Flow Velocity Profiles Research Articles

Effect of additional periodic motion on gas-liquid two-phase secondary flow behavior in inclined pipes

Secondary flow significantly changes the flow structure and increases flow resistance. The pipeline motion further contributes to the evolution of secondary flow. This study aims to elucidate the characteristics of two-phase secondary flow in inclined pipelines under additional periodic motion conditions. Based on the CFD technique, three-dimensional oscillating two-phase flow fields were simulated using the VOF model and dynamic mesh method. The focus was on four common flow patterns observed in inclined pipes, namely stratified flow, slug flow, turbulence flow, and transitional flow. The impact mechanisms of swaying, heaving, and coupling motion on the structural evolution, velocity profile, and relative intensity of secondary flow were analyzed. The results indicate that additional periodic motion exhibits a significant dominant behavior on secondary flow when the amplitude exceeds 1.0D. Heave motion has a more pronounced effect on the secondary flow structure. Additional periodic motion induces periodic evolution of secondary flow structure in stratified flow, with the evolution period aligning with the period of the additional motion. Under additional periodic motion, there is no one-to-one correspondence between secondary flow velocity and axial velocity. Additional motion significantly suppresses the axial velocity of slug flow. Furthermore, additional periodic motion significantly increases the relative intensity of secondary flow, exceeding 10%. When the amplitude is less than 1.5D, additional motion suppresses the relative intensity of secondary flow in turbulence flow and transitional flow.

Couette flow at high Knudsen number between wall and liquid boundaries

This paper presents molecular dynamics simulations of the Couette flow of a rarefied gas between the liquid and wall boundaries and, in particular, investigates the boundary conditions for the Boltzmann equation at the liquid interface. The simulation results for various Knudsen numbers show that the slip velocity decreases at the liquid boundary and increases at the smooth wall as the Knudsen number increases, indicating that the velocity profile of the rarefied Couette flow is asymmetric. One reason for this is backscattering, in which molecules are reflected in the opposite direction to the mainstream flow, owing to molecular-scale roughness at the liquid boundary. It has also been suggested that the backscattering effect decreases when the gas density increases. This can be understood using the local Knudsen numbers near the liquid boundary.

Determining the flow transition from laminar to turbulence using simple spin-echo magnetic resonance techniques

We have recently introduced a methodology to determine the average velocity and flow behavior index of laminar pipe flow of a power-law fluid using simple magnetic resonance (MR) techniques. In general, MR techniques are noninvasive and capable of working on optically opaque fluids. Knowledge of the average velocity and flow behavior index provides the information needed to reconstruct the flow velocity profile. However, as the flow velocity increases, the flow will begin to develop turbulence. For pipe flow of a particular fluid, the velocity profile is flatter in the center of the pipe at turbulent flow rates compared with laminar flow. An effective flow behavior index can approximate the time-averaged velocity profile, as the Reynolds number increases, as a fluid transitions from laminar to turbulent flow. Here, we show the results of testing the utility of such a simplification in monitoring that transition. For the present study, Reynolds numbers ranged from approximately 490 to 6800, which corresponds to flow rates of 200 to 2750 ml/min and average velocity of 5 to 80 cm/s. We found that visual inspection of the data would be sufficient to determine the state of the flow. With some external knowledge of the flow rate, the shape of the time-averaged velocity profile and eddy diffusivity can be estimated (and potentially also an average fluid particle acceleration).

