Friction factor analysis for a nanofluid circulating in a microchannel filled with a homogeneous porous medium

This work presents the numerical solution for different velocity profiles and friction factors on a rectangular porous microchannel fully saturated by the flow of a nanofluid introducing different viscosity models, including one nanofluid density model. The Darcy-Brinkman-Forchheimer equation was used to solve the momentum equation in the porous medium. The results show that the relative density of the fluid, the nanoparticle diameters and their volumetric concentration have a direct influence on the velocity profiles only when the inertial effects caused by the presence of the porous matrix are important. Finally, it was found that only viscosity models that depend on temperature and nanoparticle diameter reduce the friction factor by seventy percent compared to a base fluid without nanoparticles; furthermore, these models show a velocity reduction of even ten percent along the symmetry axis of the microchannel.

Ankle-Injury Patients Perform More Microadjustments during Walking: Evidence from Velocity Profiles in Gait Analysis

Introduction. We evaluated the velocity profiles of patients with lateral collateral ligament (LCL) injuries of the ankle with a goal of understanding the control mechanism involved in walking. Methods. We tracked motions of patients’ legs and feet in 30 gait cycles recorded from patients with LCL injuries of the ankle and compared them to 50 gait cycles taken from normal control subjects. Seventeen markers were placed on the foot following the Heidelberg foot measurement model. Velocity profiles and microadjustments of the knee, ankle, and foot were calculated during different gait phases and compared between the patient and control groups. Results. Patients had a smaller first rocker percentage and larger second rocker percentage in the gait cycle compared to controls. Patients also displayed shorter stride length and slower strides and performed more microadjustments in the second rocker phase than in other rocker/swing phases. Patients’ mean velocities of the knee, ankle, and foot in the second rocker phase were also significantly higher than that in control subjects. Discussion. Evidence from velocity profiles suggested that patients with ligament injury necessitated more musculoskeletal microadjustments to maintain body balance, but these may also be due to secondary injury. Precise descriptions of the spatiotemporal gait characteristics are therefore crucial for our understanding of movement control during locomotion.

Forced and mixed convection experiments in a confined vertical backward facing step at low-Prandtl number

In this paper, we present experimental results for a non-isothermal vertical confined backward facing step conducted with a low-Prandtl number fluid. The eutectic alloy gallium–indium–tin is used as the working fluid. We conducted experiments for different Reynolds and Richardson numbers covering both forced and mixed convection regimes. Time-averaged velocity profiles were measured at six streamwise positions along the test section center-plane with so-called permanent magnet probes. The local Nusselt number was measured in streamwise and spanwise directions along the heating plate mounted right after the step. We further ran RANS simulations of the experiment to study the qualitative influence of assuming a constant specific heat flux thermal boundary condition for the experiment heating plate. The measured velocity profiles show the expected behavior for both studied convection regimes, while the measured streamwise local Nusselt number profiles do not. This is explained by how the heating plate thermal boundary condition is defined. We performed an order of magnitude estimate to estimate the forced- to mixed convection transition onset. The estimate shows good agreement with the experimental data, although further measurements are needed to further validate the estimated transition threshold. The measurement of fluctuating quantities remains an open task to be addressed in future experiments, since the permanent magnet probe measurement equation needs further adjustments. Graphical Abstract

Growth of vortical disturbances entrained in the entrance region of a circular pipe

The development and growth of unsteady three-dimensional vortical disturbances entrained in the entry region of a circular pipe is investigated by asymptotic and numerical methods for Reynolds numbers between $1000$ and $10\,000$ , based on the pipe radius and the bulk velocity. Near the pipe mouth, composite asymptotic solutions describe the dynamics of the oncoming disturbances, revealing how these disturbances are altered by the viscous layer attached to the pipe wall. The perturbation velocity profiles near the pipe mouth are employed as rigorous initial conditions for the boundary-region equations, which describe the flow in the limit of low frequency and large Reynolds number. The disturbance flow is initially primarily present within the base-flow boundary layer in the form of streamwise-elongated vortical structures, i.e. the streamwise velocity component displays an intense algebraic growth, while the cross-flow velocity components decay. Farther downstream the disturbance flow occupies the whole pipe, although the base flow is mostly inviscid in the core. The transient growth and subsequent viscous decay are confined in the entrance region, i.e. where the base flow has not reached the fully developed Poiseuille profile. Increasing the Reynolds number and decreasing the frequency causes more intense perturbations, whereas small azimuthal wavelengths and radial characteristic length scales intensify the viscous dissipation of the disturbance. The azimuthal wavelength that causes the maximum growth is found. The velocity profiles are compared successfully with available experimental data and the theoretical results are helpful to interpret the only direct numerical dataset of a disturbed pipe-entry flow.

