Newtonian Model Research Articles

Effects of stenosis and aneurysm on blood flow in stenotic-aneurysmal artery

Blood is indeed a suspension of the different type of cells along with shear thinning, yield stress and viscoelastic characteristics, which can be expressed by Newtonian and a lot of non-Newtonian models. Choosing Newtonian fluid as a sample, an unsteady solver for Newtonian fluid is constructed to determine the transient flow of blood in the obscure region. In this probe, the computational unsteady flow of blood in artery with aneurysm and symmetric stenosis has been considered, which is novelty of current research. The results of this investigation can be applied to detect stenotic-aneurysmal diseases and enhance knowledge of the stenotic-aneurysmal artery, which may increase the understanding of medical science. The blood artery is modeled as a circular tube having a 0.3-m radius and a 2-m length along the horizontal axis. The velocity of blood is taken at 0.12 ms−1 so that the geometry satisfies the characteristics of the blood vessel. The governing mass and momentum equations are then solved by finite difference technique of discretization. In this research, important variations in blood pressure and velocity at stenosis and aneurysms in the artery are found. The significant influences on blood flow of the stenotic-aneurysmal artery for pressure and velocity profiles of blood are displayed graphically for the Newtonian model.

Electro-osmotic effect on the heat and mass transfer of a viscoelastic nanofluid flow in a curved channel

For the past two decades, nanofluids have become the interest of researchers and engineers because of their thermo-physical features. The aim of the current investigation is to investigate the thermal behavior of peristaltically supporting viscoelastic tiny particles endorsed by electro-osmotic force. The Debye-Huckel linearization scheme and zero Reynolds assumptions are used to simplify the governing equations. The current formulation deals with the peristaltic motion of nanofluid in a two-dimensional curved channel. The complex arrangement of sinusoidal waves is used to enhance the pumping performance at the boundary walls. In the present analysis, the Buongiorno formulation is used for nanofluids. The Jeffrey fluid model is used in the current study as a viscoelastic fluid due to its both viscous and elastic features. The numerical solution is obtained using the NDsolve procedure. The graphs of flow features, such as stream function, axial velocity, temperature field, mass concentration, and electric potential function are plotted for various rheological parameters. Quantitative results related to the heat transfer coefficient and Sherwood number for different values of flow parameters are also provided. The asymmetry nature is observed in the diagram of axial velocity due to the curved shape of the flow regime. The mass concentration is enhanced (reduced) by aggregating thermal (Brownian) motion parameter. The temperature and mass concentration are enhanced by increasing Prandtl and Eckert numbers. Comparison between Newtonian and viscoelastic model is also argued in the current formulation. This study gives information of biological fluids flow relevance to micro-medical devices, nanoscale devices, electro-osmotic separation devices and complex pumps via peristaltic pumping.

Non‐Newtonian blood flow with magnetic nanoparticles in a W‐shaped stenosed arterial segment: A numerical study

AbstractFlow of blood, infused with magnetic nanoparticles, in a W‐shaped stenosed human arterial segment is studied numerically using a realistic non‐Newtonian blood rheology model. It is observed that the Newtonian model predicts less time to reach a steady state than the non‐Newtonian blood rheology model. An increased drug retention time at the target site with an increase in nanoparticle concentration is predicted. Detailed simulations further reveal that the skin friction coefficient does not increase significantly with the increase in nanoparticle concentration. Hence, it is anticipated from our study that the infusion of drug‐carrying nanoparticles in blood flow does not excessively enhance wall shear stress that may lead to arterial wall damage. An overall increase in heat transfer rates and wall shear stress at the stenosed section is seen with an increase in Reynolds number. The present study provides valuable information for designing computer‐assisted drug delivery systems.

