Rectangular Constriction Research Articles

A numerical technique to solve a problem of the fluid motion in a straight plane rigid duct with two axisymmetric rectangular constrictions. An alternative approach

A numerical technique is devised to solve a problem of the steady laminar fluid motion in a straight plane hard-walled duct with two local axisymmetric rectangular constrictions. It uses the stream function, the vorticity and the pressure as the basic variables, has the second order of accuracy in the spatial and the first order of accuracy in the temporal coordinates, provides high stability of a solution, and needs significantly less computational time to obtain a result compared to appropriate techniques available in a scientific literature. The technique consists in: a) introducing the stream function and the vorticity, and subsequent transiting from the non-dimensional governing relations for the fluid velocity and the pressure to the corresponding non-dimensional relations for the stream function, the vorticity and the pressure; b) deriving their discrete counterparts in the nodes of the chosen space-time computational grid; c) integrating the systems of linear algebraic equations obtained after making the discretization. The discretization is based on applying appropriate differencing schemes to the terms of the equations for the basic variables. These are the two-point temporal onward difference for the unsteady term of the vorticity equation, as well as the two-point backward differences (for its convective term) and the five-point approximations (for its diffusive term and for the Poisson’s equations for the stream function and the pressure) in the axial and cross-flow coordinates. As for the velocity components, the appropriate central differences are applied to discretize their expressions. The above-mentioned systems of linear algebraic equations for the stream function and the pressure are integrated by the iterative successive over-relaxation method. The algebraic relation for the vorticity does not need application of any method to be solved, because it is a computational scheme to find this quantity based on the known magnitudes computed at the previous instant of time.

A numerical technique to solve a problem of the fluid motion in a straight plane rigid duct with two axisymmetric rectangular constrictions

A second-order numerical technique is developed to study the steady laminar fluid motion in a straight two-dimensional hard-walled duct with two axisymmetric rectangular constrictions. In this technique, the governing relations are solved via deriving their integral analogs, performing a discretization of these analogs, simplifying the obtained (after making the discretization) coupled nonlinear algebraic equations, and the final solution of the resulting (after making the simplification) uncoupled linear ones. The discretization consists of the spatial and temporal parts. The first of them is performed with the use of the TVD-scheme and a two-point scheme of discretization of the spatial derivatives, whereas the second one is made on the basis of the implicit three-point asymmetric backward differencing scheme. The above-noted uncoupled linear algebraic equations are solved by an appropriate iterative method, which uses the deferred correction implementation technique and the technique of conjugate gradients, as well as the solvers ICCG and Bi-CGSTAB.

A high-throughput microfluidic device inspired by the Wheatstone bridge principle for characterizing the mechanical properties of single cells.

The mechanical properties of single cells have been recognized as biomarkers for identifying individual cells and diagnosing human diseases. Microfluidic devices based on the flow cytometry principle, which are not limited by the vision field of a microscope and can achieve a very high throughput, have been extensively adopted to measure the mechanical properties of single cells. However, these kinds of microfluidic devices usually required pressure-driven pumps with a very low flow rate and high precision. In this study, we developed a high-throughput microfluidic device inspired by the Wheatstone bridge principle for characterizing the mechanical properties of single cells. The microfluidic analogue of the Wheatstone bridge not only took advantage of flow cytometry, but also allowed precise control of a very low flow rate through the constricted channel with a higher input flow rate generated by a commercially available pressure-driven pump. Under different input flow rates of the pump, the apparent elastic moduli and the fluidity of osteosarcoma (U-2OS) cells and cervical carcinoma (HeLa) cells were measured by monitoring their dynamic deformations passing through the bridge-channel with different sizes of rectangular constrictions. The results showed that the input flow rate had little effect on measuring the mechanical properties of the cells, while the ratio of cell radius to effective constriction radius was different, i.e., for U-2OS cells it was 1.20 and for HeLa cells it was 1.09. Under this condition compared with predecessors, our statistic results of cell mechanical properties exhibited minimal errors. Furthermore, the cell viability after measurements was kept above 90% that demonstrated the non-destructive property of our proposed method.

