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Biomolecular condensates play a key role in cytoplasmic compartmentalization and cell functioning. Despite extensive research on the physico-chemical, thermodynamic, or crowding aspects of the formation and stabilization of the condensates, one less studied feature is the role of external perturbative fluid flow. In fact, in living cells, shear stress may arise from streaming or active transport processes. Here, we investigate how biomolecular condensates are deformed under different types of shear flows. We first model Couette flow perturbations via two-way coupling between the condensate dynamics and fluid flow by deploying Lattice Boltzmann Molecular Dynamics. We then show that a simplified approach where the shear flow acts as a static perturbation (one-way coupling) reproduces the main features of the condensate deformation and dynamics as a function of the shear rate. With this approach, which can be easily implemented in molecular dynamics simulations, we analyze the behavior of biomolecular condensates described through residue-based coarse-grained models, including intrinsically disordered proteins and protein/RNA mixtures. At lower shear rates, the fluid triggers the deformation of the condensate (spherical to oblated object), while at higher shear rates, it becomes extremely deformed (oblated or elongated object). At very high shear rates, the condensates are fragmented. We also compare how condensates of different sizes and composition respond to shear perturbation, and how their internal structure is altered by external flow. Finally, we consider the Poiseuille flow that realistically models the behavior in microfluidic devices in order to suggest potential experimental designs for investigating fluid perturbations in vitro. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose an efficient numerical scheme to deal with heat transfer problems in pipe flow with a large length/diameter ratio. The generalized finite difference method (GFDM) is combined with a space stepping algorithm (SSA) for the solution. The SSA divides the solution domain into a number of overlapping sections in the length direction of the pipe. Due to the large Peclet number, the heat transport process is dominated by advection, which allows an approximate boundary condition to be applied at the downstream cross section. The problem is then solved section by section. Using the uniform distributed points, the solution matrix for each section does not change, and only the right hand side needs to be refreshed for the changing boundary conditions. This leads to a highly efficient scheme for problems with a large pipe length. To show the accuracy of the numerical scheme, a problem with available analytical solution is studied. Then the method is applied to problems of single pipe with different pipe wall temperature and flow Reynolds number, and concentric annular pipe. Numerical results confirm the stability and efficiency of the GFDM-SSA. The method can be applied to many real world transient heat transfer problems in which the pipe is heated or cooled along its length with arbitrary wall temperature for heat exchange and other purposes. [ABSTRACT FROM AUTHOR]

This study theoretically investigates the temperature and velocity spatial distributions in the flow of a copper–water nanofluid induced by a rotating rigid disk in a porous medium. Unlike previous work on similar systems, we assume that the disk surface is well polished (coated); therefore, there are velocity and temperature slips between the nanofluid and the disk surface. The importance of considering slip conditions in modeling nanofluids comes from practical applications where rotating parts of machines may be coated. Additionally, this study examines the influence of heat generation on the temperature distribution within the flow. By transforming the original Navier–Stokes partial differential equations (PDEs) into a system of ordinary differential equations (ODEs), numerical solutions are obtained. The boundary conditions for velocity and temperature slips are formulated using the effective viscosity and thermal conductivity of the copper–water nanofluid. The dependence of the velocity and temperature fields in the nanofluid flow on key parameters is investigated. The major findings of the study are that the nanoparticle volume fraction significantly impacts the temperature distribution, particularly in the presence of a heat source. Furthermore, polishing the disk surface enhances velocity slips, reducing stresses at the disk surface, while a pronounced velocity slip leads to distinct changes in the radial, azimuthal, and axial velocity components. The study highlights the influence of slip conditions on fluid velocity as compared to previously considered non-slip conditions. This suggests that accounting for slip conditions for coated rotating disks would yield more accurate predictions in assessing heat transfer, which would be potentially important for the practical design of various devices using nanofluids. [ABSTRACT FROM AUTHOR]

This study aims to investigate the flow characteristics of mixed convection in a parallel plate channel filled with bidisperse porous medium (BDPM). The objective is to understand the effects of momentum slip and convective boundary conditions on the channel walls. A two-velocity two-temperature model is employed to analyze the flow and temperature distributions in both the fluid and solid phases. The governing equations are made dimensionless using appropriate similarity transformations. The Homotopy Analysis Method (HAM) is utilized to solve the resulting equations and analyze the velocity and temperature profiles. The influence of thermal radiation on temperature regulation is explored by controlling its intensity. The impact of the Biot number on enhancing the Nusselt number, a measure of convective heat transfer, is identified. Additionally, the study investigates the effects of various parameters on velocity, temperature, Nusselt number and skin friction. Graphical representations of these relationships are presented, and the findings are discussed comprehensively. [ABSTRACT FROM AUTHOR]

The flow of air inside a vertical slender long duct with a temperature difference between the horizontal walls characterized by the Rayleigh number R a and a pressure gradient in the horizontal direction characterized by the Reynolds number R e is studied using the lattice Boltzmann method. In this case, the longitudinal rolls found in ducts with a width larger than the height cannot develop and the flow remains quasi-two-dimensional. Therefore, a two-dimensional approach is used, considering periodic boundary conditions on the vertical walls. For R a c < R a ≤ 2. 0 × 1 0 5 with R a c the critical Rayleigh number for thermal convection, there are two transitions at R e 0 (R a) and R e C P (R a) , R e 0 < R e C P . The first transition at R e 0 has a sharp decrease in the average Nusselt number and for 0 < R e < R e 0 the temperature difference between the horizontal walls is more important than the pressure gradient. The second transition at R e C P marks the appearance of a conductive Poiseuille flow with no thermal convection. For 1. 0 × 1 0 5 ¡ R a there is a third transition at R e M , R e 0 < R e M < R e C P . For R a < 1. 0 × 1 0 5 and R e 0 < R e < R e C P , and for 1. 0 × 1 0 5 < R a and R e M < R e < R e C P , the pressure gradient dominates over the pressure gradient. Both the temperature difference and the pressure gradient are important for 1. 0 × 1 0 5 < R a and R e 0 < R e < R e M with an appreciable decrease of the average Nusselt number at R e 0 and R e M . [ABSTRACT FROM AUTHOR]