Carbon–oxygen ultra-massive white dwarfs in general relativity

ABSTRACT We employ the La Plata stellar evolution code, lpcode, to compute the first set of constant rest-mass carbon–oxygen ultra-massive white dwarf evolutionary sequences for masses higher than 1.29 M⊙ that fully take into account the effects of general relativity on their structural and evolutionary properties. In addition, we employ the lp-pul pulsation code to compute adiabatic g-mode Newtonian pulsations on our fully relativistic equilibrium white dwarf models. We find that carbon–oxygen white dwarfs more massive than 1.382 M⊙ become gravitationally unstable with respect to general relativity effects, being this limit higher than the 1.369 M⊙ we found for oxygen–neon white dwarfs. As the stellar mass approaches the limiting mass value, the stellar radius becomes substantially smaller compared with the Newtonian models. Also, the thermo-mechanical and evolutionary properties of the most massive white dwarfs are strongly affected by general relativity effects. We also provide magnitudes for our cooling sequences in different passbands. Finally, we explore for the first time the pulsational properties of relativistic ultra-massive white dwarfs and find that the period spacings and oscillation kinetic energies are strongly affected in the case of most massive white dwarfs. We conclude that the general relativity effects should be taken into account for an accurate assessment of the structural, evolutionary, and pulsational properties of white dwarfs with masses above ∼1.30 M⊙.

The effects of non-Newtonian blood modeling and pulsatility on hemodynamics in the food and drug administration's benchmark nozzle model.

Computational fluid dynamics (CFD) is an important tool for predicting cardiovascular device performance. The FDA developed a benchmark nozzle model in which experimental and CFD data were compared, however, the studies were limited by steady flows and Newtonian models. Newtonian and non-Newtonian blood models will be compared under steady and pulsatile flows to evaluate their influence on hemodynamics in the FDA nozzle. CFD simulations were validated against the FDA data for steady flow with a Newtonian model. Further simulations were performed using Newtonian and non-Newtonian models under both steady and pulsatile flows. CFD results were within the experimental standard deviations at nearly all locations and Reynolds numbers. The model differences were most evident at Re =500, in the recirculation regions, and during diastole. The non-Newtonian model predicted blunter upstream velocity profiles, higher velocities in the throat, and differences in the recirculation flow patterns. The non-Newtonian model also predicted a greater pressure drop at Re =500 with minimal differences observed at higher Reynolds numbers. An improved modeling framework and validation procedure were used to further investigate hemodynamics in geometries relevant to cardiovascular devices and found that accounting for blood's non-Newtonian and pulsatile behavior can lead to large differences in predictions in hemodynamic parameters.

P78: Risk Assessment of Thrombus Formation in the left Ventricle during VAD Support using computational Models. “How simple is too simple?”

Background: Thrombus formation is a major complication in LVAD treatment, and is influenced by intraventricular blood flow dynamics. Many numerical studies have investigated left ventricular (LV) blood flow patterns with LVAD support using various assumptions which are needed to simplify the highly complex physiological processes for a computational environment. Until now, these various assumptions have not been investigated systematically. This study aimed to assess the effect of modelling assumptions on the risk assessment of thrombus formation in the LV during VAD support. Methods: A patient-specific LV and left atrium (LA) was modelled from CT data of a VAD patient. The impact of the turbulence model (laminar vs turbulent), fluid model (Newtonian vs Carreau approach vs Multiphase approach), model geometry (cylindrical LA vs segmented LA, absent MV vs present MV) and boundary conditions (continuous inflow vs periodic inflow) were evaluated systematically, resulting in eleven simulation set ups in total (Figure 1). They were compared quantitatively over 5 s simulation time by the difference of averaged velocities, residence time, washout, turbulent kinetic energy and computing time for the various simulation models. Results: Geometrical LA changes resulted in the biggest quantitative impact, with a 30.7% lower residence time with a cylindrical LA compared to the segmented LA. The comparison of a laminar and a turbulent flow showed a 26.8 % lower residence time in the laminar flow model compared to a model with turbulent flow. The most significant difference in computational time was found when comparing a Newtonian fluid model and a multiphase approach: The simulation with a multiphase approach took 81 core hours longer than the model with a Newtonian fluid model. Conclusion: The recommended model for achieving a low computing time with minimized loss of accuracy compared to current numerical models assumes a turbulent viscous model with Newtonian-modelled blood, a segmented left atrium, a mitral valve geometry, and pulsatile inflow.Figure 1. Simplification study: Steps and result.

