flows of suspensions.

We report the development and analysis of a velocimetry technique based on the short time displacement of molecular tracers, tagged thanks to photobleaching. We use confocal microscopy to achieve a good resolution transverse to the observation field in the direction of the velocity gradient. The intensity profiles are fitted by an approximate analytical model which accounts for hydrodynamic dispersion, and allow access to the local velocity. The method is validated using pressure driven flow in microfluidic slits having a thickness of a few tens of micrometers. We discuss the main drawbacks of this technique which is an overestimation of the velocity close to the walls due to the combination of molecular diffusion and shear. We demonstrate that this error, limited to a near wall region of a few micrometers thick, could be controlled by limiting the diffusion of fluorophore molecules or minimizing the bleaching time. The presented technique could be combined with standard particle imaging velocimetry to access velocity differences and allow particle trajectory analysis in microflows of suspensions.

Self-regulation in flow-induced structure formation of polypropylene.

Flow-induced structure formation is investigated with in situ wide-angle X-ray diffraction with high acquisition rate (30 Hz) using isotactic polypropylene in a piston-driven slit flow with high wall shear rates (up to ≈900 s(-1) ). We focus on crystallization within the shear layers that form in the high shear rate regions near the walls. Remarkably, the kinetics of the crystallization process show no dependence on either flow rate or flow time; the crystallization progresses identically regardless. Stronger or longer flows only increase the thickness of the layers. A conceptual model is proposed to explain the phenomenon. Above a certain threshold, the number of shish-kebabs formed affects the rheology such that further structure formation is halted. The critical amount is reached already within 0.1 s under the current flow conditions. The change in rheology is hypothesized to be a consequence of the "hairy" nature of shish. Our results have large implications for process modelling, since they suggest that for injection molding type flows, crystallization kinetics can be considered independent of deformation history.

Wall slip heating

When molten plastic is extruded, the upper limiting throughput is often dictated by fine irregular distortions of the extrudate surface. Called sharkskin melt fracture, plastics engineers spike plastics formulations with processing aids to suppress these distortions. Sharkskin melt fracture is not to be confused with gross melt fracture, a larger scale distortion arising at throughputs higher than the critical throughput for sharkskin melt fracture. Sharkskin melt fracture has been attributed to a breakdown of the no slip boundary condition in the extrusion die, that is, adhesive failure at the die walls, where the fluid moves with respect to the wall. In this article, we account for the frictional heating at the wall, which we call slip heating. We focus on slit flow, which is used in film casting, sheet extrusion, curtain coating, and when curvature can be neglected, slit flow is easily extended to pipe extrusion and film blowing. In slit flow, the magnitude of the heat flux from the slipping interface is the product of the shear stress and the slip speed. We present the solutions for the temperature rise in pressure-driven slit flow and simple shearing flow, each subject to constant heat generation at the adhesive slip interface, with and without viscous dissipation in the bulk fluid. We solve the energy equation in Cartesian coordinates for the temperature rise, for steady temperature profiles. For this simplest relevant nonisothermal model, we neglect convective heat transfer in the melt and use a constant viscosity. We arrive at a necessary dimensionless condition for the accurate use of our results: Pe≪1. We find that slip heating can raise the melt temperature significantly, as can viscous dissipation in the bulk. We conclude with two worked examples showing the relevance of slip heating in determining wall temperature rise, and we show how to correct wall slip data for this temperature rise. POLYM. ENG. SCI., 55:2042–2049, 2015. © 2014 Society of Plastics Engineers

