Homogeneous Newtonian Fluid Research Articles

Mechanism study on spreading dynamics of nanofluids droplet coupled with thermal evaporation

Droplet-wall interactions occur in many advanced engineering technologies, such as 3D printing, spray coating, and even quantum light-emitting diode(QLED). Nanofluids (colloids of nanoparticles) are becoming increasingly important working fluids for more excellent performances. Computer modeling of fluid flows with the large deformation of free surface usually presents great challenges for conventional grid-based numerical methods. The smoothed particle hydrodynamics (SPH) method has been widely used in such droplet dynamics because of its meshless Lagrange methods, as well as the applicability to macro-scale simulation. In the paper, the numerical model based on the SPH method is presented to predict the detailed outcome of sessile and transient nanofluid droplets. The surface tension of droplets is taken into consideration by the inter-particle interaction force (IIF) model for its advantages in modeling the contact angle during wetting. The properties of nanofluids are obtained by averaging the properties of base fluids and nanoparticles, based on the assumption that nanofluids of low concentration are a homogeneous mixture and Newtonian fluid. The assumption is proposed based on the rheological measurement of nanofluids. Heat conduction is added into the SPH model when the impacted surfaces are heated, and the evaporation is modeled by “extinguishing” the SPH particles. The SPH model predicts the evolution of the droplet surface from spreading to receding, even rebounding on the wall. Moreover, the normalized droplet diameters predicted by the SPH model agree well with the experimental data from the high-speed camera. The proposed SPH models have been used to study the effects of heating temperatures and nanofluids concentration on droplet-wall interactions. The modified SPH models can handle the nanofluids droplet dynamics, along with large deformation, thermal transfer, and evaporation. The results demonstrate that the SPH model is a powerful tool to study the complex droplet dynamics and to predict the patterns of droplet deformation as well as the thermal distribution.

Дослідження періодичної вісесиметричної течії в’язкопружної рідини по циліндричній трубці

A generalized Womersley model of a nonstationary axisymmetric flow of a viscous incompressible fluid through a tube of circular cross-section to periodic pressure fluctuations at the inlet of the tube is obtained due for the case of a fluid with complicated rheology. The rheological parameters of the fluid are viscosity and four relaxation coefficients for strains and stresses of the first and second order. Such rheology is proper to the non-Newtonian viscoelastic fluids with mesostructure, namely technical and biological micro/ nanofluids. It was shown that with the increase of the relaxation coefficients of the first/second order the flow rate, the average and maximum velocities decrease/increase, accordingly. Simultaneous changes in these parameters can lead to complex changes in the velocity profile, especially for higher harmonics. The studied regularities can explain the deviations of the flow parameters of different micro/nanofluids from the values predicted by the classical Womersley solution for a homogeneous Newtonian fluid, which does not take into account viscous dissipation during the rearrangement of the fluid mesostructure.

Estimates of the evolution of small perturbations in the radial spread (drain) of a viscous ring

This paper studies the evolution of small perturbations in the kinematic and dynamic characteristics of the radial flow of a flat ring filled with a homogeneous Newtonian fluid or an ideal incompressible fluid. When the flow rate is specified as a function of time, the main motion is completely determined by the incompressibility condition regardless of the properties of the medium. A biparabolic equation for the stream function with four homogeneous boundary conditions which simulate adhesion to the expanding (contracting) walls of the ring is derived. Upper bounds for the perturbation are obtained using the method of integral relations for quadratic functionals. The case of an exponential decay of initial perturbations is considered in a finite or infinite time interval. The admissibility of the inviscid limit in this problem is proved, and upper and lower bounds for this limit are estimated.