Computational analysis of yield stress buildup and stability of deposited layers in material extrusion additive manufacturing

This paper investigates the stability of deformable layers produced by material extrusion additive manufacturing. A Computational Fluid Dynamics (CFD) model is developed to predict the deposition flow of viscoplastic materials such as ceramic pastes, thermosets, and concrete. The viscoplastic materials are modelled with the Bingham rheological equations and implemented with a generalized Newtonian fluid model. The developed CFD model applies a scalar approach to differentiate the rheology of two layers in order to capture the deposition of a wet layer onto a semi solidified printed layer (i.e., wet-on-semisolid printing). The semi solidification is modelled by a yield stress buildup. The cross-sectional shapes of the deposited layers are predicted, and the relative deformation of the first layer is studied for different yield stress buildups and processing conditions such as printing- and extrusion-speed, layer height, and nozzle diameter. The results of the CFD model illustrate that the relative deformation of the first layer decreases non-linearly with an increase in yield stress, and that stable prints can be obtained when taking into account the semi solidification. Furthermore, it is found that the deformation is dependent on a non-trivial interplay between the extrusion pressure, the shape of the cross-section, and the contact area between the layers. Finally, the results highlight which process conditions can be changed with benefit in order to limit the requirement on the yield stress buildup and still provide stable prints.

Application of Newtonian approximate model to LIGO gravitational wave data processing

With the observation of a series of ground-based laser interferometer gravitational wave (GW) detectors such as LIGO and Virgo, nearly 100 GW events have been detected successively. At present, all detected GW events are generated by the mergers of compact binary systems and are identified through the data processing of matched filtering. Based on matched filtering, we use the GW waveform of the Newtonian approximate (NA) model constructed by linearized theory to match the events detected by LIGO and injections to determine the coalescence time and utilize the frequency curve for data fitting to estimate the parameters of the chirp masses of binary black holes (BBHs). The average chirp mass of our results is , which is very close to provided by GWOSC. In the process, we can analyze LIGO GW events and estimate the chirp masses of the BBHs. This work presents the feasibility and accuracy of the low-order approximate model and data fitting in the application of GW data processing. It is beneficial for further data processing and has certain research value for the preliminary application of GW data.

Computational fluid dynamics based Taguchi analysis on shear stress in microfluidic cerebrovascular channels.

The cerebrovascular blood vessels feed necessary agents such as oxygen, glucose, and so forth. to the brain which maintains the smooth functioning of the human body. However, the blood-brain barrier as a vascular border restricts the entry of drugs that can be necessary for the treatment of neurological disorders. The fluid shear stress in the cerebrovascular blood vessels may regulate the drug delivery in the interface between the cerebrovascular blood vessels and the brain. The intensity of influence by various factors that affects the shear stress in the cerebrovascular blood vessels is scarcely addressed in the present study. A hybrid approach of computational fluid dynamics and Taguchi analysis is proposed to evaluate the influence of various geometrical and operating factors on the shear stress in the microfluidic cerebrovascular channel. Furthermore, the non-Newtonian behavior of blood flow is considered to evaluate the shear stress in the microfluidic cerebrovascular channel. The Newtonian and six non-Newtonian fluids models of Carreau, Carreau-Yasuda, Casson, Cross, Ostwald-de Waele, and Herschel-Bulkley are numerically tested under various conditions of the flow rate, width, and height of the channel to find the viscosity influence on the shear stress. The Taguchi analysis consisting of range and variance analyses is applied to the L16 orthogonal array to evaluate the effect of various factors on shear stress in terms of influence order, range, F value, and percentage contribution. The parameters for the considered six non-Newtonian fluid models are proposed to accurately map the viscosity behavior with shear strain compared to the actual blood flow behavior. The Newtonian, Carreau, and Carreau-Yasuda non-Newtonian fluid models are found accurately with maximum errors between the experimental and numerical shear stress results as 2.17%, 1.30%, and 1.48%, respectively. The shear stress decreases with an increase in the width and height of the channel and a decrease in the viscosity for all flow rates. The porosity is evaluated as a highly influential factor followed by the flow rate, width, and height of the channel in decreasing order based on their effects on the shear stress. The modified shear stress equation is proposed with an accuracy of 0.96 by integrating the effect of porosity in addition to width, height, flow rate, and viscosity. The in-vitro microfluidic cerebrovascular model could be designed and manufactured based on the proposed results on influence order, F value, and percentage contribution of various factors in direction of achieving the in-vivo level shear stress.