Flow induced crystallization in isotactic polypropylene during and after flow

Using a unique slit flow device and in situ synchrotron X-ray methods, the entire evolution of flow induced crystallization in isotactic polypropylene (iPP) was studied from the start-up of flow up to completion of crystallization. Two WAXD detectors, including the ultrafast Pilatus and the two-dimensional Frelon, were combined to achieve a sufficient time resolution for a fairly short period (during and just after flow) and a sufficient spatial resolution for measuring the kinetics of different crystallites oriented in different directions. The complete evolution of these structures is obtained and this reveals several important issues on crystallization. Firstly, the appearance of crystallites can occur already within a short flow duration of maximum 0.25 s. The specific formation time strongly depends on the flow strength. The formation of crystallites just after flow can be distinguished from that occurring during flow, although both happen on the sub-second time scale. Next, we quantified the subsequent appearance of iPP daughter lamellae and determine the time dependent ratio between parent and daughter lamellae as a function of the flow strength. The average orientation of the initial shish is relatively high while the orientation of parent lamellae decreases with their lateral growth. Finally, at the experimental temperature of 145 °C and depending on the shear strength, iPP β-phase can be induced. The quantitative information provided by this data set is well suited for validation and extension of our models for flow induced crystallization of polymers. Such complete data sets, including the fully specified initial and boundary conditions are not available yet for the (nearly) processing conditions as we applied in this study.

Three‐dimensional numerical simulation of red blood cell motion in Poiseuille flows

SUMMARYAn immersed boundary method based on an FEM has been successfully combined with an elastic spring network model for simulating the dynamical behavior of a red blood cell (RBC) in Poiseuille flows. This elastic spring network preserves the biconcave shape of the RBC in the sense that after the removal of the body force for driving the Poiseuille flow, the RBC with its typical parachute shape in a tube does restore its biconcave resting shape. As a benchmark test, the relationship between the deformation index and the capillary number of the RBCs flowing through a narrow cylindrical tube has been validated. For the migration properties of a single cell in a slit Poiseuille flow, a slipper shape accompanied by a cell membrane tank‐treading motion is obtained for Re , and the cell mass center is away from the center line of the channel due to its asymmetric slipper shape. For the lower Re ⩽0.0137, an RBC with almost undeformed biconcave shape has a tumbling motion. A transition from tumbling to tank‐treading happens at the Reynolds number between 0.0137 and 0.03. In slit Poiseuille flow, the RBC can also exhibit a rolling motion like a wheel during the migration when the cell is released in the fluid flow with φ = π/2 and θ = π/2 (see Figure 12 for the definition of φ and θ). The lower the Reynolds number, the longer the rolling motion lasts; but the equilibrium shape and position are independent from the cell initial position in the channel. Copyright © 2014 John Wiley & Sons, Ltd.

Multimorphological Crystallization of Shish-Kebab Structures in Isotactic Polypropylene: Quantitative Modeling of Parent–Daughter Crystallization Kinetics

A model is presented for the crystallization kinetics of flow-induced shish-kebab structures in isotactic polypropylene. The model accounts for two phenomena that affect the crystal growth of kebab structures. First, the temperature of the material increases due to latent heat release. Second, polymer chains are deformed in such a way that growth of kebabs (with their c-axis in flow direction) is promoted. Furthermore, we incorporate crystallization kinetics of the daughter morphology which nucleate on the (010) lateral surface of kebabs. The model is validated with in-situ wide-angle X-ray diffraction data from an in-house-developed extensional flow device and a modified multipass rheometer used to apply a flow pulse in a slit flow geometry. Excellent agreement is found between the model and experimental data, in terms of crystallization kinetics as well as parent/daughter ratio. The well-known Avrami model, in which it is assumed that crystal growth rate is constant, is widely used to analyze (quasi-)isothermal flow-induced crystallization experiments. We show that, because the growth rate of kebabs is strongly time dependent due to temperature and orientation effects, this analysis fails for experiments like the ones presented in this study. This is manifested in noninteger Avrami coefficients typically smaller than 2, which have been observed in a number of different studies. The current model explains these observations.

Electroosmotic flow in polymer-coated slits: a joint experimental/simulation study

The quality of separation in capillaries electrophoresis is strongly affected by the magnitude of the electroosmotic flow (EOF). The EOF can be efficiently suppressed by coating the capillary wall with hydrophilic polymers. In this paper, experimental data are presented to show the effect of coating thickness and charge on mass transport. Simulations performed with the lattice Boltzmann technique quantitatively reproduce the EOF with and without the coating and with either a neutral or charged coating layer. Experimental, simulation and theoretical analyses converge toward the interpretation that EO suppression arises from the frictional forces acting on the ionic currents and that a detailed representation of the polymeric coating is not needed in order to capture the phenomenon.