Direct current-tunable MHz to multi-GHz skyrmion generation and control

Skyrmions offer high density, low power, and nonvolatile memory functionalities due to their nanoscale and topologically-protected chiral spin structures. For integrated high-bandwidth devices, one needs to control skyrmion generation and propagation rates using current. Here, we introduce a skyrmion initialization and control method to generate periodic skyrmions from 114 MHz to 21 GHz using spin-polarized direct current. We first initialize a stable magnetic domain profile that is pinned between a notch and a rectangular constriction using a DC pulse. Next, we pass spin-polarized DC charge current to eject periodic skyrmions at a desired frequency. By changing the DC current density, we demonstrate in micromagnetic simulations that skyrmion generation frequencies can be controlled reversibly over more than seven octaves of frequencies. By using domain pinning and current-driven skyrmion motion, we demonstrate a highly tunable and DC-controlled skyrmion signal source, which pave the way towards ultra wideband, compact and integrated skyrmionic circuits.

Mixing Performance of a 3D Micro T-Mixer with Swirl-Inducing Inlets and Rectangular Constriction.

In this paper, three novel 3D micro T-mixers, namely, a micro T-mixer with swirl-inducing inlets (TMSI), a micro T-mixer with a rectangular constriction (TMRC), and a micro T-mixer with swirl-inducing inlets and a rectangular constriction (TMSC), were proposed on the basis of the original 3D micro T-mixer (OTM). The flow and mixing performance of these micromixers was numerically analyzed using COMSOL Multiphysics package at a range of Reynolds numbers from 10 to 70. Results show that the three proposed 3D micro T-mixers have achieved better mixing performance than OTM. Due to the coupling effect of two swirl-inducing inlets and a rectangular constriction, the maximum mixing index and pressure drop appeared in TMSC among the four micromixers especially; the mixing index of TMSC reaches 91.8% at Re = 70, indicating that TMSC can achieve effective mixing in a short channel length, but has a slightly higher pressure drop than TMSI and TMRC.

Chaotic dynamics of magnetic domain walls in nanowires

The nonlinear dynamics of a transverse domain wall (TDW) in Permalloy and Nickel nanostrips with two artificially patterned pinning centers is studied numerically up to rf frequencies. The phase diagram frequency - driving amplitude shows a rich variety of dynamical behaviors depending on the material parameters and the type and shape of pinning centers. We find that T-shaped traps (antinotches) create a classical double well Duffing potential that leads to a small chaotic region in the case of Nickel and a large one for Py. In contrast, the rectangular constrictions (notches) create an exponential potential that leads to larger chaotic regions interspersed with periodic windows for both Py and Ni. The influence of temperature manifests itself by enlarging the chaotic region and activating thermal jumps between the pinning sites while reducing the depinning field at low frequency in the notched strips.

Motion of an elastic capsule in a constricted microchannel.

We study the motion of an elastic capsule through a microchannel characterized by a localized constriction. We consider a capsule with a stress-free spherical shape and impose its steady-state configuration in an infinitely long straight channel as the initial condition for our calculations. We report how the capsule deformation, velocity, retention time, and maximum stress of the membrane are affected by the capillary number, Ca , and the constriction shape. We estimate the deformation by measuring the variation of the three-dimensional surface area and a series of alternative quantities easier to extract from experiments. These are the Taylor parameter, the perimeter and the area of the capsule in the spanwise plane. We find that the perimeter is the quantity that best reproduces the behavior of the three-dimensional surface area. This is maximum at the centre of the constriction and shows a second peak after it, whose location depends on the Ca number. We observe that, in general, area-deformation-correlated quantities grow linearly with Ca , while velocity-correlated quantities saturate for large Ca but display a steeper increase for small Ca . The velocity of the capsule divided by the velocity of the flow displays, surprisingly, two different qualitative behaviors for small and large capillary numbers. Finally, we report that longer constrictions and spanwise wall bounded (versus spanwise periodic) domains cause larger deformations and velocities. If the deformation and velocity in the spanwise wall bounded domains are rescaled by the initial equilibrium deformation and velocity, their behavior is undistinguishable from that in a periodic domain. In contrast, a remarkably different behavior is reported in sinusoidally shaped and smoothed rectangular constrictions indicating that the capsule dynamics is particularly sensitive to abrupt changes in the cross section. In a smoothed rectangular constriction larger deformations and velocities occur over a larger distance.

