Fluid Stirring Research Articles

Magneto-hydrodynamics based microfluidics

In microfluidic devices, it is necessary to propel samples and reagents from one part of the device to another, stir fluids, and detect the presence of chemical and biological targets. Given the small size of these devices, the above tasks are far from trivial. Magnetohydrodynamics (MHD) offers an elegant means to control fluid flow in microdevices without a need for mechanical components. In this paper, we review the theory of MHD for low conductivity fluids and describe various applications of MHD such as fluid pumping, flow control in fluidic networks, fluid stirring and mixing, circular liquid chromatography, thermal reactors, and microcoolers.

Transport and stirring induced by vortex formation

The purpose of this study is to analyse the transport and stirring of fluid that occurs owing to the formation and growth of a laminar vortex ring. Experimental data was collected upstream and downstream of the exit plane of a piston-cylinder apparatus by particle-image velocimetry. This data was used to compute Lagrangian coherent structures to demonstrate how fluid is advected during the transient process of vortex ring formation. Similar computations were performed from computational fluid dynamics (CFD) data, which showed qualitative agreement with the experimental results, although the CFD data provides better resolution in the boundary layer of the cylinder. A parametric study is performed to demonstrate how varying the piston-stroke length-to-diameter ratio affects fluid entrainment during formation. Additionally, we study how regions of fluid are stirred together during vortex formation to help establish a quantitative understanding of the role of vortical flows in mixing. We show that identification of the flow geometry during vortex formation can aid in the determination of efficient stirring. We compare this framework with a traditional stirring metric and show that the framework presented in this paper is better suited for understanding stirring/mixing in transient flow problems. A movie is available with the online version of the paper.

Chaotic stirring in a new type of mixer with rotating rigid blades

The present study suggests a new conceptual apparatus that can be used to stir fluids at low velocities. This consists of a circular container equipped with one or two blades arranged along the perimeter which drive the fluid motion. It modifies a previous apparatus in which fluid was driven by two flexible belts, which is more difficult to implement in experiments. Using the new device, fluid can be stirred completed with very high fluid stretch-rates in a short time. This could not be obtained in the previous studies by the belts. Based on extensive computations, the greatest averaged fluid stretch-rate is created by rotating two blades of lengths 3 π / 4 and π / 2 , with the second blade actuated at a frequency ten times higher than the first blade. When only one blade is employed, shorter periods are beneficial to stirring of fluid and produce higher fluid stretch-rates.

Topology, braids and mixing in fluids

Stirring of fluid with moving rods is necessary in many practical applications to achieve homogeneity. These rods are topological obstacles that force stretching of fluid elements. The resulting stretching and folding is commonly observed as filaments and striations, and is a precursor to mixing. In a space-time diagram, the trajectories of the rods form a braid, and the properties of this braid impose a minimal complexity in the flow. We review the topological viewpoint of fluid mixing, and discuss how braids can be used to diagnose mixing and construct efficient mixing devices. We introduce a new, realizable design for a mixing device, the silver mixer, based on these principles.

Measuring the mixing efficiency in a simple model of stirring: some analytical results and a quantitative study via frequency map analysis

We prove the existence of invariant curves for a $T$--periodic Hamiltonian system which models a fluid stirring in a cylindrical tank, when $T$ is small and the assigned stirring protocol is piecewise constant. Furthermore, using the Numerical Analysis of the Fundamental Frequency of Laskar, we investigate numerically the break down of invariant curves as $T$ increases and we give a quantitative estimate of the efficiency of the mixing.

Sustained plankton blooms under open chaotic flows

We consider a predator–prey model of planktonic population dynamics, of excitable character, living in an open and chaotic fluid flow, i.e., a state of fluid motion in a region from which fluid trajectories are continuously escaping, but such that it contains a chaotic subset. During the time trajectories spend in this chaotic area they are characterized by a positive maximum Lyapunov exponent, so that close fluid particles separate exponentially. Despite that excitability in the predator–prey dynamics is a transient phenomenon and that fluid trajectories are continuously leaving the system, there is a regime of parameters where the excitation remains permanently in it, given rise to a persistent plankton bloom. This regime is reached when the time scales associated to fluid stirring become slower than the ones associated to biological growth.

Bifurcations for fluid stirring in circular cavity

Lagrangian chaos associated with Stokes flows in a circular cavity is addressed in the present study. Two belts arranged on the boundary to be rotated at various speeds are employed to drive this flow motion. The evolutions of several tori are examined when the periods are increased. Then the types of transitions through which the flows change from regular motions to chaotic ones are clearly identified. The routes to chaos for the present studied flows are subject to some successive bifurcations of island‐chains. Those include period‐5, 4, 3, 5, 7 along the direction with increased periods and finally the flows arrive at random motion. The detailed processes of the fluid stirring were numerically visualized and some animations were produced for instructional uses.