Scalings for unsteady natural convection boundary layers on a vertical plate at time-dependent temperature

In this paper, a scaling analysis using a simple three-region structure was used to develop scalings for the unsteady natural convection boundary layer (NCBL) of a homogeneous Newtonian fluid with Pr>1 adjacent to a finite vertical plate evenly heated with a time-varying sinusoidal temperature, where Pr is the Prandtl number. Three distinct sub-stages are identified in the heating stage, i.e., a start-up stage, a transitional stage, and a quasi-steady stage. After the heating stage, there is a very short cooling stage, in which a double thermal boundary layer structure is developed, which leads to a new, thinner thermal boundary layer adjacent to the plate co-existing with the original thermal boundary layer. A series of scalings are developed for the thermal and viscous boundary thicknesses, the maximum vertical velocity within the boundary layer, and the Nusselt number which are the major parameters representing the flow behavior, in terms of the governing parameters of the flow, i.e., the Rayleigh number Ra, Pr, and the dimensionless natural frequency of the time-varying sinusoidal temperature at various flow development stages. These scalings are tested by full numerical solutions of the governing equations and are shown to, in general, provide an accurate description of the flow.

Local Oscillatory Rheology from Echography

Local Oscillatory Rheology from Echography (LORE) consists in a traditional rheology experiment synchronized with high-frequency ultrasonic imaging which gives access to the local material response to oscillatory shear. Besides classical global rheological quantities, this method provides quantitative time-resolved information on the local displacement across the entire gap of the rheometer. From the local displacement response, we compute and decompose the local strain in its Fourier components and measure the spatially-resolved viscoelastic moduli. After benchmarking our method on homogeneous Newtonian fluids and soft solids, we demonstrate that this technique is well suited to characterize spatially heterogeneous samples, wall slip, and the emergence of nonlinearity under large amplitude oscillatory stress in soft materials.

Modeling of Blood Flow in a Constricted Porous Vessel Under Magnetic Environment: An Analytical Approach

A theoretical investigation concerning the effect of arterial constriction on the flow of blood through a porous vessel in the presence of externally applied magnetic field has been carried out. In this study blood is assumed to be homogeneous Newtonian fluid flowing through a large blood vessel. In order to solve the problem, Adomian’s decomposition method is employed for obtaining its analytical solution. The analytical expressions for stream function, axial velocity component, wall shear stress are obtained and the corresponding numerical solutions for a specific set of dimensionless parameters have shown graphically. The results obtained for different values of the parameters show that the flow is appreciably influenced by the presence of magnetic field as well as the porosity of fluid medium. Thus the method developed here can capture small changes in the complex flow domain.

Scalings for unsteady natural convection boundary layers on an evenly heated plate with time-dependent heating flux

It is of fundamental significance, especially with regard to application, to fully understand the flow behavior of unsteady natural convection boundary layers on a vertical plate heated by a time-dependent heat flux. Such an understanding is currently scarce. In this paper, the scaling analysis by Lin et al. [Phys. Rev. E 79, 066313 (2009)] using a simple three-region structure for the unsteady natural convection boundary layer of a homogeneous Newtonian fluid with Pr>1 under isothermal heating was substantially extended for the case when the heating is due to a time-varying sinusoidal heat flux. A series of scalings was developed for the thermal boundary thickness, the plate temperature, the viscous boundary thicknesses, and the maximum vertical velocity within the boundary layer, which are the major parameters representing the flow behavior, in terms of the governing parameters of the flow, i.e., the Rayleigh number Ra, the Prandtl number Pr, and the dimensionless natural frequency f(n) of the time-varying sinusoidal heat flux, at the start-up stage, at the transition time scale which represents the ending of the start-up stage and the beginning of the transitional stage of the boundary-layer development, and at the quasi-steady stage. These scalings were validated by comparison to 10 full numerical solutions of the governing equations with Ra, Pr, and f(n) in the ranges 10(6)≤Ra≤10(9), 3≤Pr≤100, and 0.01≤f_{n}≤0.1 and were shown in general to provide an accurate description of the flow at different development stages, except for high-Pr runs in which a further, although weak, Pr dependence is present, which cannot be accurately predicted by the current scaling analysis using the simple three-region structure, attributed to the non-boundary-layer nature of the velocity field with high-Pr fluids. Some scalings at the transition time scale and at the quasi-steady stage also produce noticeable deviations from the numerical results when f(n) is reduced, indicating that there may be a further f(n) dependence of the scalings which also cannot be accurately predicted by the current scaling analysis.