A passive control of Casson hybrid nanofluid flow over a curved surface with alumina and copper nanomaterials: A study on sodium alginate-based fluid

Scientists are paying close attention to Casson fluids due to their remarkable industrial and technical applications. Among the non-Newtonian substances, Casson fluid is one of the most significant types. Generally, the viscosity becomes zero at infinity shear rate for a shear-diminishing substance with zero-shear rate. In this work, the flow of a sodium alginate–based Casson hybrid nanofluid composed of copper and aluminum oxide nanoparticles is studied. The hybrid nanofluid flow is considered to be magnetically influenced and chemically reactive. Additionally, the effects of the heat source, non-Newtonian heating, thermophoretic, Brownian motion, and activation energy are considered. It is anticipated that stretching curved surface is thermally convective and that there is no mass flow. The mathematical formulation is given in the form of PDEs, which are then converted into ODEs by using suitable similarity variables. The HAM and bvp4c MATLAB function is applied on the converted ODEs to accomplish the semi-analytical and numerical solutions of the modeled equations. By contrasting the new data with those that have already been published, the correctness of current model is confirmed. According to the findings, the hybrid nanofluid over a flat surface resulted in enhancements in velocity, temperature, and concentration compared to its performance on a curved surface. The hybrid nanofluid demonstrated superior performance in terms of temperature, surface drag, concentration, and rate of heat transfer. Moreover, the velocity and temperature of the classical Newtonian model were observed to be higher on the flat surface in contrast to the curved surface. The streamlines become closer with the increasing magnetic factor, while the streamlines become farther apart with the increasing curvature parameter.

A coupled particle model with particle shifting technology for simulating transient viscoelastic fluid flow with free surface

In this work, the decoupled finite particle coupled with smoothed particle hydrodynamics (DFP-SPH) method is firstly developed to simulate the viscoelastic fluid flow with free surface. A particle shifting technology is introduced to eliminate the tensile instability and nonuniformity of fluid particles. The motivations and embodiments include: (a) the partial derivatives of physical quantities of velocity, density and viscoelastic stress are calculated based on multivariate Taylor series and dominated contributions from diagonal matrices, which avoid the inversion of encountered ill-conditioned matrices potentially and improve the precision of numerical approximation to a certain extent; (b) a particle shifting technology is added to remove the tensile instability and nonuniformity of fluid particles in the frame of proposed DFP-SPH, and the determination of free surface particles is also proceeded in nature; (c) the dynamic boundary particles possessing computational simplicity are introduced and adopted in the proposed method. A moderate uniformization is proposed to eliminate the spatial effect of nonphysical boundary layers. Subsequently, the accuracy, consistency and convergence of present method are investigated on some benchmarks of Newtonian and Oldroyd-B fluids with analytical solutions. The validity of particle shifting technology in DFP-SPH is verified and multiple inter miscible viscoelastic drops impacting on the rigid wall are simulated and analyzed numerically for the capacity of proposed method. The procedure of jet bulking is well demonstrated through using Newtonian and Oldroyd-B models at different Weissenberg numbers, which possesses flexible free surfaces and tangled interfaces of multifluid layers. Numerical results show that the coupled particle model has a good performance on the viscoelastic fluid flow with free surface.

