Intermittent two-phase flow study by NMR

Co-circulation of gas and liquid in a pipe can generate, depending on inlet conditions, various kinds of flow patterns. Few investigations have been performed on intermittent two-phase flows (slug flows) using classical techniques (optical probe, hot-wire anemonetry, etc.), because these techniques are difficult to apply in this flow regime. Here we show that nuclear magnetic resonance is a powerful technique to study such flows. The presented results deal with controlled isolated Taylor bubbles. In addition to a classical Pulsed Field Gradient Spin Echo (PFGSE), a magnetic field gradient was applied during the π/2)_X radio frequency pulse, which produces a selective irradiation. Thus, cutting up of the flow into slices provides the longitudinal evolution of the liquid fraction and of the velocity probability distribution in the entire region perturbed by the Taylor bubble. The existence of a recirculatory flow under the Taylor bubble is clearly demonstrated.     

Nonlinear Rayleigh-Taylor instability for hydromagnetic Darcian flow: effect of free surface currents

Capillary-gravity waves of permanent form at the interface between two unbounded magnetic fluids in porous media are investigated. The system is influenced by the horizontal direction of the magnetic field to the separation face of two semi-infinite homogeneous and incompressible fluids, so that the fields allow free-surface currents at the interface. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement. This equation is accomplished by using the cubic nonlinearity. Taylor theory is used to expand the governing nonlinear equation in the light of the multiple scales in both space and time. The perturbation analysis leads to imposition of two levels of solvability conditions, which are used to construct the well-known nonlinear Ginzburg-Landau equation. The stability criteria are discussed theoretically and numerically and stability diagrams are obtained. Regions of stability and instability are identified for the surface current density. It is found that the stabilizing role for the magnetic field is retarded when the flow is in porous media. Moreover, the increase in the values of resistance parameters plays a dual role, in stability behavior and in the increase in surface current density.     

Stability of the periodic deformations in planar nematic layers

The periodic deformations induced by external fields have been analysed by means of the Taylor expansion method based on the theorems of catastrophe theory. The analysis is restricted to the planar nematic slab influenced by a magnetic field. Two different configurations of the field which lead to periodic deformations with prevailing splay or twist we considered. The ranges of material constants at which the periodic state is stable and the threshold magnetic field strength have been found. The problem of transitions between the undeformed, uniformly deformed and periodic states is discussed.     

Residence time distribution from a continuous Couette flow device

This paper describes an experimental study of residence time distribution (RTD) by pulse response analysis in a continuous Couette flow device with rotating inner cylinder and stationary outer cylinder. The experiments were performed under conditions of (a) negligible and (b) significant influence of molecular diffusion and (c) Taylor vortex flow. Diethylene glycol and water were used as the test fluids with congo red dye and potassium permanganate solution as tracers respectively. A unique RTD described by an analytical expression was observed for experiments with low axial Reynolds number under the condition of negligible influence of molecular diffusion. For most experiments performed under conditions of significant influence of molecular diffusion and Taylor vortex flow regime over the ranges 0 < Ta < 118 and 0.4 < Re < 5.5, the RTD can be described by a dispersion model. The system behaves as a near-plug flow vessel at Ta ≈ 60. The critical Taylor number for this geometry as defined by the minimum dispersion number for a given flowrate is slightly higher than that without axial flow.     

Die swell ratio of polystyrene melt from an electro‐magnetized capillary die in an extrusion rheometer: effects of barrel diameter,shear rate and die temperature