A microchip filter device incorporating slit arrays and 3-D flow for detection of circulating tumor cells using CAV1-EpCAM conjugated microbeads

Circulating tumor cells (CTCs) are rare cells and the presence of these cells may indicate a poor prognosis and a high potential for metastasis. Despite highly promising clinical applications, CTCs have not been investigated thoroughly, due to many technical limitations faced in their isolation and identification. Current CTC detection techniques mostly take the epithelial marker epithelial cell adhesion molecule (EpCAM), however, accumulating evidence suggests that CTCs show heterogeneous EpCAM expression due to the epithelial-to-mesenchymal transition (EMT). In this study, we report that a microchip filter device incorporating slit arrays and 3-dimensional flow that can separate heterogeneous population of cells with marker for CTCs. To select target we cultured breast cancer cells under prolonged mammosphere culture conditions which induced EMT phenotype. Under these conditions, cells show upregulation of caveolin1 (CAV1) but down-regulation of EpCAM expression. The proposed device which contains CAV1-EpCAM conjugated bead has several tens of times increased throughput. More importantly, this platform enables the enhanced capture yield from metastatic breast cancer patients and obtained cells that expressed various EMT markers. Further understanding of these EMT-related phenotypes will lead to improved detection techniques and may provide an opportunity to develop therapeutic strategies for effective treatment and prevention of cancer metastasis.

Application of the Finite Piece Method to Simulate Viscoelastic Fluid Flows in L-Shaped Channel

The finite piece method is established to solve the flows of K-BKZ fluid in L-shaped channel. Numerical results are given to compare to the three-dimensional simulation using the finite element method (FEM). It is found that the results are highly consistent as a whole. The error of flow distribution is smaller than 2% at the outlet. There is a minor discrepancy of the pressure in the convergence region of channel but they are restricted to a small region. The present approach demonstrates its superiority over the conventional FEM for analyzing slit flow.

Acoustic-excited vortex shedding and acoustic nonlinearity at a rectangular slit with bias flow

Abstract The acoustical response of a slit with a mean bias flow is numerically studied. By means of a potential flow model based on the discrete vortex method and a spanwise-averaged three-dimensional Green׳s function, both unsteady vortical flow and slit impedance are obtained in a unified theoretical framework. The numerical simulation focuses on the acoustic-excited vortex structures of the slit flow while neglecting the viscous damping effect. Three representative flow features are demonstrated, which are the destabilized jet flow, the rolling up of vortex sheets and formation of vortex pairs, and the reversal flow with alternating vortex shedding on both sides of the slit. These features are corresponding to low, moderate, and high sound amplitude, respectively. The acoustic behavior of the slit can be divided into linear, transition, and nonlinear regimes. During its evolution through the three regimes, the resistance exhibits a constant value, a slight decrease, and a significant increase with the increasing sound amplitude. Correspondingly, the reactance first remains constant and then shows a modest decrease as the sound amplitude increases. The nonlinear effect also causes the gradual decrease of the mean bias velocity in company with the marked increase of the amplitude of the fluctuating velocity in the slit. The mean bias velocity decreases to about 80 percent of its linear value at the transition point where reversal flow begins to occur, and further decreases to only 10 percent in the highly nonlinear region. The slit impedance is also presented as a function of frequency and for different aspect ratios. And the effects of frequency and slit geometry are discussed.

Evaluation of the Physicochemical Properties of Fine Globular Granules Prepared by a Multi-functional Rotor Processor

Multiple regression analysis (MRA) and principal component analysis (PCA) have been used in the present study to examine the relationships between the operational conditions of a unique multi-functional rotor processor, material attributes such as water content during granulation, and a series of associated micromeritics, including the flowability, granule mean size and granule density values. A variety of different operational conditions were tested, including the binder flow rate, atomization pressure, slit air flow rate, rotating speed and temperature of the inlet air. The results of MRA revealed several trends, including (1) the granule mean size was negatively affected by the atomization pressure, and positively affected by the binder flow rate; (2) the granule flow property, Carr's index was positively affected by the atomization pressure, and negatively affected by the slit air flow rate; and (3) the granule density was positively affected by the rotating speed. Taken together, these results suggested that the binder flow rate, atomization pressure and slit airflow rate were critical process parameters for the preparation of fine globular granules. Using PCA, it was possible to examine each relationship of all 19 batches and 10 variables, as well as determine which process parameters or material attributes impacted on the quality of the final product. The PCA results revealed that the roundness was positively correlated with the water content. Therefore, we believe this fundamental information will be important for the development of processes for the facile manufacture of fine globular granules.