Numerical modeling of Joule heating effects in insulator‐based dielectrophoresis microdevices

Insulator-based DEP (iDEP) has been established as a powerful tool for manipulating particles in microfluidic devices. However, Joule heating may become an issue in iDEP microdevices due to the local amplification of electric field around the insulators. This results in an electrothermal force that can manifest itself in the flow field in the form of circulations, thus affecting the particle motion. We develop herein a transient, 3D, full-scale numerical model to study Joule heating and its effects on the coupled transport of charge, heat, and fluid in an iDEP device with a rectangular constriction microchannel. This model is validated by comparing the simulation results with the experimentally obtained fluid flow patterns and particle images that were reported in our recent works. It identifies a significant difference in the time scales of the electric, temperature, and flow fields in iDEP microdevices. It also predicts the locations of electrothermal flow circulations in different halves of the channel at the upstream and downstream of the constriction.

Transient dynamics of an elastic capsule in a microfluidic constriction.

In this paper we investigate computationally the transient dynamics of an elastic capsule flowing in a square microchannel with a rectangular constriction, and compare it with that of a droplet. The confinement and expansion dynamics of the fluid flow results in a rich deformation behavior for the capsule, from an elongated shape at the constriction entrance, to a flattened parachute shape at its exit. Larger capsules are shown to take more time to pass the constriction and cause higher additional pressure difference, owing to higher flow blocking. Our work highlights the effects of two different mechanisms for non-tank-treading transient capsule dynamics. The capsule deformation results from the combined effects of the surrounding and inner fluids' normal stresses on the soft particle's interface, and thus when the capsule viscosity increases, its transient deformation decreases, as for droplets. However, the capsule deformation is not able to create a strong enough inner circulation (owing to restrictions imposed by the material membrane), and thus the viscosity ratio does not affect much the capsule velocity and the additional pressure difference. In addition, the weak inner circulation results in a positive additional pressure difference ΔP+ even for low-viscosity capsules, in direct contrast to low-viscosity droplets which create a negative ΔP+. Our findings suggest that the high cytoplasmatic viscosity, owing to the protein hemoglobin required for oxygen transport, does not affect adversely the motion of non-tank-trading erythrocytes in vascular capillaries.

Numerical investigation of domain walls in constrained geometries

In recent years, magnetic domain wall structures in ferromagnetic nanowires have attracted growing attention, opening paths to develop novel devices which exploit magnetoresistive effects. A reduction of the domain wall length in geometrically constrained areas has been predicted and observed. In this article, we consider a rectangular constriction (width s0, length 2d0) in form of a thin film, attached to a rectangular pad (width s1) on either side. The material considered is Ni (Ms=490kA∕m) with a weak in-plane anisotropy (K1=2000J∕m3). We investigate the dependence of the domain wall length as a function of the constriction geometry. Micromagnetic simulations are used to systematically study the head-to-head domain walls between head-to-head domains (case A) and Néel walls between sidewise domain orientations (case B). We present the resulting domain wall length w as a function of 2d0 and s0 and analyze the magnetization patterns. A reduction of the domain wall length to below 11nm is found (where the corresponding unconstrained domain wall length is 69nm). For constriction lengths above a critical value (case B only), the single 180° domain wall splits into two 90° domain walls.

Experimental and computational analysis of droplet formation in a high-performance flow-focusing geometry

Detailed experimental and simulation studies are performed and presented to further substantiate the previously reported high-performance flow-focusing geometry for droplet generation. In this geometry, water-in-oil droplets are formed through a three-dimensional (3D) circular orifice directly integrated inside a silicon microchannel. The geometry ensures controlled breakup of droplets for a wide range of flow rates. Simulations are provided using computational fluid dynamics software to elucidate the flow behavior nearby the 3D circular orifice. In addition, experimental results on the droplet generation characteristics are obtained both from the 3D circular constriction as well as quasi-2D (2D) rectangular constriction that are typically used in flow-focusing devices. Direct comparison of these results further supports the claim that droplets formed by the 3D circular orifice show noticeably increased sensitivity against the flow rate of the continuous oil-phase both in droplet size and generation frequency.

The influence of pool length on local turbulence production and energy slope: a flume experiment

