We show that the energy norm of weak solutions to Vlasov equation coupled with a shear thickening fluid on the whole space has a decay rate the energy norm $E(t) \leq {C}/{(1+t)^{\alpha }}, \forall t \geq 0$ for $\alpha \in (0,3/2)$.

In this study, we compare different diffuse and sharp interface schemes of direct-forcing immersed boundary — thermal lattice Boltzmann method (IB-TLBM) for non-Newtonian flow over a heated circular cylinder. Both effects of the discrete lattice and the body force on the momentum and energy equations are considered, by applying the split-forcing Lattice Boltzmann equations. A new technique based on predetermined parameters of direct forcing IB-TLBM is presented for computing the Nusselt number. The study covers both steady and unsteady regimes (20<Re<80) in the power-law index range of 0.6<n <1.4, encompassing both shear-thinning and shear-thickening non-Newtonian fluids. The numerical scheme, hydrodynamic approach and thermal parameters of different interface schemes are compared in both steady and unsteady cases. It is found that the sharp interface scheme is a suitable and possibly competitive method for thermal-IBM in terms of accuracy and computational cost.

Newtonian and non-Newtonian dispersed phase droplet formation in non-Newtonian continuous phase in T-junction and cross junction microchannels are investigated by the immiscible lattice BGK model. The effects of the non-Newtonian fluid power-law exponent, viscosity and interfacial tension on the generation of the droplet are studied. The final droplet size, droplet generation frequency, and detachment point of the droplet change with the power-law exponent. The results reveal that it is necessary to take into account the non-Newtonian rheology instead of simple Newtonian fluid assumption in numerical simulations. The present analysis also demonstrates that the lattice Boltzmann method is of potential to investigate the non-Newtonian droplet generation in multiphase flow.

Understanding blood flow in human body’s cerebral arterial system is of both fundamental and practical significance for prevention and treatment of vascular diseases. The mechanism and treatment for the growth of daughter aneurysm on its mother aneurysm are not yet fully understood. Themain purpose of the present paper is to elucidate the relationships between hemodynamics and the genesis, growth, subsequent rupture of the mother and daughter aneurysm on the cerebral vascular. The intensified stents with different porosities and structures are investigated to reduce the wall shear stress and pressure of mother and daughter aneurysm. The simulation is based on a lattice Boltzmann modeling of non-Newtonian blood flow. A novel stent structurewith “dense in front and sparse in rear” is proposed,which is verified to have good potential to reduce the wall shear stress of both mother and daughter aneurysm. The simulation is based on a lattice Boltzmann modeling of non-Newtonian blood flow. A novel stent structurewith “dense in front and sparse in rear” is proposed,which is verified to have good potential to reduce the wall shear stress of both mother and daughter aneurysm.

A stenosis is the narrowing of the artery, this narrowing is usually the result of theformation of an atheromatous plaque infiltrating gradually the artery wall, forming a bumpin the ductus arteriosus. This arterial lesion falls within the general context ofatherosclerotic arterial disease that can affect the carotid arteries, but also thearteries of the heart (coronary), arteries of the legs (PAD), the renal arteries... It cancause a stroke (hemiplegia, transient paralysis of a limb, speech disorder, sailing beforethe eye). In this paper we study the blood-plaque and blood-wall interactions using afluid-structure interaction model. We first propose a 2D analytical study of thegeneralized Navier-Stokes equations to prove the existence of a weak solution forincompressible non-Newtonian fluids with non standard boundary conditions. Then, coupled,based on the results of the theoretical study approach is given. And to form a realisticmodel, with high accuracy, additional conditions due to fluid-structure coupling areproposed on the border undergoing inetraction. This coupled model includes (a) a fluidmodel, where blood is modeled as an incompressible non-Newtonian viscous fluid, (b) asolid model, where the arterial wall and atherosclerotic plaque will be treated as nonlinear hyperelastic solids, and (c) a fluid-structure interaction (FSI) model whereinteractions between the fluid (blood) and structures (the arterial wall and atheromatousplaque) are conducted by an Arbitrary Lagrangian Eulerian (ALE) method that allowsaccurate fluid-structure coupling.

Stent placement is considered as a promising and minimally invasive technique to prevent rupture of aneurysm and favor coagulation mechanism inside the aneurysm. Many scholars study the effect of the stent on blood flow in cerebral aneurysm by numerical simulations, and usually regard blood as the Newtonian fluid, blood, however, is a kind of non-Newtonian fluid in practice. The main purpose of the present paper is to investigate the effect of non-Newtonian behavior on the hemodynamic characteristics of blood flow in stented cerebral aneurysm with lattice Boltzmann method. The Casson model is used to describe the blood non-Newtonian character, which is one of the most popular models in depicting blood fluid. In particular, hemodynamic characteristics derived with Newtonian and non-Newtonian models are studied, and compared in detail. The results show that the non-Newtonian effect gives a great influence on hemodynamic characteristics of blood flow in stented cerebral aneurysm, especially in small necked ones.

Vibration and wear debris analyses are the two main conditions monitoring techniques for machinery maintenance and fault diagnosis. In addition, numerical simulation can provide useful tools to assess the proper functioning of industrial machines. We use different suspension theories with a concern of the effect of solid particles liquid lubricant itself on bearing behavior. We consider both simple models based on the Einstein’s mixture theory and a micropolar fluid theory, which is characterized by the presence of suspended rigid micro-structured particles. We suppose in this study that there are no abrasion and no wear (which are not beneficial for the contact performances) due to the presence of particles. Thus in this case we found theoretically that the presence of rigid particles in the lubricant increases the effective viscosity which enhances the load-carrying capacity as well as the minimum film thickness.