In situ flow visualization of capillary flow of concentrated alumina suspensions

A new approach was taken to understand the flow behavior of concentrated particle suspensions in pressure-driven capillary flow. The flow of concentrated alumina suspensions in a slit channel was visualized and quantitatively analyzed with modified capillary rheometer. The suspensions showed complex flow behaviors; unique solid–liquid transition and shear banding. At low flow rates, 55 vol% alumina suspension showed a unique transient flow behavior; there was no flow at first and continuous change of flow profile was observed with time. At low shear rates in particular, the suspensions exhibited shear-banded flow profile which could be divided into three regions: the region with low flow rate near the wall, the region with rapid increase of flow velocity to maximum, and the region of velocity plateau. Based on both flow visualization and measurement of shear stress, it was found that the shear-banded flow profile in pressure-driven slit channel flow was strongly correlated with shear stress. The banding in pressure-driven flow was different from that in Couette flow. The banding of concentrated alumina suspensions was unique in that sluggish velocity profile was pronounced and two inflection points in velocity profile was exhibited. In this study, shear banding of concentrated alumina suspensions in slit channel flow was visualized and quantitatively analyzed. We expect that this approach can be an effective method to understand the flow behavior of particulate suspensions in the pressure-driven flow which is typical in industrial processing.

Die drool theory

Abstract When molten plastic is extruded from a die, it sometimes collects on the open face of the die. Known as die drool, this phenomenon costs plastics manufacturers by requiring die cleaning. This has been attributed to many causes, but none of these has led to an equation for the drool rate. In this work, we provide an exact analytical solution for the drool rate, and we base this solution on a postulate of a cohesive slip layer near the die walls. We thus attribute die drool to cohesive failure within the fluid at an internal surface where the fluid slips on itself. We adimensionalize the drool rate with the production rate, and call this the buildup ratio, BR. We provide an exact analytical solution for BR when the cohesive slip layer either slips at the die wall, or when it does not. We examine two important extrusion geometries: slit (which we then extend to pipe) and tube flow. We identify two new experiments: one to measure BR as a function of pressure drop, and another as a function of the die aspect ratio, and we then use our new theory to design droolometers.

Load and rheometric unit for the test of magnetorheological fluid

The article describes the original design of a slit flow rheometer. The behavioral problems of MR fluids and the main deviation from the commonly introduced Bingham model, which describes the MR fluid, are explained at the beginning of this article. Furthermore, the usual operating parameters of the MR fluids and devices are defined, such as: shear rate, viscosity in the off-state, yield stress, their dependence on temperature and the expected life of the filling. In the absence of a suitable rheometer a new design of rheometer was proposed, which allows long-term testing of MR fluids under real loading conditions. This article describes the important details of the construction. Particular attention is devoted to temperature measurement, calibration of the rheometer and data analysis, including mathematical tools and statistical evaluation of a set of measured points.