A Turbulence Closure for the Convective Boundary Layer Based on a Two-Scale Mass-Flux Approach

The closure problem for the convective turbulence of the shear-free and low to moderate wind atmospheric boundary layer is considered. Non-Gaussian parameterizations are developed for fourth-order moments based on a two-scale mass-flux approach. With this approach the ballistic stirring of fluid by coherent structures is taken into account and the differences in the horizontal scales and spacing of the velocity and temperature fields are recognized. The fractional coverage of positive temperature variations is introduced, as well as the fractional coverage of positive vertical velocity fluctuations. The parameterizations are compared to those of the traditional mass-flux scheme and of the classical eddy-damped quasi-normal approach, and the principal similarities and dissimilarities are outlined. The results of testing the parameterizations against aircraft measurements at moderate wind and against large eddy simulation data of free convective conditions show good agreement between model predictions and data.

A Laboratory Model of Exchange and Mixing between Western Boundary Layers and Subbasin Recirculation Gyres*

Chaotic advection is suggested as a possible mechanism for fluid exchange and mixing among a western boundary current and subbasin recirculation gyres. Applications include the North Atlantic Deep Western Boundary Current and its adjacent mesoscale recirculation gyres. Visualization and quantification of certain aspects of chaotic advection in a laboratory analog are described. Depending on the strength of the forcing, recirculating fluid offshore of the western boundary layer may be contained in a single gyre (not favorable for chaotic advection) or twin gyre with a ‘‘figure-eight’’ geometry (favorable for chaotic advection). When time dependence is imposed on these steady flows by varying the forcing periodically, the resulting fluid exchange, stirring, and mixing is most dramatic in the case of the twin gyre. A template for these processes can be formed by highlighting certain material contours (invariant manifolds) using dye and other techniques. These objects can be used to identify blobs of fluid (turnstile lobes) that are carried into and out of the gyres. The associated transports and flushing times can be estimated. The preferential stirring and mixing in the twin-gyre case is quantified by calculating the effective diffusivity of the flow field based on snapshots of the dye fields at longer times. The experiment suggests how tracers in a western boundary current might be transported into and out of neighboring recirculations and where regions of strong zonal or meridional transport might occur.

Chaotic advection by two interacting finite-area vortices

This article deals with the advection of fluid particles in the velocity field of two identical vortices with various vorticity distributions. The two-dimensional velocity field is aperiodic in the range of parameters studied here, namely, the neighborhood of the critical distance for merger. Ideas and methods from the theory of transport in dynamical systems are used to describe and quantify particle advection. These methods are applied to the numerical representation of the velocity field, which is obtained by solving the Euler equations with the vortex-in-cell method. It is found that the strongest stirring of vortex fluid occurs slightly above the critical distance for merger. In this regime the fluid located between the vortices is subjected to intense stirring, and some vortex fluid may be entrained into the chaotic region depending on the smoothness of the vorticity distribution. Initial conditions below the critical distance lead to stirring of fluid mainly before merger. In this case the flow geometry is used to quantify the efficiency of merger, which is defined as the ratio of the circulation of the resultant vortex to the total circulation of the original vortices. It is found that the vortices with the smoothest vorticity profile have the lowest efficiency. Experimental visualizations in a two-dimensional rotating fluid confirm the intense stretching and folding of fluid elements that occurs before the vortices merge.

Passive mixing in a three-dimensional serpentine microchannel

A three-dimensional serpentine microchannel design with a C shaped repeating unit is presented in this paper as a means of implementing chaotic advection to passively enhance fluid mixing. The device is fabricated in a silicon wafer using a double-sided KOH wet-etching technique to realize a three-dimensional channel geometry. Experiments using phenolphthalein and sodium hydroxide solutions demonstrate the ability of flow in this channel to mix faster and more uniformly than either pure molecular diffusion or flow in a channel for Reynolds numbers from 6 to 70. The mixing capability of the channel increases with increasing Reynolds number. At least 98% of the maximum intensity of reacted phenolphthalein is observed in the channel after five mixing segments for Reynolds numbers greater than 25. At a Reynolds number of 70, the serpentine channel produces 16 times more reacted phenolphthalein than a straight channel and 1.6 times more than the square-wave channel. Mixing rates in the serpentine channel at the higher Reynolds numbers are consistent with the occurrence of chaotic advection. Visualization of the interface formed in the channel between streams of water and ethyl alcohol indicates that the mixing is due to both diffusion and fluid stirring.

The topology of stirred fluids

There are simple idealized mathematical models representing the stirring of fluids. The models we consider involve two fluids entering a chamber, with the overflow leaving it. The stirring creates a Cantor-like, but connected, boundary between the fluids that is best described point-set topologically. We prove that in many cases the boundary between the fluids is an indecomposable continuum.