The Application of OpenFOAM in Modelling Flow for Vegetated Channel

Vegetation plays an important role in the hydrodynamic behaviour of an open channel flow. This study attempted to investigate the flow characteristics of an emergent vegetated channel using Open-source Operations and Manipulation (OpenFOAM). InterFoam is an OpenFOAM solver used to model this simulation. It is one of the methods available to model free-flow surface flow. Results for flow velocity profile can be generated using ParaView software. This study used a constant inlet velocity of 0.0417 m/s. There are two sets of models including model L8 with a solid volume fraction (SVF) of 8% using 9 rigid dowels, and model 4S with SVF of 4% using 17 dowels within a 1.2 m2 study area. Dowels in L8 are arranged in linear formation compared to the 4S model in a staggered arrangement. The study found that in model 4S, the stem-scale vortices are developed individually after each dowel due to sparse staggered vegetation. Meanwhile, model 8L suggests oppositely the vortex is cramped from the closeness of the dowels. The shear layer is formed as the flow enters the vegetation patch at upstream and the instability causes the shear layer vortices between inside and outside the vegetation region. Both models agreed that as the flow moves downstream the vortices are greater and make the streamwise velocity region become slower. The vertical velocity profile acknowledges the shear layer patch-scale vortices have a greater influence on the flow of both models. The magnitude of turbulence intensity in lateral directions is bigger in model 4S than in model 8L. The influence of vortices shed by upstream cylinders has an increasing impact on the irregular shedding behaviour of downstream cylinders as plant density increases. In general, the TKE values of the Model 4S are higher than those of the Model 8L. Regardless of the solid volume percentage difference, the vegetation pattern between linear and staggered has an effect on the flow. Computational Fluid Dynamic (CFD) is indeed capable to solve complex hydrodynamic characteristics.

Heat and mass transfer analysis for MHD non‐miscible micropolar and Newtonian fluid flow in a rectangular porous channel

AbstractThe aim of the present work is to examine the entropy production characteristics, thermal profile, and flow behaviour of two non‐miscible natures of Newtonian and micropolar fluids, which take place through a rectangular porous enclosure channel. The flow region is divided into two distinct porous zones of the channel and is subjected to a constant oriented magnetic field. The Eringen's micropolar fluid is taking place in the upper porous zone, whereas in the lower porous zone, the Newtonian fluid is flowing. The wall surface of a rectangular porous channel is isothermal, and the flow of immiscible fluid through a porous channel takes place because of a constant pressure gradient. No slip condition is imposed on the static walls and continuity of vorticity, velocity, shear stress component, thermal distribution, and thermal flux are prescribed at the interface. Here, the production of entropy due to fluid friction and thermal exchange for non‐miscible Newtonian and micropolar fluids is evaluated. The characteristics of various estimated parameters on thermal and flow properties, such as Bejan number distribution, flow velocity, entropy production, and thermal profile, are discussed. The obtained results show that entropy production is directly proportional to viscous dissipation and Reynolds number, whereas it has a reverse nature with micropolarity parameter, inclination angle parameter, and Hartman number. Our results corroborate with previous published results.

The hunt for the Kármán ‘constant’ revisited

The log law of the wall, joining the inner, near-wall mean velocity profile (MVP) in wall-bounded turbulent flows to the outer region, has been a permanent fixture of turbulence research for over hundred years, but there is still no general agreement on the value of the prefactor, the inverse of the Kármán ‘constant’ $\kappa$ , or on its universality. The choice diagnostic tool to locate logarithmic parts of the MVP is to look for regions where the indicator function $\varXi$ (equal to the wall-normal coordinate $y^+$ times the mean velocity derivative $\mathrm {d} U^+/\mathrm {d} y^+$ ) is constant. In pressure-driven flows, however, such as channel and pipe flows, $\varXi$ is significantly affected by a term proportional to the wall-normal coordinate, of order $O({Re}_{\tau }^{-1})$ in the inner expansion, but moving up across the overlap to the leading $O(1)$ in the outer expansion. Here we show that, due to this linear overlap term, ${Re}_{\tau }$ values well beyond $10^5$ are required to produce one decade of near constant $\varXi$ in channels and pipes. The problem is resolved by considering the common part of the inner asymptotic expansion carried to $O({Re}_{\tau }^{-1})$ , and the leading order of the outer expansion. This common part contains a superposition of the log law and a linear term $S_0 \,y^+{Re}_{\tau }^{-1}$ , and corresponds to the linear part of $\varXi$ , which, in channel and pipe, is concealed up to $y^+ \approx 500\unicode{x2013}1000$ by terms of the inner expansion. A new and robust method is devised to simultaneously determine $\kappa$ and $S_0$ in pressure-driven flows at currently accessible ${Re}_{\tau }$ values, yielding $\kappa$ values which are consistent with the $\kappa$ values deduced from the Reynolds number dependence of centreline velocities. A comparison with the zero-pressure-gradient turbulent boundary layer, further clarifies the issues and improves our understanding.