The dam-break problem for concentrated suspensions of neutrally buoyant particles

AbstractThis paper addresses the dam-break problem for particle suspensions, that is, the flow of a finite volume of suspension released suddenly down an inclined flume. We were concerned with concentrated suspensions made up of neutrally buoyant non-colloidal particles within a Newtonian fluid. Experiments were conducted over wide ranges of slope, concentration and mass. The major contributions of our experimental study are the simultaneous measurement of local flow properties far from the sidewalls (velocity profile and, with lower accuracy, particle concentration) and macroscopic features (front position, flow depth profile). To that end, the refractive index of the fluid was adapted to closely match that of the particles, enabling data acquisition up to particle volume fractions of 60 %. Particle migration resulted in the blunting of the velocity profile, in contrast to the parabolic profile observed in homogeneous Newtonian fluids. The experimental results were compared with predictions from lubrication theory and particle migration theory. For solids fractions as large as 45 %, the flow behaviour did not differ much from that of a homogeneous Newtonian fluid. More specifically, we observed that the velocity profiles were closely approximated by a parabolic form and there was little evidence of particle migration throughout the depth. For particle concentrations in the 52–56 % range, the flow depth and front position were fairly well predicted by lubrication theory, but taking a closer look at the velocity profiles revealed that particle migration had noticeable effects on the shape of the velocity profile (blunting), but had little impact on its strength, which explained why lubrication theory performed well. Particle migration theories (such as the shear-induced diffusion model) successfully captured the slow evolution of the velocity profiles. For particle concentrations in excess of 56 %, the macroscopic flow features were grossly predicted by lubrication theory (to within 20 % for the flow depth, 50 % for the front position). The flows seemed to reach a steady state, i.e. the shape of the velocity profile showed little time dependence.

Granular suspension avalanches. I. Macro-viscous behavior

We experimentally studied the flow behavior of a fixed volume of granular suspension, initially contained in a reservoir and released down an inclined flume. Here “granular suspension” refers to a suspension of non-Brownian particles in a viscous fluid. Depending on the solids fraction, density mismatch, and particle size distribution, a wealth of behaviors can be observed. Here we report and interpret results obtained with granular suspensions, which consisted of neutrally buoyant particles with a solids fraction (ϕ = 0.575–0.595) close to the maximum random packing fraction (estimated at ϕm = 0.625). The particles had the same refractive index as the fluid, which made it possible to measure the velocity profiles inside the moving bulk and far from the sidewalls. Additional information such as the front position and the flow depth was also recorded. Three regimes were observed. At early times, the flow features were reminiscent of homogeneous Newtonian fluids (e.g., the same dependence of the front position on time). At later times, the free surface became more and more bumpy as fractures developed within the bulk. This fracture process ultimately gave rise to a stick-slip regime, in which the suspension moved intermittently. In this paper, we focus on the first regime referred to as the macro-viscous regime. Although the bulk flow properties looked like those of Newtonian fluids, the internal dynamics were much richer.

CFD Modelling of Abdominal Aortic Aneurysm on Hemodynamic Loads Using a Realistic Geometry with CT

The objective of this study is to find a correlation between the abdominal aortic aneurysm (AAA) geometric parameters, wall stress shear (WSS), abdominal flow patterns, intraluminal thrombus (ILT), and AAA arterial wall rupture using computational fluid dynamics (CFD). Real AAA 3D models were created by three-dimensional (3D) reconstruction of in vivo acquired computed tomography (CT) images from 5 patients. Based on 3D AAA models, high quality volume meshes were created using an optimal tetrahedral aspect ratio for the whole domain. In order to quantify the WSS and the recirculation inside the AAA, a 3D CFD using finite elements analysis was used. The CFD computation was performed assuming that the arterial wall is rigid and the blood is considered a homogeneous Newtonian fluid with a density of 1050 kg/m3 and a kinematic viscosity of 4 × 10−3 Pa·s. Parallelization procedures were used in order to increase the performance of the CFD calculations. A relation between AAA geometric parameters (asymmetry index (β), saccular index (γ), deformation diameter ratio (χ), and tortuosity index (ε)) and hemodynamic loads was observed, and it could be used as a potential predictor of AAA arterial wall rupture and potential ILT formation.