Chaotic advection by laminar flow in a twisted pipe

The appearance of chaotic particle trajectories in steady, laminar, incompressible flow through a twisted pipe of circular cross-section is demonstrated using standard dynamical systems diagnostics and a model flow based on Dean's perturbation solutions. A study is performed to determine the parameters that control fluid stirring in this mixing device that has no moving parts. Insight into the chaotic dynamics are provided by a simple one-dimensional map of the pipe boundary onto itself. The results of numerical experiments illustrating the stretching of material lines, stirring of blobs of material, and the three-dimensional trajectories of fluid particles are presented. Finally, enhanced longitudinal particle dispersal due to the coupling between chaos in the transverse direction and the non-uniform longitudinal transport of particles is shown.

Calculation of shear rate gradient during stirring of non-Newtonian fluids in horizontal apparatuses

Calculation of shear rate gradient during stirring of non-Newtonian fluids in horizontal apparatuses

Relationships of mammalian sperm motility and morphology to hydrodynamic aspects of cell function.

This study investigated the relationships of sperm body morphology and flagellar beat frequency and shape with the swimming velocity, power output, and stirring of nearby fluid by the spermatozoa of several mammals. Hamster spermatozoa were studied before and after the motility activation which is associated with capacitation and the acrosome reaction in that species. Human spermatozoa were assessed while swimming progressively in semen, and also while exhibiting the figure-of-eight beat pattern seen in cervical mucus and other media of high viscosity. Ram spermatozoa were studied while swimming in diluted semen. Data obtained from high-speed cinemicrography were applied to a computerized mathematical model of the hydrodynamics of sperm movement. The results demonstrate the relationships between sperm hydrodynamics and morphology, flagellar beat frequency, and shape. Many of these relationships are highly nonlinear, so that small differences in geometrical parameters of morphology and movement can produce large differences in hydrodynamic characteristics. Thus, hamster spermatozoa (preactivated) swim faster and expend more energy than ram spermatozoa which, in turn, exceed human spermatozoa in these measures. However, there is sufficient geometrical similarity in the morphologies and movement characteristics of these spermatozoa that appropriate grouping of various parameters results in dimensionless expressions with general applicability. Thus, the conclusions resulting from the present work can be used in studying the spermatozoa of other mammals as well. It was also shown that fluid stirring by spermatozoa, as opposed to smaller microorganisms, is an important mechanism of transfer of dissolved ions, molecules, and gases to and from the cell surface. In this regard, activated hamster sperm stir substantially more fluid than do preactivated hamster sperm, even though their power outputs are not significantly different.

Factors affecting 3H2O transfer capacity of isolated perfused trout gills.

Tritiated water (3H2O) transfer capacity (PdA) and vascular impedance (Zg) of isolated trout (Salmo gairdneri) gills perfused with or without epinephrine were studied under conditions of altered osmotic gradients, fluid stirring, perfusion rate (Qa), and efferent pressure (Pe). Transfer capacity was unaffected by osmotic gradients, indicating that 3H2O moves across gills by diffusion and that PdA is independent of hydraulic water movement. Fluid stirring increased PdA asymptotically, suggesting that boundary layers significantly affect diffusion across isolated gills. Transfer capacity was directly related to Qa; Zg was inversely related to Qa. The PdA results can be explained in terms of lamellar recruitment and the distribution of flow between secondary lamellae. Increased Qa reduced Zg due to recruitment and distension of gill vessels. Elevated Pe decreased Zg and PdA. The effects of Pe on Zg resulted from distension of the gill vasculature and increased venous drainage, whereas the effects of Pe on PdA can be explained by changes in the distribution of perfusion between secondary lamellae.

Low cost visualizer for mixing and stirring phenomena in some real gaseous flow reactors

The observation of the light emission due to the chemiluminescent gas phase oxidation of phosphorus gives information on the stirring of gaseous fluids in real flow reactors. Three types of reaction vessels have been tested.

An Apparatus for Measuring Fluid Stirring Temperatures

An apparatus utilizing quartz thermometer probe as a fluid stirring agitator is described.

A NEW TYPE OF MICRO PO2-ELECTRODE UNIT.

This paper describes a practical micro pO2-electrode unit with an analysing-chamber with in- and outlets of a capacity of less than 50 microliter. Determination of the pO2 in minute quantities of fluids and gases is possible with this unit. Stirring of fluids is superfluous. Thermostasis is ensured in a simple manner in a double-walled vessel which, like the analysing-chamber, consists entirely of glass.

An adiabatic calorimeter for measuring the specific heats of liquids in the range 0 to 100 C

A calorimeter of the adiabatic type is described, capable of measuring the specific heats of liquids within small temperature intervals (2 or 3° C) over the range 0 to 100° C. An accuracy of ±0.5% can be maintained throughout the full working range, with a small increase in precision between 10 and 30° C. Features of the design include: an electrically heated annular metal jacket; stirring of the calorimetric fluid (125 ml.) by an oscillation of the calorimeter about its vertical axis (this has certain advantages over the conventional motor-driven shaft and paddle); a calorimeter heater design giving wide dispersal of heat without local overheating; ease of assembling and dismantling. Primarily designed for measurements on liquid dairy products, it can be used for other liquids. Typical results with the former are illustrated.