Residence time distribution of ultrafine aerosol particles in a tube with transient and parabolic laminar flow

This paper presents a theoretical investigation concerning the residence time distribution (RTD) of ultrafine monodisperse aerosol particles flowing in a circular tube in laminar flow regime. If a fully developed, parabolic flow (PF) velocity profile is assumed for the whole tube length, the convection-diffusion process undergone by the aerosol particles can be described by means of two parameters, the dimensionless particle diffusion coefficient D and the tube aspect ratio a (radius/length). An additional parameter, the Reynolds number Re, must be taken into consideration when the flow develops starting from a given velocity profile at the tube entrance, which we have assumed to be a uniform (plug) flow. The latter situation is referred to as transient flow (TF). The RTD has been determined using two different variations of a Monte Carlo (MC) technique to simulate the particle trajectory within the tube. The difference between the two MC methods is the assumed distribution of Brownian random displacements of the particles; in both cases the distribution had zero mean and variance 2DΔt, but the distribution was uniform in one method and normal in the other. The simulation results obtained with the two methods were almost coincident. In either PF or TF, even for relatively small values of D the aerosol RTD is quite different from that of the fluid where the particles are suspended. In particular, the dimensionless mean particle residence time, which initially decreases with D, soon attains an asymptotic value of 0.65 for D ≥ 0.3 (the mean residence time of the fluid is 1) in PF; a similar asymptotic value is attained for TF but in this case it depends on the particular combination of a and Re considered. The relative influence of axial diffusion on the RTD is insignificant unless the tube ratio a is of the order of 0.5 (tube with a length equal to its diameter).

Numerical study of the influence of blade inlet design parameters on the internal flow characteristics and energy performance of a Francis turbine

One of the challenges of hydraulic turbine design is the creation of a conveyor with high hydraulic performance in accordance with the parameters of the hydraulic energy. The blade inlet parameters, such as blade beta angle, lean angle, and ellipse axis ratio, have an effect on the performance and cavitation characteristics of the runner, among the numerous geometric elements that regulate turbine performance. All of these parameters must be optimized to ensure that the runner inlet is matched to the guide vane under design conditions and a wider range of off-design conditions. For hydraulic designers, computational fluid dynamics based performance prediction methods can provide rapid turbine performance predictions and expedite runner development. Finding a collection of accessible parameters, meanwhile, strongly depends on the designer’s previous design work, which is frequently time-consuming. In this article, the internal flow characteristics and energy performance of a Francis turbine with moderate specific-speed, as well as the blade leading edge geometrical parameters that influence them, are investigated in depth. The Francis turbine is designed in accordance with the rated head H (m), rated flow rate Q (m), and rated speed n (rpm) within the constraints of the fixed meridional projection, including the leading-edge and trailing-edge positions. The energy performance, internal flow characteristics, velocity profile, flow angles, pressure distribution, blade loading, and cavitation characteristics are computed, analyzed, and compared. The main findings can serve as a guide for the development of Francis turbines with moderate specific-speed.

Ultrasound Speckle Decorrelation-Based Blood Flow Measurements.