A constant shear‐rate extrusion rheometer with an electro‐magnetized capillary die was utilized to investigate die swell behavior and flow properties of a polystyrene melt as the application of an electro‐magnetic field to the capillary die was relatively novel in polymer processing. The test conditions such as magnetic flux density, barrel diameter, extrusion rate and die temperature were studied. The results suggest that the maximum swelling of the polystyrene melt with application of the electro‐magnetic field could be enhanced up to 2.6 times (260%) whereas that without the electro‐magnetic field was 1.9 times (190%). The barrel diameter of 30 mm was found to be a critical value in the case of the die swell ratio and flow properties of the polystyrene melt were significantly affected by the magnetic flux density. This involved the number and angle of magnetic flux lines around the barrel part. Under the electro‐magnetic field, there were two mechanical forces influencing the die swell ratio and the flow properties; magnetic torque and shearing force. The die swell at wall shear rates less than 11.2 sec^?1 was caused by the magnetic torque, whereas at higher wall shear rates it was dependent on the shearing force. For a given magnetic flux density, the maximum increase in the die swell ratio as a result of the magnetic torque was calculated to be approximately 20%. Increasing the die temperature from 180 to 200°C reduced the overall die swell ratio and suppressed the effect of the magnetic flux density. Copyright © 2004 John Wiley & Sons, Ltd.     

Microfluidic capturing-dynamics of paramagnetic bead suspensions

We study theoretically the capturing of paramagnetic beads by a magnetic field gradient in a microfluidic channel treating the beads as a continuum. Bead motion is affected by both fluidic and magnetic forces. The transfer of momentum from beads to the fluid creates an effective bead-bead interaction that greatly aids capturing. We demonstrate that for a given inlet flow speed a critical density of beads exists above which complete capturing takes place.     

Rheological properties and orientational distributions of dilute ferromagnetic spherocylinder particle dispersions. Part II. Analysis for the two typical magnetic field directions

We have investigated the orientational distributions and rheological properties of dilute colloidal dispersions, which consist of ferromagnetic spherocylinder particles. First, the governing equation of the orientational distribution function has been derived for the typical two cases of magnetic field directions: the direction parallel to the shear flow and the direction parallel to the angular velocity vector of the shear flow. The equation has been solved approximately by Galerkin's method. With these numerical solutions we have obtained the results of the orientational distribution and viscosity. The results obtained for the magnetic field in the shear flow direction are summarized as follows. In the case of a weak magnetic field, the particle tends to orient nearly toward the shear flow direction and its opposite direction. As the magnetic field increases, the orientation of the particle is restricted and the viscosity increases significantly. As the influence of the magnetic field becomes dominant, an overshoot in the viscosity curve appears. This is due to the fact that there is a maximum deviation of the averaged particle direction from the magnetic field direction. When the strength of the magnetic field increases significantly, the particle inclines close to the magnetic field direction and the viscosity converges to a constant value. Particles with a larger aspect ratio give rise to a larger increment in the viscosity since such elongated particles induce larger resistance in a flow field. We also have obtained results for the case of the magnetic field in the direction parallel to the angular velocity vector of the shear flow. When the flow field is dominant over both the rotational Brownian motion and the magnetic interaction, the particle rotates in the plane nearly perpendicular to the magnetic field direction. As the magnetic field increases, the particle inclines toward the magnetic direction. For this direction of field, the viscosity is independent of the magnetic field and is always zero.     

Shear-induced crystallization of polymers. I. The four-roller apparatus

We describe a new technique for producing fibrous crystals from shear-induced crystallization of polymer solutions and polymer melts. Our technique makes use of a modified version of the 4-Roller apparatus originally developed by G. I. Taylor to study the formation of emulsions. This apparatus generates a planar extensional flow field in which macromolecules are extended more easily than in flow fields with transverse velocity gradients.     

Effective cross-sections for molecular aggregation in external orienting fields

Effects of an external orienting field and orientational cross-section for molecular association on the kinetics of crystal nucleation and critical temperature of crystallization is discussed. Dipole and quadrupole effects of an electric (magnetic) field and quadrupole effects of hydrodynamic potential of uniaxial flow are considered. Critical temperature of crystallization, free energy barrier of nucleation and nucleation rates are orientation-dependent. Smaller orientational cross-sections result in stronger anisotropy of the nucleation rates.     