Numerical Simulation of Temperature profile in New Reactor with Homogeneous Newtonian Fluid

Numerical Simulation of Temperature profile in New Reactor with Homogeneous Newtonian Fluid

Biomagnetic fluid flow in a driven cavity

In this study, the fundamental problem of the biomagnetic fluid flow in a lid driven cavity under the influence of a steady localized magnetic field is studied. The mathematical model used for the formulation of the problem is consistent with the principles of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). The biomagnetic fluid is considered as a homogeneous Newtonian fluid and is treated as an electrically conducting magnetic fluid which also exhibits magnetization. A known biomagnetic fluid which exhibits such magnetic properties is blood. For the numerical solution of the problem, which is described by a coupled, non linear system of PDEs, with appropriate boundary conditions, the SIMPLE algorithm is used. The solution is obtained by the development of a numerical methodology using finite volumes on a staggered, properly stretched, grid. Results concerning the velocity indicate that the presence of the magnetic field influences considerably the flow field.

Simulation of Homogeneous Newtonian Fluid in the New Reactor under Turbulent flow

Simulation of Homogeneous Newtonian Fluid in the New Reactor under Turbulent flow

How Malaria Parasites Reduce the Deformability of Infected Red Blood Cells

The pathogenesis of malaria is largely due to stiffening of the infected red blood cells (RBCs). Contemporary understanding ascribes the loss of RBC deformability to a 10-fold increase in membrane stiffness caused by extra cross-linking in the spectrin network. Local measurements by micropipette aspiration, however, have reported only an increase of ∼3-fold in the shear modulus. We believe the discrepancy stems from the rigid parasite particles inside infected cells, and have carried out numerical simulations to demonstrate this mechanism. The cell membrane is represented by a set of discrete particles connected by linearly elastic springs. The cytosol is modeled as a homogeneous Newtonian fluid, and discretized by particles as in standard smoothed particle hydrodynamics. The malaria parasite is modeled as an aggregate of particles constrained to rigid-body motion. We simulate RBC stretching tests by optical tweezers in three dimensions. The results demonstrate that the presence of a sizeable parasite greatly reduces the ability of RBCs to deform under stretching. With the solid inclusion, the observed loss of deformability can be predicted quantitatively using the local membrane elasticity measured by micropipettes.

INFLUENCE OF SLIP VELOCITY ON BLOOD FLOW THROUGH AN ARTERY WITH PERMEABLE WALL: A THEORETICAL STUDY

A theoretical investigation concerning the influence of slip velocity on the flow of blood through an artery having its wall permeable has been carried out. Here blood is treated as a homogeneous Newtonian fluid. The flow is characterized by three parameters: β the ratio of radius to length of the arterial segment, Re the characteristic Reynolds number associated with the pressure outside the arterial segment and ϵ the filtration coefficient. The problem has been solved by the use of a perturbation technique. ϵ is considered to be very small, ensuring the validity of the perturbation method. The computed numerical results are presented graphically to depict the variations in velocity, volumetric flow rate, wall shear stress and flow resistance.

Haemodynamic imaging of thoracic stent-grafts by computational fluid dynamics (CFD): presentation of a patient-specific method combining magnetic resonance imaging and numerical simulations