Ultrasound imaging is the preferred noninvasive technique to measure blood flow to diagnose cardiovascular disease such as heart failure, carotid stenosis, and renal failure. Conventional ultrasound techniques such as Doppler ultrasound, ultrasound imaging velocimetry, vector Doppler and transverse oscillation beamforming have been used for blood flow velocity profile measurement. However, these techniques were limited to measuring blood flow velocities within the 2-D lateral (across the ultrasound beam) plane of a vessel, and the blood flow velocity profile was derived by assuming that blood vessels have a circular cross-section with axis symmetry. This assumption is incorrect because most vessels have complex geometries, such as tortuosity and branches, and an asymmetric flow profile in the presence of vascular plaque. Consequently, ultrasound speckle decorrelation has been proposed to measure blood flow from transverse views of blood vessels wherein the ultrasound beam is perpendicular to the vessel axis. In this review, we present a summary of recent progress in ultrasound speckle decorrelation-based blood flow measurement techniques.

Energy Transfer and Reverse Flow Characteristics in the Interaction Process between Non-Breaking Solitary Wave and a Steep Seawall: A Case Study

This study utilized a two-dimensional numerical viscous wave tank to simulate the run-up and run-down processes of non-breaking solitary waves on a steep seawall. The research aimed to investigate the transformation between wave potential energy and kinetic energy, the evolution mechanisms of the wave and flow fields, and the correlation between the dynamic pressure gradient and the reverse flow near the sloping bed. The numerical model results were consistent with laboratory measurements of free surface elevations and flow velocity profiles, demonstrating the accuracy of the numerical model. This study focused on a solitary wave with a wave-height-to-water-depth ratio of 0.15, propagating on a representative seawall with a steep slope of 1:3 along the western coast of Taiwan. The simulation results indicate that the maximum run-up height occurs when the potential energy is at its highest. Undertow is caused by the adverse pressure gradient within the flow field, and the dynamic pressure on the sloping bed is directly proportional to the free surface elevation. Therefore, by observing the spatial changes in the free surface elevation, we can indirectly determine the occurrence time of undertow.

Calibration and Verification of Operation Parameters for an Array of Vectrino Profilers Configured for Turbulent Flow Field Measurement around Bridge Piers—Part II

High-frequency velocimeters used for flow measurements during laboratory experiments allow the user to select the range for several operation parameters to set up the instrument for optimal velocity measurement. The discrepancies between velocity measurements collected with different instrument configurations can be significant, depending on the flume bed configuration and boundary conditions. The aim of this paper is to quantify the differences in flow velocity profiles measured with Acoustic Doppler Velocimeter Profilers (ADVPs) configured using a combination of profiling parameters: Ping Algorithm (PA), Transmit Pulse Size (TPS), and Cell Size (CS). Whereas in Part I of this research, the goal was to identify the optimal probe configuration for downstream measurement of the complex hydraulic structure (pier protected with riprap) based on a match of the flow rate with measurements from other instruments, in this paper, effect of distinct probe configuration on velocity profile and turbulent kinetic energy (TKE) is demonstrated. Differences between ADVPs’ configurations were analyzed through sensitivity analysis with the intention to calculate and compare any discrepancies in the velocity measurements for all the three measured velocity components: streamwise u, spanwise v and vertical w collected on two characteristic flume cross-sections. The results show that each parameter change has a significant effect on the measured values of each velocity component when compared to the Target Configuration (TC). The largest root-mean-square-error (RMSE) is observed when TPS is changed, followed by CS and PA. Absolute RMSE calculated for TPS change from 4 mm to 1 mm is, on average, 6.30 cm/s, 0.90 cm/s, and 0.82 cm/s for velocity components u, v and w, respectively. Absolute RMSE calculated for CS change from 1 mm to 4 mm is, on average, 4.49 cm/s, 0.88 cm/s, and 0.71 cm/s for velocity components u, v and w, respectively. Absolute RMSE calculated for PA change from Adaptive to Max interval is, on average, 4.04 cm/s, 0.63 cm/s, and 0.68 cm/s for velocity components u, v and w, respectively. For a change in all parameters, RMSE is greater for the cross-section downstream of the pier than for the approach cross-section: on average, 90%, 57% and 54% for a change in the PA, TPS, and CS, respectively.