RARE Velocimetry of Shear Banded Flow in Cylindrical Couette Geometry

<p>A flow phenomena called ‘shear banding’ is often observed for a certain class of complex fluids, namely wormlike micellar solutions. Wormlike micelles are elongated flexible self-assembly structures formed by the aggregation of amphiphiles, which may entangle into a dynamic network above a certain concentration threshold. The entanglement results in the sample having both solid-like (elastic) and liquid-like (viscous) properties, an ambiguity commonly found in complex fluids. Under certain shear conditions, the flow couples with the structure of the micellar network, leading to the formation of (shear) bands with differing viscosity. The principle goal of this work is to address open questions regarding the temporal and spatial stability of shear banded flow. Shear banding is often studied in cylindrical Couette cells, where the fluid is sheared in a gap between differentially rotating concentric cylinders. For the sake of an accurate description of the flow in such a shear cell, the methodology for a 2D Nuclear Magnetic Resonance (NMR) velocimetry technique (known as PGSE-RARE), which offers high temporal and spatial resolution, is improved and refined. Two main challenges are identified and overcome. The first concerns the fact that the velocity imaging process operates on a Cartesian grid, whereas the flow in the Couette cell is of cylindrical symmetry. Numerical calculations and NMR simulations based on the Bloch equations, as well as experimental evidence, give insight on the appropriate selection of the fluid volume over which velocity information is accumulated and the preferred scheme through which the NMR image is acquired in the so-called k-space. The small extent of the fluid gap for the cells in use is the second challenge. In this respect, a variant of the velocimetry technique is developed, which offers ultra high resolution in the gap direction, necessary for a detailed description of the flow profile in the banded state. The refined methodology is applied in a thorough study of a certain wormlike micellar solution (‘10% CPCl’), which is known to exhibit spatiotemporal fluctuations and has been subject of numerous studies over the past 20 years. NMR results are supported by a recently developed 2D Rheo-USV (Ultrasonic Speckle Velocimetry) method, which offers an even higher temporal resolution. The two complementary methods show good agreement for averaged velocity profiles. In line with previous studies the fluid is found to follow a standard anomalous lever rule, which is characterized by a constant shear rate in the high viscosity band and a varying shear rate and proportion of the high shear rate band. In particular, the high resolution NMR variant allows a refined picture on the dynamics of the interface between the two bands. Furthermore, slip is observed for all investigated shear rates. The amount of slip, however, is found to strongly depend on the specifities of the Couette cells in use. Spatially and temporally resolved flow maps reveal various flow instabilities. Ultrasound measurements show vorticity structures in the order of the gap width. In the NMR case no such structures are observed due to the lower resolution in the axial direction. For higher shear rates the occurrence of turbulent bursts is detected for USV. No direct evidence of similar flow instabilities is found in the NMR case. Finally, broad distributions dominate the high shear rate band in temporally and spatially resolved velocity profiles, showing the fluctuative nature of the flow.</p>

RARE Velocimetry of Shear Banded Flow in Cylindrical Couette Geometry

<p>A flow phenomena called ‘shear banding’ is often observed for a certain class of complex fluids, namely wormlike micellar solutions. Wormlike micelles are elongated flexible self-assembly structures formed by the aggregation of amphiphiles, which may entangle into a dynamic network above a certain concentration threshold. The entanglement results in the sample having both solid-like (elastic) and liquid-like (viscous) properties, an ambiguity commonly found in complex fluids. Under certain shear conditions, the flow couples with the structure of the micellar network, leading to the formation of (shear) bands with differing viscosity. The principle goal of this work is to address open questions regarding the temporal and spatial stability of shear banded flow. Shear banding is often studied in cylindrical Couette cells, where the fluid is sheared in a gap between differentially rotating concentric cylinders. For the sake of an accurate description of the flow in such a shear cell, the methodology for a 2D Nuclear Magnetic Resonance (NMR) velocimetry technique (known as PGSE-RARE), which offers high temporal and spatial resolution, is improved and refined. Two main challenges are identified and overcome. The first concerns the fact that the velocity imaging process operates on a Cartesian grid, whereas the flow in the Couette cell is of cylindrical symmetry. Numerical calculations and NMR simulations based on the Bloch equations, as well as experimental evidence, give insight on the appropriate selection of the fluid volume over which velocity information is accumulated and the preferred scheme through which the NMR image is acquired in the so-called k-space. The small extent of the fluid gap for the cells in use is the second challenge. In this respect, a variant of the velocimetry technique is developed, which offers ultra high resolution in the gap direction, necessary for a detailed description of the flow profile in the banded state. The refined methodology is applied in a thorough study of a certain wormlike micellar solution (‘10% CPCl’), which is known to exhibit spatiotemporal fluctuations and has been subject of numerous studies over the past 20 years. NMR results are supported by a recently developed 2D Rheo-USV (Ultrasonic Speckle Velocimetry) method, which offers an even higher temporal resolution. The two complementary methods show good agreement for averaged velocity profiles. In line with previous studies the fluid is found to follow a standard anomalous lever rule, which is characterized by a constant shear rate in the high viscosity band and a varying shear rate and proportion of the high shear rate band. In particular, the high resolution NMR variant allows a refined picture on the dynamics of the interface between the two bands. Furthermore, slip is observed for all investigated shear rates. The amount of slip, however, is found to strongly depend on the specifities of the Couette cells in use. Spatially and temporally resolved flow maps reveal various flow instabilities. Ultrasound measurements show vorticity structures in the order of the gap width. In the NMR case no such structures are observed due to the lower resolution in the axial direction. For higher shear rates the occurrence of turbulent bursts is detected for USV. No direct evidence of similar flow instabilities is found in the NMR case. Finally, broad distributions dominate the high shear rate band in temporally and spatially resolved velocity profiles, showing the fluctuative nature of the flow.</p>