A new mean field SA-SA' critical point in a symmetry breaking field

We consider a S_A-S_A' critical point in the presence of a symmetry-breaking external magnetic (electric) field with a positive magnetic (dielectric) anisotropy or a dislocation layer. Via a renormalization group analysis of the model hamiltonian, we show that the upper critical dimensions below which mean-field theory breaks down is d_c = 2·5. Thus the S_A-S_A' transition in three dimensions becomes mean-field like in the presence of a symmetry-breaking field. We estimate the reduced temperature region where we can expect to see the mean field S_A-S_A' critical point in the presence of a magnetic field or a dislocation layer.     

Linear analysis of pattern formation in nematics in oblique magnetic fields

The dynamics of nematic director field reorientation in non-Freedericksz geometries, after a magnetic field H is applied at an oblique angle relatively to the initial homogeneous director n 0 ( H not normal to n 0), is studied considering a magnetic reorientation driven by hydrodynamic instabilities (with backflow). This study is carried out for bounded samples between two parallel plates with planar boundary conditions and with rigid anchoring. Linear stability and wave vector selection analysis predict that, when the angle of the magnetic to the initial director field is increased, for a given magnetic field intensity, two transitions from a homogeneous to a transient distorted director field reorientation can occur: a transition at a first critical angle to an aperiodic distorted director field and a transition at a second critical angle to a periodic distorted director field. It is shown that the periodic mode is cut off at a higher reduced field when the magnetic field acts away from the normal direction.     

Rheological Properties and Orientational Distributions of Dilute Ferromagnetic Spherocylinder Particle Dispersions

We have investigated the rheological properties and the orientational distributions of particles of a dilute colloidal dispersion, which is composed of ferromagnetic spherocylinder particles, subject to a simple shear flow. The governing equation of an orientational distribution function has been derived from the balance of the torques acting on a particle in an applied magnetic field. After a spherical harmonic expansion, an approximate solution to the governing equation has been found by Galerkin's method. The results obtained are summarized as follows. The orientational distribution function has a sharper peak for a stronger magnetic field, and the position of the peak changes from the flow direction to the magnetic field direction as the magnetic field comes to govern the shear flow. Since the orientation of the particle is highly restricted in the field direction as the magnetic field becomes strong, the viscosity increases significantly. The particles with a larger aspect ratio lead to the larger increment in the viscosity, since they induce a larger resistance in a flow field. Copyright 2001 Academic Press.     

Dynamics of field-induced droplet ionization: time-resolved studies of distortion, jetting, and progeny formation from charged and neutral methanol droplets exposed to strong electric fields

We recently reported that strong electric fields may be employed to directly extract positive and negative ions for mass analysis, including intact proteins, from neutral droplets. The present study investigates the dynamics of this process using switched high electric fields to enable time-resolved studies of droplet distortion, Taylor cone formation, and charged progeny droplet extraction from neutral and charged 225 microm methanol droplets. After a specific time in the field, a flashlamp is triggered to record droplet distortions using shadow photography. At a critical field strength E(c)0 corresponding to the Taylor limit, neutral droplets exhibit a prolate elongation along the field axis forming symmetric cone-jets of positive and negatively charged progeny droplets, approximately 10 microm in diameter. This process is termed field-induced droplet ionization (FIDI). Because the time scale of FIDI is related to the frequency of shape oscillations that occur below the Taylor limit, models of field-dependent oscillation become an important predictor of the time scale for progeny jet formation. Droplets with a net charge q distort into asymmetric tear shapes and emit a single charged jet of progeny at a critical field E(c)(q) that is less than E(c)0. The measured decrease in droplet stream charge indicates that total charge loss can be greater than the original charge on the droplet, resulting in oppositely charged droplets. Interestingly, above E(c)0, charged droplets sequentially emit a jet of the same polarity as the net charge followed by a jet of reverse polarity emitted in the opposite direction. For both neutral and charged droplets, increasing the electric field decreases the time to form jets and the combination of net charge and higher-than-critical fields has a compound effect in accelerating progeny formation. The implications of our results for using switched fields in FIDI-mass spectrometry for on-demand ion sampling from neutral and charged droplets are discussed.     