Hydraulic circuit for pulse flow simulation in the tissue-mimicking aortic phantom

BACKGROUND: Computed tomographic angiography (CTA) is the gold standard in the diagnosis of most vascular pathologies. The optimal method to improve this technique is the use of anthropomorphic tissue-mimicking phantoms, since CTA is accompanied by radiation exposure and the risk of allergic reactions when using contrast agents. In addition to compliance with the X-ray properties of the vessel, the pulsations occurring in the aorta in vivo must be simulated. A review of existing solutions demonstrates a small number of national developments in this area at a relatively high cost of foreign analogues. Moreover, the lack of reproducible methodology for creating pulse flow simulation devices using available and inexpensive materials is worth noting.
 AIM: To develop a hydraulic circuit to simulate pulse blood flow in a tissue-mimicking aortic phantom.
 METHODS: A literature analysis of existing pulse flow simulation devices and tissue-mimicking phantoms of the abdominal aorta was conducted. The medical and technical requirements for the designed device were formulated. The control circuit was developed, the circuit element base was determined, and the hydraulic circuit prototype was assembled. Based on a literature review, a material suitable for reproducing the biomechanical characteristics of arterial tissue was selected. A simplified phantom of the abdominal aortic segment was made. The device model included a simplified abdominal aortic phantom, a control system, a pump, a pressure sensor, a flow meter, and a flow regulator. Initial testing of the developed circuit in the basic signal mode and in the real flow profile simulation mode was performed. The basic signals were periodic rectangular signals reproduced at different frequencies, simulating normal, rapid, and slow heart rate. Using pulse-width modulation, a profile of the pressure pulse wave was obtained.
 RESULTS: The developed hydraulic circuit allowed successful reproduction of pressure and flow velocity profiles in a tissue-mimicking aortic phantom. Further development of the project will involve fabrication and validation of the circuit (using anthropomorphic versions of the phantom) and simulation of the angiographic study.
 CONCLUSIONS: The results may be useful for the improvement of CTA techniques and the development of angiosurgical training stands.

Smoothed Particle Hydrodynamics Simulations of Porous Medium Flow Using Ergun’s Fixed-Bed Equation

A popular equation that is often employed to represent the relationship between the pressure loss and the fluid flow in fluidized or packed granular beds is the Ergun equation, which is an extension of Darcy’s law. In this paper, the method of Smoothed Particle Hydrodynamics (SPH) is used to numerically study the flow field across a rectangular channel partially filled with a porous layer both at the Representative Elementary Volume (REV) scale using the Ergun equation and at the pore scale. Since the flow field can be estimated at the REV scale with a much lower cost compared to the pore scale, it is important to evaluate how accurately the pore-scale results can be reproduced at the REV scale. The comparison between both scales is made in terms of the velocity profiles at the outlet of the rectangular channel and the pressure losses across the clear and porous zones for three different arrays of solid grains at the pore scale. The results show that minimum differences in the flow structure and velocity profiles between the REV and the pore scale always occur at intermediate values of the porosity (ϕ=0.44 and 0.55). As the porosity increases, the differences between the REV and the pore scale also increase. The details of the pressure losses are affected by the geometry of the porous medium. In particular, we find that the pressure profiles at the REV scale match those at the pore scale almost independently of the porosity only when the grains are uniformly distributed in a non-staggered square array.