Vessel-Specific Shear Stress Distribution and Heterogeneity in Angiogenic Rat Mesenteric Microvascular Networks

Fluid shear stress has been identified as an important player in regulating endothelial cell behaviors and angiogenesis, defined as the sprouting of new blood vessels from existing vessels. However, the correlative or functional linking of shear stress to vessel-specific endothelial cell dynamics requires a better understanding of the shear stress values at the capillary level in microvascular networks. Critical questions remain unanswered. What is the shear stress experienced by endothelial cells along capillaries? Do all capillaries experience similar shear stress magnitudes? Can variations in shear stress along different capillary segments explain vessel-specific responses? The objective of this project was to estimate shear stress values in regions of angiogenic microvascular networks. Rat mesenteric tissues were harvested from adult male Wistar rats post the stimulation of angiogenesis via 48-80 mast cell degranulation. Microvascular networks were identified by perfusion of a 40kDa fixable dextran prior to harvesting and immunolabelling for PECAM. Dextran presence identified perfused segments along the hierarchy of microvascular networks, which were characterized by increased vessel density indicative of angiogenesis. Representative network regions with arteriole input and venule output vessels were selected for analysis. Vessel segments were defined by adjacent nodes, and the measurements of lengths and diameter. Assuming an inlet pressure of 75 mmHg and outlet pressure of 10 mmHg, a network segmental Newtonian flow model was used to computationally estimate vessel-specific shear stresses and velocities. Viscosity was set to 4 cP and assumed to be constant. In the results, shear stresses along vascular segments in 3 medium microvascular regions ranged from 0.1 to 1114.3 dyne/cm2 (average = 81.3 ± 3.5 dyne/cm2), in 4 small regions ranged from 0.1 to 518.7 dyne/cm2 (average = 61 ± 3.4 dyne/cm2), and in 1 large region ranged from 0.003 to 2328.1 dyne/cm2 (average = 39.8 ± 1.6 dyne/cm2). For all regions, the highest shear stress values located at capillary segments, defined as vascular segments with diameters lower than 10 μm. As segment diameters increased, the matched maximum shear stresses decreased accordingly. Also, the high heterogeneity of shear stresses in capillaries indicates the possibility for segment-specific regulation. For 3 medium regions, shear stresses along proximal capillaries branching from arteriolar inlets to venular outlets were higher than stresses along capillaries in regions distal to inlets and outlets. The results highlight the variability of segment-specific shear stresses along capillaries in microvascular regions and motivate research looking into how endothelial cells respond to segment-specific microenvironment and regulation. This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Heat transfer analysis of the non-Newtonian polymer in the calendering process with slip effects

In this paper, a non-isothermal study of the calendering processes is presented using Carreau–Yasuda model along with nonlinear slip condition introduced at the upper roll surface. The flow equations for the problem are developed and converted into dimensionless form with the help of dimensionless variables and then finally simplified by a well-known lubrication approximation theory. The final equations are solved numerically using “bvp4c” to find stream function and velocity profiles, while the hybrid numerical method which is the combination of shooting and finite difference methods is used to solve the energy equation. Graphs show the impact of the concerned material parameters on various quantities of interest. The pressure distribution decreases with the increasing values of the slip parameter and Weissenberg number. The mechanical variables show an increasing trend with the increasing values of the slip parameter and Weissenberg number. The temperature distribution increases with an increase in the Brinkman number, while temperature shows declining trend near the roll surface with the increasing values of the slip parameter. The force separating the two rollers, total power input into both rolls, increase with the increasing values of the Weissenberg number and slip parameters. The results show that the Newtonian model predicts higher pressure in the nip zone than the Carreau–Yasuda model. It is interesting to note that for the case of shear thinning, the Carreau–Yasuda model predicts 30% less pressure in the nip region when compared to the Newtonian model.