We study theoretically the elongational viscosity (or Trouton ratio, in dimensionless form) for steady viscoelastic flows in confined and symmetric hyperbolic tubes considering Navier-type slip along the wall(s). Both the planar and the cylindrical axisymmetric geometrical configurations are addressed. Under the classic lubrication approximation, and for a variety of constitutive models such as Phan-Thien and Tanner, Giesekus, and Finite Extensibility Nonlinear Elastic with the Peterlin approximation models, the same general analytical formula for the Trouton ratio is derived as for the Oldroyd-B model, in terms of the velocity at the midplane/axis of symmetry and the Deborah number only. Assuming that the velocity field is approximated by the Newtonian lubrication profile, based on our previous study in the absence of slip, we show that a constant extensional strain rate can be achieved in the limits of zero or infinite slip. For finite slip, a slight modification of the geometry is required to achieve a constant strain rate. In these cases, the formula for the steady state Trouton ratio reduces to that for transient homogeneous elongation. We also provide analytical formulae for the modification (decrease) for both the extensional strain rate and the Hencky strain achieved in the confined geometries because of introducing wall slip. [ABSTRACT FROM AUTHOR]

For its application in cancer therapy, targeted drug delivery, radiofrequency ablation, and magnetic resonance imaging, the dynamics of electro-magnetohydrodynamic flow of blood-gold nanomaterial over a nonlinearly stretching surface utilizing the Casson model has been elucidated numerically. The impact of second-order hydrodynamic-slip, nanoparticle radius, first-order thermal-slip, inter-particle spacing and non-uniform heat source are also accounted. The modeled flow equations are transmuted into a nonlinear system of first-order ODEs (with the aid of apposite similarity variables) which are then resolved numerically utilizing the bvp5c scheme. The thermal field augments with an increase and a decrease in the inter-particle spacing and radius of gold-nanoparticles, respectively. However, a reverse trend is noted for the velocity profile when the radius and inter-particle spacing of gold-nanoparticles are altered. The trend and magnitude of the change in the drag rate and heat transfer rate under the influence of effectual parameters have been demonstrated statistically using slope of linear regression. It is noticed that per unit increase in the volume fraction of gold nanoparticles augments the heat transfer rate by 81.71% and reduces the surface drag by 163.51%. Further, per unit increase in the inter-particle spacing of gold nanoparticles augments the drag coefficient by 85.92% whereas per unit increase in the radius of gold nanoparticles reduces the skin friction coefficient by 49.71%. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem for the three dimensional parabolic-elliptic Keller-Segel equation with the large plane Couette-Poiseuille flow. Without advection, there exist solution with arbitrarily mass which blow up in finite time. Firstly, we introduce three dimensional plane Couette-Poiseuille flow and study the enhanced dissipation effect of such flows by resolvent estimate method. Next, we show that the enhanced dissipation effect of such flows can suppress blow-up of solution to three dimensional parabolic-elliptic Keller-Segel equation and establish global classical solution with large initial data. [ABSTRACT FROM AUTHOR]

The thermal applications of nanofluids are extremely high and researchers have suggested multidisciplinary applications of nanomaterials in heat transfer problems, thermal systems, chemical industries, thermal energy systems, nuclear processes, extrusion mechanism, etc. The aim of this work is to discuss thermal properties of nanofluids for Poiseuille flow with hydrodynamic effects. The magnetohydrodynamic Poiseuille flow of thermo-capillary levels of nanoparticles with apparent viscosity nanofluids is focused. The graphene oxide (GO) nanoparticles are immersed in water-based fluid. The formulated system is solved numerically by using the Chebyshev collocation method. The mathematical technique Qualitat and Zuverlassigkeit (QZ) is applied to find out eigenvalues from comprehensive Orr–Sommerfeld technique. It is noted that the flow of nanofluids becomes stable due to the wave number and magnetic field. The Reynolds and Prandtl numbers have dynamic role on destabilizing the nanofluids transportation. The outcomes of this study are utilized in drug-delivery systems, photodynamic therapy and delivery of antitumor. [ABSTRACT FROM AUTHOR]

This paper describes hybrid fiber's influence on the crack permeability of cracked concrete exposed to freeze–thaw cycles. A permeability setup and a laser-scanning setup have been designed to measure the crack permeability and the fractured surface roughness of cracked hybrid fiber-reinforced concrete, containing polypropylene fiber and steel fiber, under a splitting tensile load. The results show that, when the effective crack width of the specimens is less than 25 μm, the rough crack surface significantly reduces the concrete's crack permeability. As the crack width increases, the effect of the concrete crack surface on crack permeability gradually decreases, and the crack permeability of the concrete is closer to the Poiseuille flow model. The permeability parameter α derived from the Poiseuille flow model is effective for assessing the crack permeability of concrete. Compared to the modified factor ξ of crack permeability, the permeability parameter α can effectively evaluate and quantify the development trend of crack permeability within a certain range of crack widths. The permeability parameter α of SF20PP2.3, subjected to the same freeze–thaw cycles, decreases by 16.3–94.8% compared to PP4.6 and SF40, and SF20PP2.3 demonstrates a positive synergistic effect on the crack impermeability of cracked concrete. The crack impermeability of SF40PP2.3, subjected to the same freeze–thaw cycles, lies between that of PP6.9 and SF60. The roughness of crack surface (X) and the crack permeability (Y) are highly correlated and follow an exponential curve (Y = 1.0415 × 107·e−6.025·X) in concrete. This demonstrates that hybrid fibers enhance crack impermeability by increasing the crack surface roughness. Furthermore, the combination of polypropylene fiber and steel fiber effectively promotes the formation of micro-cracks and facilitates the propagation of multiple cracks in the concrete matrix. This combination increases the head loss of water flow through the concrete and decreases the crack permeability. [ABSTRACT FROM AUTHOR]

