Stationary Flow Pattern Research Articles

Characterization of Mixing Performance Induced by Double Curved Passive Mixing Structures in Microfluidic Channels

Functionalized sensor surfaces combined with microfluidic channels are becoming increasingly important in realizing efficient biosensing devices applicable to small sample volumes. Relaxing the limitations imposed by laminar flow of the microfluidic channels by passive mixing structures to enhance analyte mass transfer to the sensing area will further improve the performance of these devices. In this paper, we characterize the flow performance in a group of microfluidic flow channels with novel double curved passive mixing structures (DCMS) fabricated in the ceiling. The experimental strategy includes confocal imaging to monitor the stationary flow patterns downstream from the inlet where a fluorophore is included in one of the inlets in a Y-channel microfluidic device. Analyses of the fluorescence pattern projected both along the channel and transverse to the flow direction monitored details in the developing homogenization. The mixing index (MI) as a function of the channel length was found to be well accounted for by a double-exponential equilibration process, where the different parameters of the DCMS were found to affect the extent and length of the initial mixing component. The range of MI for a 1 cm channel length for the DCMS was 0.75–0.98, which is a range of MI comparable to micromixers with herringbone structures. Overall, this indicates that the DCMS is a high performing passive micromixer, but the sensitivity to geometric parameter values calls for the selection of certain values for the most efficient mixing.

Stability and nonlinear secondary modes of double-periodic flows with pumping

We investigate, both qualitatively and numerically, the family of forced doubly periodic plane flows of viscous fluids. These flows generalize the seminal Kolmogorov flow to the case of two-dimensional periodicity of the driving force and to the presence of pumping in two spatial directions. The dimensionless parameters of the problem are the flow rates in two perpendicular directions, the forcing intensity, and two spatial periods of the force. The Kolmogorov flow itself corresponds to the particular case when the force depends on a single coordinate and the mean drift is absent. When the forcing amplitude is increased, the basic stationary flow pattern, described by the explicit solution of the Navier-Stokes equations, displays structural rearrangements: isolated vortices appear on the background of the global flow. In the present study, we consider destabilization of the basic flow pattern: there, onset of time dependence can influence the previously reported unusual spectral and transport properties of Lagrangian dynamics. Analysis of possible stationary states, of their stability and forms of the secondary oscillatory and stationary modes is performed. Equations of fluid dynamics are solved numerically through the spectral and finite-difference methods. Stability of explicit stationary solutions with respect to small hydrodynamical perturbations is investigated.

Nonlinear MHD Rossby wave interactions and persistent geomagnetic field structures

The geomagnetic field presents several stationary features that are thought to be linked to inhomogeneities at the core-mantle boundary. Particularly important stationary structures of the geomagnetic field are the flux lobes, which appear in pairs in mid- to high mid- to high latitudes. A recently discovered stratified layer at the top of the Earth's core poses important constraints on the dynamics at this layer and on the interaction of the core dynamics and the base of the mantle. In this article, we introduce the linear and nonlinear theories of magnetic Rossby waves in a thin shell at the top of the Earth's core. We study the nonlinear interaction of these waves in the presence of prescribed forcings at the base of the mantle of both a thermal and a topographic nature. We show that the combined effects of forcing and nonlinear interaction can lead the wave phases to be locked around a particular geographical longitude, generating a quasi- stationary flow pattern with a significant meridional component. The solutions of the system are shown to be analogous to atmospheric blocking phenomena. Therefore, we argue that persistent and long-lived structures of the geomagnetic field, such as the geomagnetic lobes, might be associated with a blocking at the top of the Earth's core due to nonlinear stationary waves.

Surface circulation in Block Island Sound and adjacent coastal and shelf regions: A FVCOM-CODAR comparison