Assessing the effect of manufacturing defects and non-Newtonian blood model on flow behaviors of additively manufactured Gyroid TPMS structures

In the field of medical engineering, Triply Periodic Minimal Surfaces (TPMS) structures have been studied widely owing to their physical attributes similar to those of human bones. Computational Fluid Dynamics (CFD) is often used to reveal the interaction between structural architectures and flow fields. Nevertheless, a comprehensive study on the effect of manufacturing defects and non-Newtonian behavior on the fluid responses in TPMS scaffolds is still lacking. Therefore, the present study fabricated Gyroid TPMS with four relative densities from 0.1 to 0.4. Non-destructive techniques were used to examine surface roughness and geometric deviation. We found that the manufacturing defects had a minor effect on fluid responses. The pressure drop comparison between defect-containing and defect-free models could be differed up to 7%. The same comparison for the average shear stress showed a difference up to 23%, in which greater deviation between both models was observed at higher relative density. On the contrary, the viscosity model played a significant role in flow prediction. By comparing the Newtonian model with Carreau-Yasuda non-Newtonian model, the resulting pressure drop and average wall shear stress from non-Newtonian viscosity could be higher than those of the Newtonian model by more than a factor of two. In addition, we matched the fluid-induced shear stress from both viscosity models with desirable ranges of shear stresses for tissue growth obtained from the literature. Up to 70% from the Newtonian model fell within the desirable range while the matching stress reduced to lower than 8% for the non-Newtonian results. Furthermore, by correlating geometric features with physical outputs, the geometric deviation was seen associated with surface curvature while the local shear stress revealed a strong correlation with inclination angle. Overall, the present work emphasized the importance of the viscosity model for CFD analysis of the scaffolds, especially when resulting fluid-induced wall shear stress is of interest. In addition, the geometric correlation has introduced the alternative consideration of structural architectures from local perspectives, which could assist the further comparison and optimization among different porous scaffolds in the future.

Correction of Stokes drag for non-Newtonian flow through pack of spheres

Non-Newtonian fluids have great relevance in a wide range of porous media applications, such as enhanced oil recovery and filtration processes. The estimation of the drag coefficient of power-law fluids flowing through simple porous media structures in the Stokes regime is typically modeled by adding a direct correction term to the Newtonian model. In this study, to calculate the non-dimensional drag for various fluid indices and volume fractions of packed spheres, extensive numerical simulations of the power-law fluid flow through single cubic, body-centered cubic, and face-centered cubic porous structures are conducted. The numerical results are used to develop a model function of the non-dimensional drag depending on the power-law fluid index and volume fraction of the sphere pack. Consequently, the drag force and coefficient of shear-thinning or shear-thickening fluid flowing through the investigated structures can be predicted. A correction is introduced for the Stokes drag correlation based on the generalized Reynolds number for non-Newtonian fluids. The results of the proposed model and numerical simulations are in excellent agreement with deviations not more than 1.2%. This implies that the modeled predictions are valid for all investigated structures.

Time‐dependent mixed convection of Prandtl–Eyring hybrid nanofluid flow over a vertical cone: Entropy analysis

AbstractThe current work is motivated by the rising applications of non‐Newtonian hybrid nanofluids and entropy optimization in large‐scale industries. The Prandtl–Eyring nanofluid model, one of the numerous non‐Newtonian fluid models, is developed using molecular theory rather than empirical formulas. This study investigates the mixed convection flow of Prandtl–Eyring nanofluids from a vertical conical surface. This problem's governing equations are highly nonlinear and linked. Mangler's nonsimilar transformations were used to obtain a nondimensional representation of the governing equations. The obtained equations were linearized and discretized using Quasilinearization and the implicit finite difference method. This study concludes that, compared to Newtonian fluids, Prandtl–Eyring fluids have reduced surface friction and fluid velocity. When comparing the Prandtl–Eyring hybrid nanofluid to the Newtonian hybrid nanofluid, we find that the latter improves energy transmission by about 11%. With the Prandtl–Eyring hybrid nanofluid model instead of the standard Newtonian model, entropy generation (EG) can be reduced. Energy transport efficiency is improved by changing the nanoparticles shape from spherical to lamina. Concisely at , the and boosted approximately by 29% and 17%, respectively, when shapes of the nanoparticles are changed from spherical to the lamina. The findings of heat transfer strength and surface friction coefficient are in excellent agreement with previously reported data.