Additives such as nano-silica and fly ash are widely used in cement and concrete materials to improve the rheology of fresh cement and concrete and the performance of hardened materials and increase the sustainability of the cement and concrete industry by reducing the usage of Portland cement. Therefore, it is important to study the effect of these additives on the rheological behavior of fresh cement. In this paper, we study the pulsating Poiseuille flow of fresh cement in a horizontal pipe by considering two different additives and when they are combined (nano-silica, fly ash, combined nano-silica, and fly ash). To model the fresh cement suspension, we used a modified form of the power-law model to demonstrate the dependency of the cement viscosity on the shear rate and volume fraction of cement and the additive particles. The convection–diffusion equation was used to solve for the volume fraction. After solving the equations in the dimensionless forms, we conducted a parametric study to analyze the effects of nano-silica, fly ash, and combined nano-silica and fly ash additives on the velocity and volume fraction profiles of the cement suspension. According to the parametric study presented here, larger nano-silica content results in lower centerline velocity of the cement suspension and larger non-uniformity of the volume fraction. Compared to nano-silica, fly ash exhibits an opposite effect on the velocity. Larger fly ash content results in higher centerline velocity, while the effect of the fly ash on the volume fraction is not obvious. For cement suspension containing combined nano-silica and fly ash additives, nano-silica plays a dominant role in the flow behavior of the suspension. The findings of the study can help the design and operation of the pulsating flow of fresh cement mortars and concrete in the 3D printing industry. [ABSTRACT FROM AUTHOR]

Shear and density stratification strongly affect the flow mechanism of the different atmospheric and ocean flows. In this paper, we investigate the stability characteristics of plane Couette–Poiseuille (CP) flow with stable density stratification in the vertical direction. A modal stability analysis is carried out to examine the exponentially growing instability of stratified plane CP flow under different controlling parameters. The domain of the flow is periodic in streamwise and vertical directions. The stability problem is solved numerically using the spectral collocation method. The present analysis is carried out for Reynolds number R e = 10 4 with different speeds of moving wall and different strengths of stratification. The results show that the mass diffusivity impact on the flow instability mechanism is almost negligible beyond the Schmidt number S c ≥ 20. The three-dimensional mode is generally the most unstable mode for density-stratified CP flow. However, the most unstable mode in unstratified CP flow is always two-dimensional. In contrast to unstratified CP flow, the density-stratified CP flow is unstable even moving wall velocity exceeds 70% of the center velocity of the plane Poiseuille flow component. It is also observed that the moving wall velocity and density stratification simultaneously affect the stability of the flow, which shows the importance of the shear and stratification in the flow. [ABSTRACT FROM AUTHOR]

In computational non-Newtonian fluid dynamics, heat transfer has obvious effects on motions of viscoelastic fluids, mechanical mechanism of elasticity, and flow regimes. This study suggests an extended numerical scheme of smoothed particle hydrodynamics and finite particle method within density smoothing (SPH_DSFPM), which involves the discretization of smoothed particle hydrodynamics (SPH) and finite particle method (FPM) within density smoothing (DS) in the weakly compressible flow scheme. A corrected particle shifting technique is incorporated to eliminate tensile instability and inhomogeneity near solid boundaries. A corrected dynamic solid coupled boundary is introduced to deal with casting molding within high-pressure operations, which has a good compatibility between virtual particle method and repulsive force model. Numerical results show that the present scheme has the nearly lower relative error (0.5%) than conventional SPH (2.6%) in the case of evolutionary thermal-viscoelastic Poiseuille flow and heat effects have active influences on velocity, pressure variations for viscoelastic fluid flow around periodic circular cylinders. Three different printing modes of moving printers significantly generate into differentiated forming regimes through high-pressure extrusion. Adaptive particle distributions possess robust flow evolutions, by which the shocked jets can be tracked well and the sinking velocities of wedge entering into solutions can be numerically probed well considering different cuspidal biting angles. In the case of macroscopic fluid–rigid body interactions, the statistical degree of deviation on probed forces with experiments is relatively 4.35% and that is 12.5% for SPH. The proposed numerical scheme has a good performance on improved accuracy, convergence, and stability for simulating transient thermal-viscoelastic flows. [ABSTRACT FROM AUTHOR]

The time-periodic plane Poiseuille flow of electrically conducting incompressible generalized Burgers fluids through a porous medium is analytically and numerically investigated in the presence of a transverse uniform magnetic field. The main purpose is to provide analytical expressions for the dimensionless steady-state fluid velocity, non-trivial shear stress and Darcy's resistance, which can be used to bring to light important characteristics concerning fluid behavior. Similar solutions corresponding to the Poiseuille flow of the same fluids induced by a constant pressure gradient are obtained as limiting cases of previous results. The present results reduce to known solutions from the literature when magnetic and porous effects are neglected, and their validation is graphically proved. The needed time to reach a steady state has been graphically determined. It was found that the steady state is later obtained in the absence of a magnetic field and porous medium. The impact of a magnetic field and porous medium on the fluid velocity, shear stress and flow resistance has been systematically examined and elucidated through graphical representations. The findings reveal that the presence of a magnetic field or porous medium results in a reduction in the fluid velocity, accompanied by an increase in the flow resistance. [ABSTRACT FROM AUTHOR]

In this paper, the Poiseuille flow of non-isothermal couple stress fluid of Reynolds model between two heated parallel inclined plates has been studied. The strongly nonlinear coupled ordinary differential equations have been investigated using the Asymptotic Homotopy Perturbation method (AHPM) and the Optimal Homotopy Asymptotic Method with DJ Polynomials (OHAM-DJ). Employing both these techniques, the approximate solutions for velocity profile, temperature distributions, shear stress, average velocity and volumetric flow rate have been achieved. The results obtained using both these methods are in the form of infinite series, hence the results can be obtained easily. Comparison of various results, obtained through these methods, is carried out. Here, it is worth to mention that the results gained by both these approaches are in excellent resemblance. The effect of different parameters on the flow problem has been studied numerically as well as presented graphically. [ABSTRACT FROM AUTHOR]