CODAR-derived surface currents in Block Island Sound over the period of June 2000 through September 2008 were compared to currents computed using the Northeast Coastal Ocean Forecast System (NECOFS). The measurement uncertainty of CODAR-derived currents, estimated using statistics of a screened nine-year time series of hourly-averaged flow field, ranged from 3 to 7cm/s in speed and 4° to 14° in direction. The CODAR-derived and model-computed kinetic energy spectrum densities were in good agreement at subtidal frequencies, but the NECOFS-derived currents were larger by about 28% at semi-diurnal and diurnal tidal frequencies. The short-term (hourly to daily) current variability was dominated by the semidiurnal tides (predominantly the M2 tide), which on average accounted for ∼87% of the total kinetic energy. The diurnal tidal and subtidal variability accounted for ∼4% and ∼9% of the total kinetic energy, respectively. The monthly-averaged difference between the CODAR-derived and model-computed velocities over the study area was 6cm/s or less in speed and 28° or less in direction over the study period. An EOF analysis for the low-frequency vertically-averaged model current field showed that the water transport in the Block Island Sound region was dominated by modes 1 and 2, which accounted for 89% and 7% of the total variance, respectively. Mode 1 represented a relatively stationary spatial and temporal flow pattern with a magnitude that varied with season. Mode 2 was characterized mainly by a secondary cross-shelf flow and a relatively strong along-shelf flow. Process-oriented model experiments indicated that the relatively stationary flow pattern found in mode 1 was a result of tidal rectification and its magnitude changed with seasonal stratification. Correlation analysis between the flow and wind stress suggested that the cross-shelf water transport and its temporal variability in mode 2 were highly correlated to the surface wind forcing. The mode 2 derived onshore and offshore water transport, and was consistent with wind-driven Ekman theory. The along-shelf water transport over the outer shelf, where a large portion of the water flowed from upstream Nantucket Shoals, was not highly correlated to the surface wind stress.

RELATIVISTIC BONDI–HOYLE–LYTTLETON ACCRETION ONTO A ROTATING BLACK HOLE: DENSITY GRADIENTS

In this work, we present, for the first time, a numerical study of the Bondi-Hoyle accretion with density gradients in the fully relativistic regime. In this context, we consider accretion onto a Kerr Black Hole (BH) of a supersonic ideal gas, which has density gradients perpendicular to the relative motion. The set of parameters of interest in this study are the Mach number, M, the spin of the BH, a, and the density-gradient parameter of the gas, {\rho} . We show that, unlike in the Newtonian case, all the studied cases, especially those with density gradient, approach a stationary flow pattern. To illustrate that the system reaches steady state we calculate the mass and angular momentum accretion rates on a spherical surface located almost at the event horizon. In the particular case of M = 1, {\rho} = 0.5 and BH spin a = 0.5, we observe a disk-like configuration surrounding the BH. Finally, we present the gas morphology and some of its properties.

Study of Under Pressure Viscous Fluid Pulsating Flow in Cylindrical Pipe of Circular Cross-Section

Often due to the pressure gradient change in pressure systems the stationary flow pattern is disturbed initiating respective time-dependent change of hydraumechanical parameters at the cross-section. As a consequence of the pressure gradient change under the influence of varying friction and inertia forces unstable flow of fluid occurs. The study of this phenomenon presents important practical and theoretical interest.

Spontaneous thermocapillary drops interaction: The effect of a surface reaction

AbstractThe spontaneous motion of small drops suspended in an immiscible viscous fluid, when an exothermal reaction occurs on their interfaces, has been studied. The heat of reaction results in an elevation of temperature on the drops' interfaces and in the external fluid. The concentration and temperature in the gap region become different from those in the outer regions. The inhomogeneous distribution of concentration and temperature induces surface tension variations, Marangoni type flow and migration of the fluid particles relative to each other. Cases studied concern two drops interaction due to thermocapillary forces induced by temperature field, the addition of a gravity field and the mutual effect of thermocapillary forces induced simultaneously by temperature and concentration. Results are presented for a variety of the governing parameters of the system. Stationary flow patterns with immobile drops configurations are predicted, which appear to be unstable for small perturbations. © 2007 American Institute of Chemical Engineers AIChE J, 2007

Structure of the Wake of a Magnetic Obstacle

We use a combination of numerical simulations and experiments to elucidate the structure of the flow of an electrically conducting fluid past a localized magnetic field, called magnetic obstacle. We demonstrate that the stationary flow pattern is considerably more complex than in the wake behind an ordinary body. The steady flow is shown to undergo two bifurcations (rather than one) and to involve up to six (rather than just two) vortices. We find that the first bifurcation leads to the formation of a pair of vortices within the region of magnetic field that we call inner magnetic vortices, whereas a second bifurcation gives rise to a pair of attached vortices that are linked to the inner vortices by connecting vortices.