Rheology and orientational distributions of rodlike particles with magnetic moment normal to the particle axis for semi-dense dispersions (analysis by means of mean field approximation)

We have considered a semi-dense dispersion composed of ferromagnetic rodlike particles with a magnetic moment normal to the particle axis to investigate the rheological properties and particle orientational distribution in a simple shear flow as well as an external magnetic field. We have adopted the mean field approximation to take into account magnetic particle-particle interactions. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the magnetic moment of the rodlike particle is strongly restricted in the field direction, so that the particle points to directions normal to the flow direction (and also to the magnetic field direction). This characteristic of the particle orientational distribution is also valid for the case of a strong particle-particle interaction, as in the strong magnetic field case. To the contrary, for a weak interaction among particles, the particle orientational distribution is governed by a shear flow as well as an applied magnetic field. When the magnetic particle-particle interaction is strong under circumstances of an applied magnetic field, the magnetic moment has a tendency to incline to the magnetic field direction more strongly. This leads to the characteristic that the viscosity decreases with decreasing the distance between particles, and this tendency becomes more significant for a stronger particle-particle interaction. These characteristics concerning the viscosity are quite different from those for a semi-dense dispersion composed of rodlike particles with a magnetic moment along the particle direction.     

Jetting liquid marbles: study of the Taylor instability in immersed marbles

The behavior of liquid marbles encapsulated with various powders, immersed in oil, and exposed to a uniform DC field was investigated. At some critical value of the electric field, the Taylor instability of the marble shape took place, accompanied by the appearance of a cone and jetting a small droplet. The squared critical electric field was linear dependent on inverse of the size parameter of the marble. In some cases, the extrapolation of this linear dependence to the zero field gave the finite value of the spherical marble radius corresponding to the Rayleigh limit that meant that the marbles were charged. Lycopodium-coated marbles remained neutral under the action of a DC field, as well as a pure water droplet. Therefore, charging marbles is determined by their powder coverage. The data on effective surface tension at marble–oil interfaces were extracted from the above linear dependence for the uncharged marble. The effective surface tension was measured in parallel by the capillary rise method.     

Bound electron states in clusters of inert atoms in a magnetic field

An external magnetic field is shown to stabilize negatively charged clusters of inert atoms. In an external magnetic field the critical number of atoms in a cluster, necessary to bound an excess electron to a neutral cluster, is less than that in the absence of a field. General conditions for creation of electron bound states in a cluster in a magnetic field are considered.     

Numerical analysis of a rapid magnetic microfluidic mixer

This paper presents a detailed numerical investigation of the novel active microfluidic mixer proposed by Wen et al. (Electrophoresis 2009, 30, 4179-4186). This mixer uses an electromagnet driven by DC or AC power to induce transient interactive flows between a water-based ferrofluid and DI water. Experimental results clearly demonstrate the mixing mechanism. In the presence of the electromagnet's magnetic field, the magnetic nanoparticles create a body force vector that acts on the mixed fluid. Numerical simulations show that this magnetic body force causes the ferrofluid to expand significantly and uniformly toward miscible water. The magnetic force also produces many extremely fine finger structures along the direction of local magnetic field lines at the interface in both upstream and downstream regions of the microchannel when the external steady magnetic strength (DC power actuation) exceeds 30 Oe (critical magnetic Peclet number Pe(m),cr = 2870). This study is the first to analyze these pronounced finger patterns numerically, and the results are in good agreement with the experimental visualization of Wen et al. (Electrophoresis 2009, 30, 4179-4186). The large interfacial area that accompanies these fine finger structures and the dominant diffusion effects occurring around the circumferential regions of fingers significantly enhance the mixing performance. The mixing ratio can be as high as 95% within 2.0 s. at a distance of 3.0 mm from the mixing channel inlet when the applied peak magnetic field supplied by the DC power source exceeds 60 Oe. This study also presents a sample implementation of AC power actuation in a numerical simulation, an experimental benchmark, and a simulation of DC power actuation with the same peak magnetic strength. The simulated flow structures of the AC power actuation agree well with the experimental visualization, and are similar to those produced by DC power. The AC and DC power actuated flow fields exhibited no significant differences. This numerical study suggests approaches to maximize the performance of the proposed rapid magnetic microfluidic mixer, and confirms its exciting potential for use in lab-on-a-chip systems.     