In this paper, we consider the hydrodynamic stability of the 2D Navier-Stokes equations on T × R around Poiseuille-Couette flow V = (y 2 , 0) + a (y , 0) with a ∈ (0 , 1). By means of the hypocoercivity method with time dependent weights and introducing a new estimate on the energy functional, we establish the enhanced dissipation estimates for the linearized Navier-Stokes equations. More precisely, for a ⩽ 10 − 3 ν 1 4 , we obtain a decay rate proportional to ν 1 2 , which is consistent with the Poiseuille flow. For a = 10 − 3 ν s with s ∈ [ 0 , 1 4 ] , the decay rate is proportional to ν 1 − 2 s. As an application of the linear estimates, we obtain the result of nonlinear stability transition threshold. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Leray problem for steady Navier–Stokes system with full slip boundary conditions in a two-dimensional channel with straight outlets. The existence of solutions with arbitrary flux in a general channel supplemented with slip boundary conditions, which tend to the associated shear flows at far fields, is established. Furthermore, if the flux is suitably small, the solution is proved to be unique. One of the crucial ingredients is to construct an appropriate flux carrier and to show a Hardy type inequality for flows with full slip boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effect of uniform vertical crossflow on the plane Poiseuille channel flow. The derivation and linearization of the Navier–Stokes equations are performed to enable numerical solution through the fourth-order Orr–Sommerfeld equation. The Chebyshev collocation method is employed for this purpose. A dual approach is employed to examine the basic velocity profile, involving both reference velocity analysis (z = 0) and maximum streamwise velocity analysis (z = z max ). The two approaches provide distinct perspectives on the flow and may yield different stability predictions, depending on the values of the parameters used. Modal analysis is conducted to comprehend the asymptotic behavior of the system, achieved through the plotting of eigenspectrum, neutral stability curves, and growth rate curves for disturbances. Accurate values of critical triplets are obtained, aligning with the existing literature. The non-modal analysis is performed to understand the short-term behavior of the system, aided by pseudospectra, evolutionary patterns of energy amplification of the disturbances G(t) over time, and delineation of regions, indicating stability, potential instability, and instability. The collective results from both analyses reveal that the crossflow serves as a dual agent, contributing to both the stabilization and destabilization of the system. [ABSTRACT FROM AUTHOR]

We investigate the dynamic behavior of a two-dimensional droplet adhering to a wall in Poiseuille flow at low Reynolds numbers, in a system where one of the phases is viscoelastic represented by a Giesekus model. The Cahn–Hilliard Phase-Field method is used to capture the interface between the two phases. The presence of polymeric molecules alters the viscoelastic drop's deformation over time, categorizing it into two stages before contact line depinning. In the first stage, the viscoelastic droplet deforms faster, while in the second stage, the Newtonian counterpart accelerates and its deformation outpaces the viscoelastic droplet. The deformation of viscoelastic drop is retarded significantly in the second stage with increasing Deborah number De. The viscous bending of viscoelastic drop is enhanced on the receding side for small De, but it is weakened by further increase in De. On the advancing side, the viscous bending is decreased monotonically for Ca < 0.25 with a non-monotonic behavior for Ca = 0.25. The non-monotonic behavior on the receding side is attributed to the emergence of outward pulling stresses in the vicinity of the receding contact line and the inception of strain-hardening at higher De, while the reduction in the viscous bending at the advancing side is the result of just strain-hardening. Finally, when the medium is viscoelastic, the viscoelasticity suppresses the droplet deformation on both receding and advancing sides, and this effect becomes more pronounced with increasing De. Increasing the Giesekus mobility parameter enhances the weakening effect of viscous bending on the advancing side. [ABSTRACT FROM AUTHOR]

A novel lattice Boltzmann (LB) model is proposed to study the gas and liquid two-phase flows with large density and viscosity ratios. In the model, both the gas and liquid phases are considered as viscous incompressible fluids, which are governed separately by the two-relaxation-time LB equations. They are coupled by a momentum exchange method at the interface. The interaction between the gas and liquid phases is explicitly described and naturally involved in the model. The interfacial conditions in the model are validated by the benchmarks of the layered Poiseuille flow and the Laplace law. The feasibility of combining this model with the bubble model and the wetting scheme is proven through transient flow problems of single bubble rising and capillary intrusion. The validity of this model is confirmed by more complex flows including solid–liquid–gas coupling and droplet breaking problems by simulating shearing a droplet on a substrate and a droplet falling on a liquid film. The results demonstrate that the present model can be used to describe both the gas and the liquid flows. This work provides a solution to model the simulation of the dynamical behaviors of multi-phase flows. [ABSTRACT FROM AUTHOR]

The plane Poiseuille flow of viscoelastic fluids with pressure-dependent viscosity is analyzed through a narrow nanochannel, combining with the electrokinetic effect. When the fluid viscosity depends on pressure, the common assumption of unidirectional flow is unsuitable since the secondary flow may exist. In this case, we must solve the continuity equation and two-dimensional (2D) momentum equation simultaneously. It is difficult to obtain the analytical electrokinetic flow characteristics due to the nonlinearity of governing equations. Based on the real applications, we use the regular perturbation expansion method and give the second-order asymptotic solutions of electrokinetic velocity field, streaming potential, pressure field, and electrokinetic energy conversion (EKEC) efficiency. The result reveals a threshold value of Weissenberg number (Wi) exists. The strength of streaming potential increases with the pressure-viscosity coefficient when Wi is smaller than the threshold value. An opposite trend appears when Wi exceeds this threshold value. Besides, the Weissenberg number has no effect on the zero-order flow velocity, but a significant effect on the velocity deviation. A classical parabolic velocity profile transforms into a wavelike velocity profile with the further increase in Wi. Finally, the EKEC efficiency reduces when pressure-dependent viscosity is considered. Present results are helpful to understand the streaming potential and electrokinetic flow in the case of the fluid viscosity depending on pressure. [ABSTRACT FROM AUTHOR]

In this paper, we mainly focus on the development of the Taylor-Galerkin/Pressure-Correction method (TG/PC) method to solve the flow of a compressible Newtonian fluid under nonisothermal conditions. The process of development needs applying the two-step Lax–Wendroff method on the energy equation, after which two new steps for energy equations will be obtained within the TG/PC algorithm. In addition, for the density component, the Tait equation of state is adopted to relate density to pressure, which also yields a new step within the novel method to give the correction formula of compressible pressure. To perform the analysis of the new algorithm, Poiseuille flow through axisymmetric rectangular channel for the Newtonian thermal flow is utilized as a simple problem test. The effect of nondimensional factors such as Reynolds number (Re) and Prandtl number (Pr) is discussed in this study. The influence of thermal conductivity (k) and viscosity (μ) on the solution components is presented as well. Also, comparison for both compressible and incompressible flows is provided in addition to a comparison between both cases' convergence, as it turns out that the convergence of the incompressible case is better than the compressible case. All the results of the effects presented in this study agree well with the approved physical trend. [ABSTRACT FROM AUTHOR]