Supersonic expansion in the Pilot-PSI plasma jet: neutral gas and MHD models

We perform a numerical investigation of the supersonic expansion of a laboratory jet produced in Pilot-PSI. Pilot is a linear device consisting of a cascaded arc plasma source, a vacuum vessel for plasma expansion and magnetic coils for jet collimation. We concentrate here on (1) the neutral gas dynamics and the detailed steady jet morphologies resulting from experimentally realized nozzle configurations; and (2) the plasma collimation due to the applied magnetic fields. The former approach analyses numerical simulations modelled by means of the compressible hydrodynamic equations, comparing 1D spherical and 2D axially symmetric results with related experimental efforts. An in-depth analysis of the characteristics of the stationary flow pattern allows a study of the properties of the supersonic expansion: a well defined free-jet flow shock structure is formed in the first region of the expansion and fully described. Also, a predicted correlation between the variation of the pressure in the vessel and the position of the Mach disc is confirmed. We investigate changes in the supersonic jet structures due to a geometrical variation of the nozzle source diameter, revealing a more complicated shock structure which we analyse using the characteristic lines. A comparison with the free-jet flow is made and the influence of the nozzle geometry on the flow is discussed. The magnetic collimation of the plasma beam is demonstrated by means of single fluid magnetohydrodynamic simulations, which clearly show the transition from compressible gas to fully ionized plasma regimes. A qualitative agreement with measured Pilot-PSI density profiles indicates to which extent such single fluid descriptions aid in the interpretation of observed plasma jet dynamics.

Transonic Magnetohydrodynamic Flows in Laboratory and Astrophysical Plasmas

Magnetohydrodynamic (MHD) waves control the dynamics of plasma, the main constituent of the universe. They occur as the natural response to global excitation. Frequency and wave forms are determined by the magnetic confinement geometry and distribution of background equilibrium variables. Hence, measurement of the spectrum of MHD waves gives direct information on the internal state of the plasma, provided a theoretical model is available to solve the forward and inverse spectral problems. This activity has been called MHD spectroscopy, [1, Goedbloed et al. Phys. Control. Fusion 35 B277 (1993)] in analogy with quantum mechanical spectroscopy which also involves eigenvalue problems of linear operators. The terminology also entails a program, viz. to improve the accuracy of our knowledge of plasmas, both in the laboratory and in astrophysics.While such a program is highly desirable a new angle to the study of MHD waves coming from the effects of transonic background flows requires a complete revision of all previous spectral results. Transonic flows in laboratory plasmas result from neutral beam heating (causing toroidal rotation) whereas they are commonplace for astrophysical plasmas (flows in coronal flux tubes, stellar winds, rotating accretion disks, jets emitted from radio galaxies, etc.). Such flows upset the standard theoretical approach to plasma dynamics, consisting of a separate study of equilibrium state and of the perturbations of this background. We will discuss a new approach to the dichotomy consisting of a study of the similarities of the nonlinear stationary flow patterns and the different linear waves structures that occur when the background speed traverses the full range of critical speeds (from "slow magnetosonic" to "Alfvén" to "fast magnetosonic"). This requires the development of new computational tools which yield a plethora of new waves and instabilities. We will illustrate this with results on tokomak and accretion disk plasmas.

Variability of the path of the Kuroshio ocean current over the past 25,000 years

The Kuroshio current is the strong northwestern component of the subtropical North Pacific Ocean gyre, and advects a large amount of heat from the tropics to northern mid-latitudes. The Kuroshio has bimodal stationary flow patterns, with small and large meander paths east of central Japan1,2 which switch on annual and decadal timescales3,4. These switches seem to be caused by changes in current velocity and volume transport of the North Equatorial Current that are associated with variations in the trade-wind intensity in the eastern equatorial North Pacific Ocean5,6. Here we present alkenone-derived sea surface temperature records at multicentennial resolution from sediment cores from the Nishishichitou ridge off central Japan. These 25,000-year records show that the Kuroshio path has also fluctuated on millennial timescales. This variability resembles that of the subtropical high pressure of the North Pacific, reconstructed from terrestrial pollen distributions, water levels in North American lakes, and marine micropalaeontological records7. Together, these data indicate that climate variability off central Japan over the past 25,000 years may be part of a circum-Pacific phenomenon, reflecting the rate of subtropical surface circulation in the North Pacific Ocean.

Effect of Reynolds number on the eddy structure in a lid-driven cavity

In this paper we apply a finite volume method, together with a cost-effective segregated solution algorithm, to solve for the primitive velocities and pressure in a set of incompressible Navier–Stokes equations. The well-categorized workshop problem of lid-driven cavity flow is chosen for this exercise, and results focus on the Reynolds number. Solutions are given for a depth-to-width aspect ration of 1:1 and a span-to width aspect ratio of 3:1. Upon increasing the Reynolds number, the flows in the cavity of interest were found to comprise a transition from a strongly two-dimensional character to a truly three-dimensional flow and, subsequently, a bifurcation from a stationary flow pattern to a periodically oscillatory state. Finally, viscous (Tollmien–Schlichting) travelling wave instability further induced longitudinal vortices, which are essentially identical to Taylor–Görtler vortices. The objective of this study was to extend our understanding of the time evolution of a recirculatory flow pattern against the Reynolds number. The main goal was to distinguish the critical Reynolds number at which the presence of a spanwise velocity makes the flow pattern become three-dimensional. Secondly, we intended to learn how and at what Reynolds number the onset of instability is generated. © 1998 John Wiley & Sons, Ltd.