Fatty acid profile and rheological behavior of annatto seed oil (Bixa orellana), cupuassu seed fat (Theobroma grandiflorum), and their blends

Annatto seed oil (ASO) and cupuassu seed fat (CSF) were combined at the ratios: 30:70, 50:50, and 70:30 (% w/w). Their fatty acid profile, nutritional quality, FTIR (Fourier Transform Infrared) spectra, and rheological behavior were evaluated. ASO increased the content of polyunsaturated fatty acids in the blends; whereas CSF conferred higher contents of monounsaturated fatty acids. The blends exhibited low atherogenicity and thrombogenicity indices, suggesting nutritional advantages. The Newtonian fluid behavior and FTIR results suggested that mixing ASO and CSF at different proportions did not affect the functional groups. ASO showed an activation energy value which indicated that this fat viscosity was more sensitive to temperature changes. The Newtonian model proved to be suitable to describe the behavior of samples, according to statistical fit parameters R2, χ2, and RSS. The resulting blends presented improved physicochemical properties and nutritional attributes, indicating their feasibility for the development of new products.

Effect of Significant Parameters on Squeeze Film Characteristics in Pathological Synovial Joints

Synovial joints are unique biological tribo-systems that allow for efficient mobility. Most of the synovial joint activities in the human body are accomplished due to the presence of synovial fluid. As a biological lubricant, synovial fluid lubricates the articular cartilage to minimize wear and friction. The key components of synovial fluid that give it its lubricating ability are lubricin, hyaluronic acid (HA), and surface-active phospholipids. Due to age and activities, synovial fluid and articular cartilages lose their properties, restricting synovial joint mobility and resulting in articular cartilage degradation, leading to the pathological synovial joint, which is a major cause of disability. In this context, synovial joint research remains significant. Even though synovial joint lubrication has been investigated, several problems linked to squeeze film lubrication need greater attention. The Newtonian model of squeeze film lubrication in synovial joints must be studied more extensively. This work aims to investigate squeeze film lubrication in diseased synovial joints. The lubrication and other properties of synovial fluid and the flow of synovial fluid in a diseased human knee joint are investigated theoretically in this work. We have investigated the effect of the synovial fluid viscosity and the effects of permeability and thickness of articular cartilage on squeeze film properties. Moreover, we have also investigated the effect of squeeze velocity and film thickness on the characteristics of the squeeze film formed between the articular cartilages of a diseased human knee joint. In this work, the articular cartilages were treated as a rough, porous material, and the geometry was approximated as parallel rectangular plates, while the synovial fluid flow is modeled as a viscous, incompressible, and Newtonian fluid. The modified Reynolds equation is obtained using the principles of hydrodynamic lubrication and continuum mechanics, and it is solved using the appropriate boundary conditions. The expressions for pressure distribution, load-bearing capacity, and squeezing time are then determined, and theoretical analysis for various parameters is conducted. Pressure is increased by squeeze velocity and viscosity, while it is decreased by permeability and film thickness, leading to an unhealthy knee joint and a reduction in knee joint mobility. The load capacity of the knee joint decreases with permeability and increases with viscosity and squeezing velocity, resulting in a reduction in the load-carrying capacity of the knee joint in diseased conditions. Synovial knee joint illness is indicated by increased pressure and squeeze time. The squeeze film properties of synovial joints are important for maintaining joint health and function. Joint diseases such as osteoarthritis, rheumatoid arthritis, and gout can affect the composition and production of synovial fluid, leading to changes in squeeze film properties and potentially causing joint damage and pain. Understanding these relationships can help in the development of effective treatments for joint diseases.