The steady pipe flow of thixotropic yield stress fluids has been investigated theoretically based on a modified isotropic kinematic hardening (mIKH) model. Analytical solution is derived for a specific case (m = n = 1) and a general semi-analytical solution is put forward as well. The effect of thixotropic yield stress on shear rate and velocity profiles is illustrated by comparing to other well-known solutions. Moreover, the influences of model parameters are examined. It is worth noting that shear banding may occur at the yielded surface in case of a sufficiently large Bingham number, thixotropic number, and flow index, but a sufficient small value of structure-related exponent. [ABSTRACT FROM AUTHOR]

This study focuses on examining the hydrodynamic stability of an incompressible fluid flowing through a bidisperse porous medium. Specifically, the impact of slip boundary conditions on instability is investigated. The study looks at a scenario in which the Darcy theory is used for micropores and the Brinkman theory is used for macropores. An incompressible fluid is located within an unbound channel with a constant pressure gradient along its length in the system under investigation. The fluid flows laminarly along the pressure gradient, resulting in a stable parabolic velocity distribution that does not alter over time. Based on our observations, it appears that increasing the values of the slip parameter, permeability ratio, porous parameter, interaction parameter and Darcy Reynolds number leads to an improvement in the stability of the system. The spectrum behavior of eigenvalues in the Orr–Sommerfeld problem for Poiseuille flow exhibits significant sensitivity and is influenced by multiple factors, encompassing both the mathematical attributes of the problem and the specific numerical techniques utilized for approximation. [ABSTRACT FROM AUTHOR]

A weakly nonlinear stability analysis of isothermal Poiseuille flow in a fluid overlying porous domain is proposed and investigated in this article. The nonlinear interactions are studied by imposing finite amplitude disturbances to the classical model deliberated in Chang, Chen, and Straughan [J. Fluid Mech., 564 (2006), pp. 287-303]. The order parameter theory is used to ascertain the cubic Landau equation, and the regimes of instability for the bifurcations are determined henceforth. The well-established controlling parameters viz. the depth ratio ( ... = depth of fluid domain/depth of porous domain), the Beavers--Joseph constant (α), and the Darcy number (δ ) are inquired upon for the bifurcation phenomena. The imposed finite amplitude disturbances are viewed for bifurcations along the neutral stability curves and away from the critical point as a function of the wave number (a) and the Reynolds number (Re). The even-fluid-layer (porous) mode along the neutral stability curves correlates to the subcritical (supercritical) bifurcation phenomena. On perceiving the bifurcations as a function of a and Re by moving away from the bifurcation/critical point, subcritical bifurcation is observed for increasing ..., α and decreasing δ. In contrast to only fluid flow through a channel, it is found that the inclusion of porous domain aids in the early appearance of subcritical bifurcation when α = 0.2, ... δ = 0.13, δ = 0.003. A considerable difference between the computed skin friction coefficient for the base and the distorted state is observed for small (large) values of ... (α). In addition, an intrinsic relation among the mode of instability, bifurcation phenomena, and secondary flow pattern is also observed. [ABSTRACT FROM AUTHOR]

In this paper, we study the initial-boundary value problem for the Poiseuille flow of a hyperbolic-parabolic Ericksen--Leslie model of nematic liquid crystals in one space dimension. We consider a simplified system by restricting the Leslie coefficients to special cases such that some quantities are constants. Due to the quasilinearity, the solution of this model in general forms cusp singularity. We prove the global existence of a H\"older continuous solution, which may include cusp singularity, for initial-boundary value problems with different types of boundary conditions. [ABSTRACT FROM AUTHOR]

The linear stability analysis of fluid flow, driven by an axial pressure gradient, inside the annular region partially filled with porous medium is investigated. The porous layer is attached to the inner cylinder. The flow is governed by the unsteady Darcy model in the porous region and the Navier–Stokes equation in the viscous region. The effect of the curvature parameter C (ratio of the inner cylinder radius to the gap between cylinders), the ratio of the fluid to the porous layer thickness (t ̂) , and the Darcy number (Da) on the stability characteristics are explored. In addition, the help of the radial velocity contours and the kinetic energy balance is taken to get an insight into the mode and the cause of instability, respectively. The results show that depending upon the value of t ̂ , a decrease in the value of C causes a shift in the neutral stability curve from bimodal to trimodal. For low values of t ̂ , when the onset of instability is dominated by a porous mode, C destabilizes the flow, whereas it has a stabilizing impact on the flow stability for the odd-fluid mode and the even-fluid mode. At high values of t ̂ , C has again destabilizing characteristics and instability is dominated by even-fluid mode. When axisymmetric disturbances are dominant, it is observed that the value of t ̂ for which similar instability characteristics are found varies directly as the square root of Da. However, the correlation between t ̂ and Da does not hold when the non-axisymmetric disturbances are least stable. Contrary to the unconditional stability of the annular Poiseuille flow under non-axisymmetric disturbances for C < 0.1325, the present system is unstable even for C = 0.005 and t ̂ ≤ 1. This shows the significant impact of the curved fluid–porous interface on the stability characteristics. [ABSTRACT FROM AUTHOR]

Several advanced medical and engineering tasks, such as microsurgery, drug delivery through arteries, pipe inspection, and sewage cleaning, can be more efficiently handled using micro- and nano-robots. Pressure-driven flows are commonly encountered in these practical scenarios. In our current research, we delve into the hydrodynamics of pitching hydrofoils within narrow channels, which may find their potential applications in designing bio-inspired robots capable of navigating through pressure-driven flows in confined channels. In this paper, we have conducted a numerical investigation into the flow characteristics of a National Advisory Committee for Aeronautics (NACA) 0012 hydrofoil pitching around its leading edge within a plane Poiseuille flow using a graphical processing unit accelerated sharp interface immersed boundary method solver. Our study considers variations of the wall clearance from 20% to 50% of the channel width. We have explored the hydrodynamic features such as instantaneous and time-averaged values of lift, drag, input power, and torque for different wall clearance ratios and oscillation frequencies in the range of Reynolds number 100–200 based on the mean velocity and channel width. We have tried to explain the force, torque, and power variations by examining the flow features in the near wake. While the hydrodynamic coefficients showed significant variations with changes in wall clearance and the Strouhal number (St), we did not observe significant variations with alterations in the Reynolds number (Re). [ABSTRACT FROM AUTHOR]