Strong magnetic field effects on solid-liquid and particle-particle interactions during the processing of a conducting liquid containing non-conducting particles

The behavior of micrometer-sized weak magnetic insulating particles migrating in a conductive liquid metal is of broad interest during strong magnetic field processing of materials. In the present paper, we develop a numerical method to investigate the solid-liquid and particle-particle interactions by using a computational fluid dynamics (CFDs) modeling. By applying a strong magnetic field, for example, 10 Tesla, the drag forces of a single spherical particle can be increased up to around 15% at a creeping flow limit. However, magnetic field effects are reduced when the Reynolds number becomes higher. For two identical particles migrating along their centerline in a conductive liquid, both the drag forces and the magnetic interaction will be influenced. Factors such as interparticle distance, Reynolds number and magnetic flux density are investigated. Shielding effects are found from the leading particle, which will subsequently induce a hydrodynamic interaction between two particles. Strong magnetic fields however do not appear to have a significant influence on the shielding effects. In addition, the magnetic interaction forces of magnetic dipole-dipole interaction and induced magneto-hydrodynamic interaction are considered. It can be found that the induced magneto-hydrodynamic interaction force highly depends on the flow field and magnetic flux density. Therefore, the interaction between insulating particles can be controlled by applying a strong magnetic field and modifying the flow field. The present research provides a better understanding of the magnetic field induced interaction during liquid metal processing, and a method of non-metallic particles manipulation for metal/ceramic based materials preparation may be proposed.     

On the behavior of an oblate spheroidal hematite particle in a simple shear flow under a uniform magnetic field applied in the flow direction

We discuss the orientational properties of an oblate spheroidal hematite particle and also its influence on the rheological characteristics of a dilute suspension of these magnetic particles, by means of an analytical approach based on the orientational distribution function. A hematite particle with oblate spheroidal shape has an important characteristic; that is, it is magnetized in a direction normal to the particle axis. From the balance of the torques acting on a particle, we have developed the basic equation of the orientational distribution function. This basic equation has been numerically solved in order to investigate the dependence of the orientational distribution on the various factors. If both the magnetic field and the shear flow are weak, the particle does not exhibit specific directional characteristics. If the magnetic field is more dominant, the particle inclines such that the oblate surface is parallel to the magnetic field direction. If the shear flow becomes more dominant, the particle shows a sharper peak of the orientational distribution in the shear flow direction. The viscosity due to the magnetic torque increases and finally converges to a constant value as the magnetic field increases. In a sedimentation process under the gravitational field, the translational diffusion coefficient decreases with increasing magnetic field strength in the present case of the magnetic field direction.     

Rheological properties and particle behaviors of a nondilute colloidal dispersion composed of ferromagnetic spherocylinder particles subjected to a simple shear flow: analysis by means of mean-field approximation for the two typical external magnetic field directions

We have analyzed the orientational distributions and rheological properties of a nondilute colloidal dispersion composed of ferromagnetic spherocylinder particles subjected to a simple shear flow. In order to understand the effects of the magnetic interactions between the particles, we have applied the mean-field theory to a nondilute colloidal dispersion for the two typical external magnetic field directions, that is, the direction parallel to the shear flow and the direction parallel to the angular velocity vector of the shear flow. The main results are summarized as follows. The particle-particle interactions suppress the Brownian motion of the particles and, therefore, make the particles incline toward the same direction. For the magnetic direction parallel to the shear flow, the influence of the particle-particle interactions makes the peak of the orientational distribution sharper and higher. The viscosity generally increases as the interactions between particles become stronger in the case where the effects of the shear flow and magnetic field are relatively small. For the magnetic direction parallel to the angular velocity vector of the shear flow, the influence of the particle-particle interactions on the orientational distribution appears significantly, when the influences of the shear flow and magnetic field are not so strong that the particles can be aligned sufficiently to form stable chainlike clusters in a certain direction.