In the last decade, there was been increasing interest in finding imaging techniques able to provide a functional vascular imaging of the thoracic aorta. The purpose of this paper is to present an imaging method combining magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) to obtain a patient-specific haemodynamic analysis of patients treated by thoracic endovascular aortic repair (TEVAR). MRI was used to obtain boundary conditions. MR angiography (MRA) was followed by cardiac-gated cine sequences which covered the whole thoracic aorta. Phase contrast imaging provided the inlet and outlet profiles. A CFD mesh generator was used to model the arterial morphology, and wall movements were imposed according to the cine imaging. CFD runs were processed using the finite volume (FV) method assuming blood as a homogeneous Newtonian fluid. Twenty patients (14 men; mean age 62.2years) with different aortic lesions were evaluated. Four-dimensional mapping of velocity and wall shear stress were obtained, depicting different patterns of flow (laminar, turbulent, stenosis-like) and local alterations of parietal stress in-stent and along the native aorta. A computational method using a combined approach with MRI appears feasible and seems promising to provide detailed functional analysis of thoracic aorta after stent-graft implantation. • Functional vascular imaging of the thoracic aorta offers new diagnostic opportunities • CFD can model vascular haemodynamics for clinical aortic problems • Combining CFD with MRI offers patient specific method of aortic analysis • Haemodynamic analysis of stent-grafts could improve clinical management and follow-up.

Investigation of Biomagnetic Fluid Flow Under Nonuniform Magnetic Fields

Electromagnetic fields have many applications in medical science. It is essential to couple the ferrohydrodynamic (FHD) and magnetohydrodynamic (MHD) principles when magnetic fields are applied to blood as a biomagnetic fluid. The purpose of the current study is to investigate the effect of a nonuniform magnetic field on blood flow. To solve the nonlinear governing equations, continuity and momentum equations, a computational fluid dynamics (CFD) code based on finite volume is utilized. The code considers blood as a homogeneous Newtonian fluid. It also takes into account the magnetization and electrical conductivity properties of blood. The results show that for low Reynolds number the blood velocity shape changes near the magnetic source. In addition, blood pressure is maximum near the magnetic field and decreases when it is away from it. In addition, the wall shear stress, an important factor, increases rapidly near the magnetic source, especially when a high-gradient magnetic field is used.

Existence of Proper Weak Solutions to the Navier-Stokes-Fourier System

The existence of proper weak solutions of the Cauchy problem constituted by the Navier-Stokes-Fourier system which characterizes the incompressible homogeneous Newtonian fluids under thermal effects is studied. We call proper weak solutions such weak solutions that verify some local energy inequalities in analogy with the suitable weak solutions for the Navier-Stokes equations.

An efficient numerical method for the equations of steady and unsteady flows of homogeneous incompressible Newtonian fluid

In the present paper, we present some numerical methods to solve the equations of steady and unsteady flows, such as those in the microcirculatory bed and large blood vessels (arteries and veins), respectively. In the case of steady flows, the method does not need neither any boundary conditions on pressure nor any small parameter, and the main computation consists of solving some Poisson equations. In the case of unsteady flows, the scheme uses a consistent Neumann boundary condition for the pressure Poisson equation. At each time step, a Poisson and heat equation are solved for the pressure and each velocity component, respectively. The accuracy and efficiency of scheme are checked by a set of numerical tests.

A sufficiency class for global (in time) solutions to the 3D Navier–Stokes equations

Let Ω be an open domain of class C 2 contained in R 3 , let L 2 ( Ω ) 3 be the Hilbert space of square integrable functions on Ω and let H [ Ω ] ≔ H be the completion of the set, { u ∈ ( C 0 ∞ [ Ω ] ) 3 ∣ ∇ ⋅ u = 0 } , with respect to the inner product of L 2 ( Ω ) 3 . A well-known unsolved problem is that of the construction of a sufficient class of functions in H which will allow global, in time, strong solutions to the three-dimensional Navier–Stokes equations. These equations describe the time evolution of the fluid velocity and pressure of an incompressible viscous homogeneous Newtonian fluid in terms of a given initial velocity and given external body forces. In this paper, we use the analytic nature of the Stokes semigroup to construct an equivalent norm for H , which provides strong bounds on the nonlinear term. This allows us to prove that, under appropriate conditions, there exists a number u + , depending only on the domain, the viscosity, the body forces and the eigenvalues of the Stokes operator, such that, for all functions in a dense set D contained in the closed ball B ( Ω ) ≕ B of radius 1 2 u + in H , the Navier–Stokes equations have unique, strong, solutions in C 1 ( ( 0 , ∞ ) , H ) .