Context: In the past decade, rapid advancements in microtechnology and nanotechnology have propelled modern science and technology into the nanoscale domain, where miniaturization and high integration have found extensive applications across various fields, including industry, biotechnology, and information technology. Mechanisms of nanofluid flow and heat transfer properties have received increasing attention. In the flow and convective heat transfer of fluids at the nanoscale, the shape and dimensions of the surfaces play a crucial role. So, the main purpose of our paper is to investigate the influence of surface roughness with different shapes and quantities on fluid flow and convective heat transfer. In this study, we have chosen argon atoms as the fluid and used copper atoms to simulate the nanochannel walls. In order to investigate the influence of the shape and quantity of roughness on the convective heat transfer of fluids within nanochannels, we computed and analyzed the velocity, temperature, and density distributions of fluids inside channels with triangular, hemispherical, and rectangular roughness. Through simulation results, we found that triangular, hemispherical, and rectangular surface roughness at the same height can result in differences in temperature and velocity of the fluid within nanochannels. With a nanochannel roughness number of 5, the temperature and velocity of the fluid at the middle position of the nano-channel for the triangular roughness increased by 6% and 25% compared to the rectangular roughness, and by 4% and 10% compared to the hemispherical roughness. The fluid temperature and velocity are highest in channels with triangular surface roughness and lowest in those with rectangular roughness. Furthermore, increasing the quantity of surface roughness decreases the temperature and velocity of the fluid within nanochannels. When the quantity of rectangular surface roughness is 5, the fluid temperature within the nanochannel decreases by 12%, and the velocity decreases by 38% compared to a roughness quantity of 1. We also found, through velocity contours, that the presence of roughness increases the local fluid velocity in the rough regions of nanochannels. Roughness also reduces the density fluctuations of the fluid near the walls within the nanochannel. Roughness significantly affects the heat transfer performance of the fluid during its flow, and this influence should not be overlooked. Methods: In this study, molecular dynamics theory was employed, and simulations were conducted using the open-source software LAMMPS to investigate the influence of different shapes and quantities of surface roughness on fluid flow within nanochannels. The model in this paper was constructed using the LAMMPS software, and the surface roughness shapes on the walls were implemented as rectangular, hemispherical, and triangular. The wall surfaces were composed of copper atoms, while the fluid consisted of argon atoms. The copper atoms were arranged in a face-centered cubic (FCC) lattice with a lattice constant of 3.615 Å. Similarly, the argon atoms were arranged in a face-centered cubic (FCC) lattice with a lattice constant of 5.62 Å. The interactions between copper atoms were modeled using the EAM (Embedded Atom Method) potential, while the interactions between argon atoms were described using the LJ (Lennard-Jones) potential. The LJ potential was also employed to represent interactions between argon and copper atoms. [ABSTRACT FROM AUTHOR]

The study of Poiseuille flow, particularly relevant in diverse scenarios such as human blood circulation, crude oil transport, and industrial fluid dynamics, forms the crux of this research. Specifically, it delves into the analysis of fluid flow within a channel inclined at an angle relative to the horizontal axis, a scenario commonly encountered in rotating frames like bioreactors and drilling rigs, where the Coriolis force plays a crucial role. Employing the Navier-Stokes equations, this research formulates the governing equations for the flow and presents an analytical solution. It has been observed that an increase in the pressure gradient correlates with a rise in flow velocity. Furthermore, an escalation in rotational speed tends to flatten and elevate the velocity profiles. Additionally, an increase in the angle of inclination of the channel is found to boost the flow velocity. These findings have significant implications for optimizing the design and operational efficiency of systems involving inclined channels, with potential applications across various industries, including biotechnology and oil extraction. [ABSTRACT FROM AUTHOR]

The theme of this study is to investigate the impact of radiation with Thompson and Troian boundary slip on CNT-Fe3O4/kerosene oil (KO) hybrid nanofluid flow across a porous exponentially stretching sheet. The viscosity is considered to be temperature-dependent using Reynolds viscosity model. A comparative analysis is done for SWCNT-Fe3O4/KO and MWCNT-Fe3O4/KO. Methodology: The nonlinear partial differential equations (PDEs) are remodeled into non-dimensional ordinary differential equations (ODEs) using suitable similarity transformation. To solve the non-dimensional equations, the Legendre wavelet collocation technique (LWCT) is applied. The code is validated numerically as well as graphically with previous works and found to be in good agreement with them. Findings: It has been observed that thermal profiles are enhanced with the rise in radiation and heat generation. Additionally, in comparison, the velocity profile of MWCNT-Fe3O4/KO is found superior to SWCNT-Fe3O4/KO. It is observed that heat transfer (HT) rate is enhanced by 30.11% on elevating the volume fraction of Fe3O4 from 1% to 10% and is represented by a scatter plot. [ABSTRACT FROM AUTHOR]

This paper deals with an initial-boundary value problem modeling the unidirectional pressure-driven flow of a second grade fluid in a plane channel with impermeable solid walls. On the channel walls, Navier-type slip boundary conditions are stated. Our aim is to investigate the well-posedness of this problem and obtain its analytical solution under weak regularity requirements on a function describing the velocity distribution at initial time. In order to overcome difficulties related to finding classical solutions, we propose the concept of a generalized solution that is defined as the limit of a uniformly convergent sequence of classical solutions with vanishing perturbations in the initial data. We prove the unique solvability of the problem under consideration in the class of generalized solutions. The main ingredients of our proof are a generalized Abel criterion for uniform convergence of function series and the use of an orthonormal basis consisting of eigenfunctions of the related Sturm–Liouville problem. As a result, explicit expressions for the flow velocity and the pressure in the channel are established. The constructed analytical solutions favor a better understanding of the qualitative features of time-dependent flows of polymer fluids and can be applied to the verification of relevant numerical, asymptotic, and approximate analytical methods. [ABSTRACT FROM AUTHOR]