Visualization of convective fluid flow in a porous medium

WHEN a horizontal layer of fluid is heated from below, it may undergo Rayleigh-Benard convection (RBC), leading to the spontaneous appearance of regular patterns of fluid flow1. The shadow-graph technique2, which allows visualization of the convection patterns, has assisted in developing an understanding of RBC. Related to RBC is convection in a fluid permeating a porous medium (called Horton-Rodgers-Lapwood convection or HRLC) when it is heated from below3–7. HRLC is relevant to geothermal applications and to flow in soils. Pattern formation in HRLC is less easily visualized by shadowgraph techniques because of the difficulties of transmitting light through the porous medium. Here we show how these difficulties can be overcome by constructing porous media in which the interfaces between solid and liquid are either parallel or perpendicular to the confining boundaries of the experimental system. Convection in such a medium can be visualized using conventional shadowgraph methods, and we compare the stationary flow patterns observed against measurements of heat transport.

Transition from time-dependent to stationary flow patterns in the Taylor-Dean system

Transition from time-dependent to stationary flow patterns in the Taylor-Dean system

Pulses of oscillatory convection.

Oscillatory convection in binary fluid mixtures can take the form of traveling waves, in contrast to the stationary flow patterns observed in pure fluids. Using both mechanical and thermal excitation methods, we have been able to create propagating pulses of oscillatory, traveling-wave convection. We report a study of such pulses and measurement of the phase and group velocity, the real and imaginary parts of the dispersion, and the reflection coefficient of the pulses at lateral walls. The collision of two counterpropagating pulses is also described.

The anomalous tracks of North Pacific drifting buoys 1981 to 1983

Satellite tracked drogued buoys, initially deployed in August 1981 along 160°W south of the Aleutians, rather than recirculate in the Alaskan Gyre, slowly moved eastward to cross the North Pacific. Their trajectories contrast sharply with earlier buoy tracks in the region which all turned north into the Gulf of Alaska consistent with the pattern of mean annual 0/500 db dynamic topography. This marked difference in buoy trajectories is shown to be related to anomalies in the large-scale atmospheric pressure distribution rather than to anomalies in the oceanic geostrophic current. Comparisons between buoy and wind velocities reveal that the buoys respond to the wind-driven Ekman current. The anomalous buoy tracks and sea-level pressure patterns occurred in late 1981 and early 1982 just prior to the El Niño Southern Oscillation event of 1982 to 1983. During their anomalous eastward transit, the two southernmost buoys deployed almost 200 km apart in latitude behaved similarly with cross correlations of about 0.9 in their latitude, longitude displacements over a year. A third buoy crossing the same region three months later followed a path similar to the earlier two buoys, suggesting a stationary flow pattern over this period. The first two buoys finally turned north near the west coast of North America in late 1982 and rapidly continued northward near the coast in early 1983 with maximum velocities > 100 cm s −1. At the same time the third buoy shifted north and moved equally rapidly westward across the northern border of the Gulf of Alaska. Trajectories of buoys deployed in the autumn of 1982 suggest a return to the traditionally accepted circulation pattern of northward flow into the Gulf of Alaska at the eastern end of the North Pacific Current between 140° and 150°W.

Time-Dependent Free Convection in Vertical Slots

Time-dependent free convective flow phenomena are investigated in slender vertical containers heated from below. Power-density spectra are calculated from time-dependent thermocouple signals. The range of oscillatory convective flow yields periodic, quasiperiodic, or stochastic structures. After stochastic flow, quasiperiodic and periodic oscillations reappear with increasing temperature difference. Finally, at even higher Rayleigh numbers, a stationary flow pattern develops.

Contribution to the theory of stationary separation zones

Experiment shows that the stationary flow pattern about a bluff body with closed separation zone, in the case of laminar flow about the body and in the separation zone, breaks down for a subsonic stream velocity in the Reynolds number range from 101 to 102. However, experiment shows that for a supersonic stream velocity a stable stationary flow pattern is observed with the existence of laminar stagnant zones adjacent to the body (the stagnant zone behind an aft-facing step on the body surface, the stagnant zone ahead of a gradual forward-facing step on the body surface, the forward separation zone formed by the tip of a spike, the stagnant zone formed when a shock impinges on a body surface) at high Reynolds numbers of the order of 104−106.