Rheological behavior of PS polymer melt under ultra high speed injection molding

Determination of the rheological behavior of a polymer melt under high shear rate is generally considered to be crucial for accurate simulation modeling of ultra high speed injection molding, a process that has been attracting more attention from researchers. In this study, a melt viscosity measurement system under high shear rate was established using an instrumented injection molding machine combined with a slit die. Polystyrene melt was studied. From measured pressure drop and volumetric flow rate, the slit flow model was used for the calculation of viscosity at wall shear strain rates up to 105 s−1. Good agreement in shear viscosity was found between results from conventional capillary rheometry and in-line measurement made using an injection molding machine for strain rates of 7 × 103 to 104 s−1. Measured shear viscosity in the test range was found to follow shear thinning power law behavior at shear rates below 7 × 104 s−1. However, the measured viscosity values are significantly lower (28%–46%) than the database obtained from the Moldflow package software (Cross-WLF model) at melt temperatures of 200, 215, and 230 °C. Further, the reduction in the viscosity value increases as the injection speed increases. It seems that the wall-slip effect plays a dominant role, becoming more significant as the melt temperature increases. Alternatively, as shear strain rates approached or exceeded 7 × 104 s−1, shear viscosity deviations from shear thinning behavior were observed and reached a rate-independent plateau. The behavior is thought to be influenced by pressure effects on viscosity. In the present study we emphasize that the measured results are significant for the design and simulation of ultra high speed injection processes such as micromolding and thin-walled injection molding.

Characterization of thermo-rheological behavior of polymer melts during the micro injection moulding process

In-line process monitoring and rheological characterization can help to understand the behaviour of polymer melt flows during manufacture and to make injection moulding a measurable process for manufacturing high quality parts. This work developed an in-line rheology measurement system using a slit die attached to a micro injection moulding machine. A series of dumbbell mould inserts was used to form the slit die with thickness ranging from 600 μm to 200 μm. Two combined pressure and temperature sensors were embedded into the slit die to measure the pressure drop. Based on the slit flow model, it was found that the viscosity of Pebax melts depends on the slit thickness in the actual injection moulding process. The competing effects of wall slip and non-isothermal conditions will determine the melt viscosity. The plastication induced thermo-mechanical history can also influence polymer viscosity, although it is neglected in conventional rheology measurements.

Lattice-Boltzmann and meshless point collocation solvers for fluid flow and conjugate heat transfer

SUMMARY The applicability and performance of the lattice-Boltzmann (LB) and meshless point collocation methods as CFD solvers in flow and conjugate heat transfer processes are investigated in this work. Lid-driven cavity flow and flow in a slit with an obstacle including heat transfer are considered as case studies. A comparison of the computational efficiency accuracy of the two methods with that of a finite volume method as implemented in a commercial package (ANSYS CFX, ANSYS Inc., Canonsburg, PA) is made. Utilizing the analogy between heat and mass transfer, an advection–diffusion LB model was adopted to simulate the heat transfer part of the slit flow problem followed by a rigorous mapping of the mass transfer variables to the heat transfer quantities of interest, thus circumventing the need for a thermal LB model. Direct comparison among the results of the three methods revealed excellent agreement over a wide range of Reynolds and Prandtl number values. Furthermore, an integrated computational scheme is proposed, utilizing the rapid convergence of the LB model in the flow part of the conjugate heat transfer problem with that of the meshless collocation method for the heat transfer part. The meshless treatment remains sufficiently rapid even for conduction-controlled processes in contrast to the LB method, which is very rapid in the convectioncontrolled case only. A single, common computational grid, composed of regularly distributed nodes is used, saving significant computational and coding time and ensuring convergence of the discrete Laplacian operator in the heat transfer part of the computations. Copyright © 2012 John Wiley & Sons, Ltd.

Mode locking effects on the playing frequency for fork fingerings on the clarinet

The non-linear excitation of wind instruments generates higher harmonics of the playing frequency. These higher harmonics are coupled to resonances in the pipe. This is called mode locking. When the pipe modes are not harmonic, the playing frequency shifts away from the fundamental in order to maximize the output. It may go up or down, depending on the position of the modes and the amplitude. The effect is especially manifest for fork fingerings. Three fork fingerings on a clarinet were investigated. They were artificially blown between the threshold and extinction pressure. A time domain simulation was carried out based on a lumped model of the excitation coupled to an input impedance calculated from the instrument dimensions. At low amplitudes the fundamental frequency dominates and the playing frequency is governed by the position of the first peak in the input impedance spectra. At higher blowing pressures the playing frequency shifts. For both blowing and simulation this follows the same pattern. The frequencies predicted by the calculations are higher than the values found by blowing, which may be due to inadequacies in the model description, to uncertainties of the various parameters, as reed stiffness, moving reed area, and the properties of the slit flow.