The fully developed, steady, incompressible, laminar flow in a channel delimited by rough and/or permeable walls is considered. The influence of the micro-structured bounding surfaces on the channel flow behavior is mimicked by imposing high-order effective boundary conditions which stem from homogenization theory and do not contain empirical parameters. A closed-form solution of the Navier–Stokes equations is found for the flow in the channel, with conditions at each virtual boundary linking the slip velocities to shear stress and streamwise pressure gradient. The boundary condition for the longitudinal velocity coincides with a little-noticed extension of the so-called Beavers-Joseph condition, first derived by Saffman (1971); it applies to both permeable and rough surfaces, including the case of separated flow (Couette-Poiseuille motion with adverse pressure gradient). The analytical solution obtained for the velocity distribution in the channel is validated against full feature-resolving simulations of the flow for either highly ordered or random textures, highlighting the accuracy and the applicability range of the model. The Stokes-based model used to identify slip and interface permeability coefficients in the effective boundary conditions is found to be reliable and accurate up to ϵ R e τ ≈ 10 , with ϵ ratio of microscopic to macroscopic length scales and R e τ the shear-velocity Reynolds number. Above this threshold, the coefficients must account for advective effects: a new upscaling procedure, based on an Oseen's approximation , is thus proposed and validated, extending considerably beyond the Stokes regime. • Laminar Poiseuille and Couette-Poiseuille flows in channels with non-smooth boundaries are studied. • Effective boundary conditions, based on homogenization theory, mimic flow interaction with textured walls. • Analytical solutions for channel flows are derived and extensively validated. • A new approach is proposed where macroscopic coefficients are advection-sensitive. • Improved model is highly accurate, beyond the Stokes regime. [ABSTRACT FROM AUTHOR]

We consider the micro- and the macro-scale to investigate the motion of single grains in a dilute suspension under shear flow and Poiseuille flow to analyze effects like shear-wall migration and rolling of grains as observed in physical experiments. To be able to simulate the behavior of fresh concrete or mud flow, as realistically as possible, we are taking into account a non-Newtonian Bingham–Papanastasiou rheology for the carrier fluid. Due to a surface coupled approach, Smoothed Particle Hydrodynamics (SPH) gives the opportunity to consider both, the motion of a solid particle, by tracking its center of mass and also surface points, and the interaction and influence on the near field of the velocity field in the fluid phase. We show an independence of the motion of solid grains from the surrounding carrier fluid. While the macroscopic flow reaches a stationary flow field quite fast, the motion of the solid grains still oscillates between parts of the fluid that flow with different velocities and does not show a stable steady state. Providing a comparison between the motion in a Newtonian and a non-Newtonian fluid, we point out the differences and thus the importance of the choice of the material model for the carrier fluid in numerical simulations. • SPH simulations of suspensions with Newtonian or non-Newtonian carrier fluid. • Detailed analysis of the motion of solid grains in a suspension on different scales. • Focus on the analysis of the near velocity field at the surface of solid grains. [Display omitted] [ABSTRACT FROM AUTHOR]

Analytical solutions are derived for the cessation of annular Poiseuille and Couette flows of a Newtonian fluid in the presence of dynamic wall slip. We employ linear dynamic slip law involving a slip relaxation parameter, which results in the appearance of the eigenvalue parameters in the boundary conditions and thus leads to distinct Sturm–Liouville problems that differ from their static slip counterparts. The proper orthogonality condition is derived and closed-form analytical solutions are obtained for both flows of interest. Representative results are then presented and discussed. In agreement with previous reports for other flows with dynamic wall slip, the present solutions show that wall slip slows down flow dynamics and this effect becomes more pronounced as the slip-relaxation parameter is increased. • Analytical solutions of Newtonian annular flows with dynamic wall slip are derived. • The proper Sturm-Liouville problems are considered. • The cessation of annular Poiseuille and annular Couette flows is investigated. • Wall slip and the slip relaxation parameter are shown to damp flow dynamics. [ABSTRACT FROM AUTHOR]

A weakly nonlinear stability analysis is carried out to study thermal instability induced by viscous dissipation in Poiseuille flows for binary fluid mixtures with a positive separation ratio. The impermeable lower boundary of the channel is considered adiabatic, while the impermeable upper boundary is isothermal. The linear stability of this problem has been performed by Ali Amar et al. [Phys. Fluids 34, 114101 (2022)] and showed that longitudinal rolls are the preferred mode of convection at the onset of instability. By employing weakly nonlinear theory, we derive a cubic Landau equation that describes the temporal evolution of the amplitude of convection rolls in the unstable regime. It is found that the bifurcation from the conduction state to convection rolls is always supercritical for the weak viscous dissipation intensity. Otherwise, the interplay between the viscous dissipation and the Soret effects determines the supercritical or the subcritical nature of the bifurcation. In the parameter range where the bifurcation is supercritical, we determine and discuss the Soret effects on the amplitude of convection rolls, iso-contours and the corresponding average heat transfer, and the mixing of the two fluid components. Similarities and differences with a one-component fluid case are highlighted. [ABSTRACT FROM AUTHOR]

An immersed boundary method for the thermo–fluid–structure interaction in rarefied gas flows is presented. In this method, the slip model is incorporated with the penalty feedback immersed boundary method to address the velocity and temperature jump conditions at the fluid–structure interface in rarefied gas flows within the slip-flow regime. In addition, the compressible flows governed by the Navier–Stokes equations are solved by using a high-order finite difference method; the elastic solid is solved by using the finite element method; the fluid and solid dynamics are solved independently, and the thermo–fluid–structure interaction is achieved by using a penalty feedback method in a partitioned way. To model the local rarefaction in the supersonic flow, an artificial viscosity is proposed by introducing the local Knudsen number to diffuse the sharp transition at the shock wave front. Several validations are conducted: the Poiseuille flow in a channel, the flow around a two-dimensional airfoil, a moving square cylinder in a channel, the flow around a sphere, and a moving sphere in quiescent flow. The numerical results from the present method show very good agreements with the previous published data obtained by other methods, confirming the good ability of the proposed method in handling the thermo–fluid–structure interaction in both weakly and highly compressible rarefied gas flows. Inspired by the micro/unmanned aerial vehicles in Martian exploration, the proposed method is applied to the aerodynamics of a flapping wing in rarefied gas flows in both two-dimensional and three-dimensional spaces to demonstrate the versatility of the proposed method for modeling flows involving large deformation and fluid–structure interaction. [ABSTRACT FROM AUTHOR]