An electromagnetic arrayed pump to create arbitrary velocity profiles in fluid

The present paper is conducted to develop a new structure of an electromagnetic pump capable of controlling the magnetic field in a rectangular channel. Common electromagnetic pumps do not create uniform velocity profiles in the cross-section of the channel. In these pumps, an M-shape profile is created since the fluid velocity in the vicinity of the walls is higher than that in its center. Herein, the arbitrary velocity profiles in the electromagnetic pump are generated by introducing an arrayed structure of the coils in the electromagnetic pump and implementing 3D numerical simulation in the finite element software COMSOL. The dimensions of the rectangular channel are 5.5 × 150 mm2. Moreover, the magnetic field is provided using a core with an arrayed structure made of low-carbon iron, as well as five couples of coils. 20% NaoH solution is utilized as the fluid (conductivity: 40 S/m). The arrayed pump is fabricated and experimentally created an arbitrary velocity profile. The pressure of the pump in every single array is 12 Pa and the flow rate is equal to 3375 mm3/s. According to the results, there is a good agreement between the experimental test carried out herein and the simulated models.Article highlights This is the first time that the idea of arrayed electromagnetic pump is presented. This pump uses a special arrayed core with coils; by controlling the current of each coil and the direction of the currents, the magnetic field under the core could be adjusted. By changing the magnetic field at any position in the width of the channel, the Lorentz force alters, which leads to different velocity and pressure profiles. Using COMSOL multiphysics software, the electromagnetic pump was simulated in real size compared to the experimental model. Subsequently, the simulation model was verified and different velocity profiles were generated by activation and deactivation of different coils. The pressure and velocity curves and contours were extracted. The experimental setup was manufactured and assembled. NaOH solution was utilized as the fluid. Afterwards, different modes of coil activations were investigated and the pressure and velocity profiles of the pump were calculated.

The Ageing and Rejuvenation of Soft, Glassy Complex Fluids

<p>Suspensions of multiarm star polymers are studied as models for soft colloidal interactionsin colloidal glasses. Establishing a pre-shearing protocol which ensures a reproducible initial state (the "rejuvenation" of the system), we report here the stress evolution from startup for two different concentrations for a range of shear rates using conventional rheological techniques. We show the existence of critical shear rateswhich are functions of the concentration. When the suspensions are sheared at rates below the critical rates, the stress rises to a common value which is also a function of the concentration. The system thus evolves into a yield stress-like fluid. This behavior manifests itself as an evolution from a monotonic, slightly shear-thinning flow curve to a flow curve dominated by a stress plateau. Complementary to the controlled-rate measurements, stress-controlled measurementsshow that for a stress below the critical stress, the rate at which strain is acquired drops several orders of magnitude, providing evidence of a lower branch of the flow curve. In stress-controlled ageing experiments, the material recovers an increasing fraction of the strain acquired under stress with waiting time upon cessation of the (less than critical) stress. The freshly rejuvenated suspension recovers a mere 2%of the acquired strain, while for a waiting time of 104 s the material recovers 97% of the acquired strain. The material thus appears to evolve from a nearly ideal fluid to a nearly ideal solid. We relate this bulk evolution to spatially and temporally resolved Rheo-NMR velocity profiles which clearly show an evolution to a strongly shear-banded state. The velocity of the suspension in the lower shear band is below the uncertainty of the experiment. The growth of the (assumed) zero-shear band is well described by a Gompertz relation. The effects of shear-rate, temperature and waiting time on the Gompertzparameters are investigated. Phenomenological understanding is provided through a scalar model that describes the stress-dependent free-energy landscape. Using a dual-minimum free-energy landscape, the model is able to replicate the behaviour of the stress after startup in shearratecontrolled experiments, the flow curve and the velocity profiles across the gap of a Couette geometry. The Large-Amplitude-Oscillatory-Shear (LAOS) response is reported along with discussions of current LAOS analysis techniques. The stress response to LAOS of the star suspensions is well described in a Cox-Merz manner by a modified Cross model. The modified Cross model highlights an asymmetry in the LAOS response. This constitutes the first ever report of asymmetric LAOS responses. The asymmetry is followed as a function of time using two complementary scalar variables. A speculativeinterpretation is given to account for the evolution of the asymmetry.</p>