Analytical solutions of flow velocity profile based on the morphological response of flexible vegetation

Hydrodynamics affected by vegetation in channel is one of the hot topics in ecological hydraulics. Flexible vegetation plays an important role in natural flow region, which changes flow structure and affects the transport of pollutants. Therefore, it is important to illustrate the physical process of the interaction between water flow and morphological response of flexible vegetation. Due to the complex resistance characteristics of flexible vegetation, the simulation of velocity distribution is more complicated. In this paper, velocity distribution in the form of Bessel function is derived by solving the governing equation based on linear resistance-velocity expression of flexible vegetation. Meanwhile, a new power law of velocity distribution is established by adopting the concept of vegetated riverbed. Moreover, a new expression of Darcy–Weisbach friction is derived for flow with flexible vegetation, and the relationship between vegetation bending angle and hydraulic parameters is given. Quantitative relationship between the power law index and the Darcy–Weisbach friction coefficient in the free surface layer is derived for flexible vegetated flow. This research reveals the velocity distribution characteristics under the influence of flexible vegetation and the resistance features on vegetated riverbed.

Resistance to sheet flow induced by raindrop impact on rough surfaces

Raindrops impact can affect the flow resistance to sheet flow by interfering with flow velocity profile. However, quantitative information regarding the flow resistance induced by raindrops impact to sheet flow (Δf) under the influence of different surface roughnesses is limited. In this study, multiple experimental simulations of rainfall and inflow were conducted on flumes with five unit width inflow discharges ranging from 0.02-0.1 m2 min−1, five rainfall intensities ranging from 40 to 120 mm h−1, and three levels of surface roughnesses ranging from 0.009 to 0.25 mm to identify flow resistance due to raindrop impact under different surfaces. Results showed that surface roughness was able to increase the total flow resistance without raindrop impact (fo) and with raindrop impact (fr), respectively. Under rainfall conditions, raindrop impact was able to increase fr on different surfaces. The surface roughness played a stronger role on contributing the fr than the raindrop impact. The major control of fr was the Reynolds number (Re), and fr decreased with the increasing Re. Δf were positively affected by surface roughness and rainfall intensity. Rough surface can increase the effects of raindrop impact on water flow by reducing the flow velocity of base flow or inflow, which leads to the increase in Δf. The major control of Δf was the Re, and Δf decreased with Re. Flow resistance induced by raindrop impact was larger for shallower and slower moving sheet flow with the low Re. In addition, a new equation has been developed to predict Δf under the conditions of Fr < 2.16 by using rainfall intensity, surface roughness, velocity, and water depth. This study helps to estimate the flow resistance induced by raindrops impact to sheet flow under surface roughness and provide the scientific insights for improving hydrologic and soil erosion models.

Outer-layer universality of the mean velocity profile in turbulent wall-bounded flows

This paper deals with discerning outer-layer universality in the mean velocity profiles of turbulent boundary layers. For that purpose we derive an objective criterion which generalizes the classical wall scaling, as well as the Rotta-Clauser and Zagarola-Smits scaling. Outer-layer universality in the present scaling clearly emerges at displacement thickness Reynolds number exceeding about 3000. We propose universal velocity distributions based on simple patched logarithmic/parabolic fitting functions, which are accurate to within less than 1%

Modeling of drag coefficient under emergent and submerged flexible vegetated flow

In an open-channel flow, vegetation study is crucial to be investigated with any type of plants including trees, shrubs, and grasses, which are growing within or near the channel banks and beds in natural or artificial waterways, such as rivers, streams, and canals. These plants are different in height, size, shape, and arrangements, which have a big impact on the turbulence and flow resistance structures. In this paper, a regression analysis has been used based on collected experimental data to improve a specific equation for the drag coefficient for rigid vegetation stems and expanded to flexible stem types under emergent and submerged flow conditions. The equation suggests a length scale metric that, by analogy with the log wake law, normalizes velocity profiles of the depth-limited open channel flow with submerged, rigid vegetation. It has been formulated by drawing regression analysis for each parameter including (Re) Reynolds number, (h*) submergence ratio, and (λ) vegetation density by considering the (Fr) Froude number ranges for the water flows and vegetated channel flows. Using the Reynolds number, which is determined by the height and diameter of the vegetation, the results demonstrate an increase and decrease in the drag coefficient. For assessing the impact of vegetation on flow resistance at the surface layer, the notion of the drag coefficient is introduced. It shows better performance than other length scales in collapsing resistance data gathered under a variety of vegetation circumstances. The proposed scaling is more accurate than those based on the logarithmic, velocity-defect, and power laws in collapsing regression analysis for the studied parameters.