Mechanical characteristics of MHD of the non-Newtonian magnetohydrodynamic Maxwell fluid flow past a bi-directional convectively heated surface with mass flux conditions

In engineering and manufacturing industries, stretching flow phenomena have numerous real-world implementations. Real-world applications related to stretched flow models are metalworking, crystal growth processes, cooling of fibers, and plastics sheets. Therefore, in this work, the mechanical characteristics of the magnetohydrodynamics of the non-Newtonian Maxwell nanofluid flow through a bi-directional linearly stretching surface are explored. Brownian motion, thermophoresis, and chemical reaction impacts are considered in this analysis. Additionally, thermal convective and mass flux conditions are taken into consideration. The mathematical framework of the existing problem is constructed on highly non-linear partial differential equations (PDEs). Suitable similarity transformations are used for the conversion of partial differential equations into ordinary differential equations (ODEs). The flow problem is tackled with the homotopy analysis method, which is capable of solving higher-order non-linear differential equations. Different flow profiles against various flow parameters are discussed physically. Heat and mass transference mechanisms for distinct flow factors are analyzed in a tabular form. The outcomes showed that both primary and secondary velocities are the declining functions of magnetic and Maxwell fluid parameters. The heat transfer rate rises with the cumulative values of the Brownian motion and thermal Biot number. In addition, the mass transfer rate decreases with the rising Schmidt number, Brownian motion parameter, and chemical reaction parameter, while it increases with the augmenting thermophoresis parameter. It has been highlighted that streamlines in the current work for Maxwell and Newtonian models are in fact different from one another.

Study and modeling of the thrombosis of small cerebral aneurysms, with and without flow diverter, by the lattice Boltzmann method

Background and objectiveSmall cerebral aneurysms are currently commonly treated non-invasively by flow diverter device. These stents lead to thrombotic occlusion of the aneurysm soon after their placement. The purpose of this work is to model clotting into intracranial aneurysms with and without stents, using a non-Newtonian of blood behavior, and to investigate the importance of stent to generate desired thrombus in intracranial aneurysms. MethodThe description of blood flow is made by the Boltzmann lattice equations, while thrombosis is modeled by the "fluid age" model. The lattice Boltzmann method is a computational technique for simulating fluid dynamics. The method is based on a mesoscopic approach, where the fluid is represented by a set of particles that move and interact on a grid. The model for blood coagulation is described by lattice Boltzmann Method, and it doesn't take into account the complicated coagulation pathway, this main idea is developed using the model of residence time of blood: all fluid in the domain is assumed to be capable of clotting, given enough time. The fluid age is measured by a passive scalar using a transport equation, and the node coagulates if the fluid age increases enough. Three small aneurysms of different sizes and shapes with three stents of various porosities were used to test the ability of the model to predict thrombosis. The "occlusion rate" parameter is used to assess the effectiveness of the flow diverter device. ResultsFor the large aspect ratio factor, the occlusion is: 91% for flow diverter devise with seven struts. For medium aspect ratio, a rate of 80% is achieved. An occlusion rate of slightly more than 30% is obtained for very small aneurysms with low aspect ratio. The Newtonian model underestimates the volume of thrombosis generated. The difference in the prediction of the thrombosis volume between the Newtonian and no-Newtonian Carreau-Yasuda models is approximately 10%. ConclusionThe occlusion rate is proportional to the aspect ratio form factor. For the large and medium aspect ratio factors, the occlusion is satisfactory. Concerning very small aneurysms with low aspect ratio, aneurysm occlusion is low. This rate can be improved to almost complete occlusion if the flow diverter device is doubled. The generality of the model suggests its extensibility toward any other type of thrombosis (stenosis, thrombosis in aortic aneurysms).