AbstractThe influence of pool length on the strength of turbulence generated by vortex shedding was investigated in a 6 m long recirculating flume. The experiment utilized a 38% constriction of flow and an average channel‐bed slope of 0·007. The base geometry for the intermediate‐length pool experiment originated from a highly simplified, 0·10 scale model of a forced pool from North Saint Vrain Creek, Colorado. Discharge in the flume was 31·6 l/s, which corresponds to a discharge in the prototype channel of 10 m3/s. Three shorter and four longer pool lengths also were created with a fixed bed to determine changes in turbulence intensities and energy slope with pool elongation. Three‐dimensional velocities were measured with an acoustic Doppler velocimeter at 31–40 different 0·6‐depth and near‐bed locations downstream of the rectangular constriction. The average velocity and root mean square (RMS) of the absolute magnitude of velocity at both depths are significantly related to the distance from the constriction in most pool locations downstream of the constriction. In many locations, pool elongation results in a non‐linear change in turbulence intensities and average velocity. Based on the overall flow pattern, the strongest turbulence occurs in the center of the pool along the shear zone between the jet and recirculating eddy. The lateral location of this shear zone is sensitive to changes in pool length. Energy slope also was sensitive to pool length due to a combination of greater length of the pool and greater head loss with shorter pools. The results indicate some form of hydraulic optimization is possible with pools adjusting their length to adjust the location and strength of turbulent intensities in the center of pools, and lower their rate of energy dissipation. Copyright © 2004 John Wiley & Sons, Ltd.

Finite element analysis of airflow in the vocal tract with lateral channels

Lateral channels are airflow paths around the tongue produced by the laterally inward movement of the tongue toward the midsagittal plane during American English /l/ sound production. If contact is made with the palate, a closure is formed in the flow path along the midsagittal line. The closure is normally formed in the anterior part of the oral cavity and is about 1–1.5 cm long. However, it is speculated that the flow may split at a location posterior to the closure, thereby giving a longer length of the lateral channels up to 3–4 cm. Lateral channels of length around 3 cm have been shown to have significant effects on the resulting sound spectrum. To investigate the flow and acoustic field involved, finite element analysis was performed on a simplified model of the vocal tract during lateral sound production. The tongue was modeled as a rectangular constriction with a tapering slope on the upstream side and two flow channels on its two sides. The results show that the rising up of the tongue causes the flow to split into three regions of different flow amplitude and phase: one main region above the tongue surface and two regions around the tongue. This flow splitting occurs at the point where the tongue first begins rising up, well before the actual constriction location. The effective length of the lateral channels is therefore much longer than the length of the lingual constriction.

Numerical simulation of electron diffraction through a narrow constriction

We performed time-evolved numerical simulations of a two-dimensional electron wave packet passing through a semicircular constriction (very short quantum wire) by solving the time-dependent Schrödinger equation using the finite difference method to understand the nature of electron diffraction phenomena in semiconductors. By Fourier transformation, we calculated the time-evolved electron wave packet in wave number space, which shows the transition from the Gaussian distribution to the circular distribution having equal energy by entering constriction. The obtained results are compared with the results of our previous simulations of an electron wave packet passing through a rectangular constriction. By analyzing the nature of diffracted subpeaks, the following results were obtained: (1) The intensity of the subpeaks diffracted by a semicircular constriction is higher than that by a rectangular one. (2) The starting point of the diffracted subpeaks is the center position of the narrowest width in a constriction, while that for rectangular ones is the center of the constriction entrance. (3) The lateral wave number of the diffracted subpeak increases with the number n, n being the number counted from the main (0th) peak which propagates straight through, although it deviates negatively from the linear relationship obtained for rectangular ones with an increase in n. (4) There is a time delay in the diffracted subpeaks similar to that for rectangular constrictions. The differences between passing through a semicircular constriction and a rectangular one were interpreted as caused by the reflection on the inside wall of the constriction and the energy spread of each quantum level.

On additional conductance quantization and related effects of an electric field in 2D quantum point contacts

Influence of the electric field on the quantum point contact (QPC) differential conductance is studied in two cases of well-developed transmission spectrum of (a) step-like and (b) resonance character. These are exemplified by a symmetric rectangular constriction and double-bend constriction in two-dimensional electron gas. It is shown that an additional structure in the constriction-conductance dependence on the Fermi energy (referred sometimes as half integer quantization) reflects the specific field distribution in the contact region at moderate fields and is washed out by nonlinear field effects produced by the potential variation inside the contact. To study field effects, we suggest an analytical expression for the transmission probability, which includes as particular cases two models used previously to confirm and to reject the possibility of the QPC conductance quantization by value e 2/ h. We also briefly discuss the case of resonance doubling accompanied by two-times decrease of the resonance intensity, representing another example of transformations in the QPC conductance, which have the same origin.

A Method of DF Error Correction

The problem of search with instruments having systematic error is examined and found to be a function of the logarithmic spiral. The case of rectangular constrictions of the search pattern is explored. Extremely simple methods of computing the sought location are disclosed. Description is in terms of locating a transmitting source.