Effect of sneeze flow velocity profiles on the respiratory droplets dispersion in a confined space: An experimental and computational fluid dynamics study

In this study, the effects of sneeze velocity profiles, including peak velocity (PV), peak velocity time (PVT), and sneeze duration time (SDT), on the dispersion of respiratory droplets were studied experimentally and numerically. Spatial–temporal datasets of droplet velocity exhaled from several subjects' mouths with different physiological characteristics were obtained by particle image velocimetry. A direct relationship was found between the forced vital capacity and PV, while the subject's body mass index significantly affected the SDT. A transient computational fluid dynamics (CFD) approach using the renormalization group k–ε turbulence model in conjunction with the Lagrangian particle tracking was developed and used to simulate sneeze droplet motion characteristics. Both one-way and two-way (humidity) coupling models were used in these simulations. The CFD results showed that the two-way (humidity) coupling model provided better agreement with the data in the turbulent and expanded puff zones than the one-way coupling model. The one-way model led to reasonably accurate results in the fully dispersed and dilute-dispersed droplet phases. The effect of injection duration time and injection angle on PVT was larger than that on PV values, while the effect of initial injection velocity on PV was higher than that on PVT values. In addition, the initial injection velocity and angle significantly affected the maximum spreading distance of droplets dmax,sp. The numerical results obtained from the dilute-dispersed droplet phase were in good agreement with the trajectories of isolated droplets in the experimental data. The findings of this study provide novel insights into the effect of sneeze velocity profiles on dmax,sp, and the sneezer subject physiological effect on the threshold distance for the transmission of respiratory pathogens in a confined space.

Arduino Based Pressure Sensor Integration in the Measurement of Flow Field

Abstract: In fluid mechanics, study of velocity profile for a fluid flow gives better understanding about the nature and physics of fluid. We use manometer and pitot static tube in conventional way to measure the velocity profile .But advances in sensor we can use Arduino with the pressure sensor and study the velocity profile with easy and portable way. The study of velocity measurement has been done with help of sensor and electronics component

Viscoelectric effect analysis in an electroosmotic flow with microchannel wall slip

In the present work, we developed a numerical analysis for an electroosmotic flow circulating in a rectangular microchannel considering electrolyte viscosity as a function of the induced electric field; which is also reflected in the slip condition imposed on the system walls, since the slip length is a function of the fluid viscosity. It should be clarified this is an entirely hydrodynamic problem, and for this reason there are no induced pressure gradients, because we are in the presence of a purely electroosmotic flow, where the fluid motion is due only to electrokinetic forces. Based on these comments, the problem is centered on high induced potentials, enabling viscoelectric effect analysis in the electroosmotic flow, which leads to significant increases in velocity and volumetric flow profiles compared to the case where the viscosity is a constant and there is no slip condition. Due to analytical analysis limitations, we implemented a dimensionless equation scheme defined by the continuity equation, the momentum equations in the x and y direction, the Poisson-Boltzmann equation, and the charge conservation equation to obtain the velocity and volumetric flow rate profiles mentioned above. This model is described in its variational form in order to implement the finite element technique using free software, FreeFem++. The results obtained show how the viscoelectric effect is relevant when working with high induced potentials; that is, for values of , when the dimensionless viscoelectric parameter increases, there is a significant decrease in the velocity profiles u, a situation that is not observed when , where there are low induced potentials, and for this reason, as the dimensionless parameter increases, the velocity profiles remain constant. This condition is preserved for different values of the slip length .