In this work, a lattice Boltzmann method (LBM) for studying microchannel gas flow is developed in the multi-flow regime. In the LBM, by comparing previous studies' results on effective viscosity in multi-flow regimes, the values of the rarefaction factor applicable to multi-flow regions were determined, and the relationship between relaxation time and Kn number with the rarefaction factor is given. The Kn number is introduced into the second-order slip boundary condition together with the combined bounce-back/specular-reflection (CBBSR) scheme to capture the gas flow in the multi-flow regime. Sensitivity analysis of the dimensionless flow rate to adjustable parameters using the Taguchi method was carried out, and the values of adjustable parameters were determined based on the results of the sensitivity analysis. The results show that the dimensionless flow rate is more sensitive to j than h. Numerical simulations of Poiseuille flow and pulsating flow in a microchannel with second-order slip boundary conditions are carried out to validate the method. The results show that the velocity profile and dimensionless flow rate simulated by the present numerical simulation method in this work are found in the multi-flow regime, and the phenomenon of annular velocity profile in the microchannel is reflected in the phases. [ABSTRACT FROM AUTHOR]

The birefringence response of aqueous cellulose nanocrystal (CNC) suspensions in a two-dimensional laminar flow is measured and studied. The suspensions have CNC concentrations of 1.0 wt% (weight percentage) and 1.2 wt%. Cellulose nanocrystals are optically anisotropic rod-like particles that align when subjected to local velocity gradients, whereas at rest, they remain randomly orientated by Brownian motion. The alignment causes birefringence, a phenomenon also known as flow-induced birefringence. We study the flow through an additively manufactured flow channel and measure the amount of birefringence as well as the position of the refractive index axes by using polarizers and a polarization camera. With the help of reference data published in a previous study (Lane, Rode, et al., 2022a), strain rates are derived from the birefringence measurements and compared with numerical simulations. Two flow situations are studied, a plane Poiseuille flow and the flow around a cosine-shaped constriction. The experimentally derived shear rates for the plane Poiseuille flow are consistent with theoretical and computational results. The derived strain rates for the flow around the cosine-shaped constriction show an unexpected asymmetric profile, with the strain rates in the contraction zone being larger than in the expansion zone. The averaged orientation of the CNCs in the flow is linked to the position of the refractive index axes. In the contraction zone, the CNCs tend to align parallel to the flow, whereas in the expansion zone, the CNCs tend to align perpendicular to the flow. The results of this study are discussed in the context of previous, similar studies. The asymmetric strain rate profile around the cosine-shaped constriction is thought to originate from history effects, and the alignment of the CNCs is influenced by extensional rates. [ABSTRACT FROM AUTHOR]

Critical Reynolds numbers for the monotone exponential energy stability of Couette and Poiseuille plane flows were obtained by Orr in 1907 [Proc. Roy. Irish Acad. A, 27 (1907), pp. 9--68, 69--138] in a famous paper, and by Joseph in 1966 [J. Fluid Mech., 33 (1966), pp. 617--621], Joseph and Carmi in 1969 [Quart. Appl. Math., 26 (1969), pp. 575--579], and Busse in 1972 [Arch. Ration. Mech. Anal., 47 (1972), pp. 28--35]. All these authors obtained their results applying variational methods to compute the maximum of a functional ratio derived from the Reynolds--Orr energy identity. Orr and Joseph obtained different results; for instance, in the Couette case Orr computed the critical Reynolds value of 44.3 (on spanwise perturbations) and Joseph 20.65 (on streamwise perturbations). Recently in [P. Falsaperla, G. Mulone, and C. Perrone, Eur. J. Mech. B Fluids, 93 (2022), pp. 93--100], the authors conjectured that the search of the maximum should be restricted to a subspace of the space of kinematically admissible perturbations. With this conjecture, the critical nonlinear energy Reynolds number was found among spanwise perturbations (a Squire theorem for nonlinear systems). With a direct proof and an appropriate and original decomposition of the dissipation terms in the Reynolds--Orr identity we show the validity of this conjecture in the space of three-dimensional perturbations. [ABSTRACT FROM AUTHOR]

In this work, we study the Cauchy problem of Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of two partial differential equations (PDEs): One is a quasi-linear wave equation for the director field representing the crystallization of the nematics, and the other is a parabolic PDE for the velocity field characterizing the liquidity of the material. We extend the work in Chen et al. (2020) [11] for a special case to the general physical setup. The Cauchy problem is shown to have global solutions beyond singularity formation. Among a number of progresses made in this paper, a particular contribution is a systematic treatment of a parabolic PDE with only Hölder continuous diffusion coefficient and rough (maybe unbounded) nonhomogeneous terms. [ABSTRACT FROM AUTHOR]

The efficacy of convection-enhanced delivery as a technique to treat disorders of the central nervous system is limited by backflow, in which the infused fluid flows backward along surface of the catheter rather than toward the targeted area. In order to improve treatment protocols, finite element models of backflow have been developed to understand the underlying physics. García et al. (2013, “Description and Validation of a Finite Element Model of Backflow During Infusion Into a Brain Tissue Phantom,” ASME J. Comput. Nonlinear Dyn., 8(1), p. 011017) presented a finite element model that accounted for the flow in the annular gap that develops between the tissue and the outer surface of the catheter by using a layer of biphasic elements with a formula for the axial hydraulic conductivity to represent annular Poiseuille flow. In this study, we present a generalization of that model using fluid-FSI and biphasic-FSI elements that are recently available in febio. We demonstrate that our model of a 0.98 mm radius catheter is able to reproduce experimental backflow lengths and maximum fluid pressures for infusions into a brain tissue surrogate and that it agrees well with the previous model by García et al. (2013, “Description and Validation of a Finite Element Model of Backflow During Infusion Into a Brain Tissue Phantom,” ASME J. Comput. Nonlinear Dyn., 8(1), p. 011017). The model predicts that the backflow length and the total amount of flow into the hemispherical region forward of the catheter tip is comparable for two different catheter sizes, albeit at a higher fluid pressure for the smaller catheter. This biphasic-FSI model has the potential to be extended to a stepped catheter geometry, which has been shown in experiments to be successful in controlling backflow. [ABSTRACT FROM AUTHOR]

A family of positivity-preserving lattice Boltzmann methods (LBMs) is proposed for compressible flow simulations in the continuum regime. It relies on the efficient collide-and-stream algorithm with a collision step based on exponential distribution functions. The latter serves as a generalization of Grad's post-collision distribution functions for which here (1) the linearized non-equilibrium contributions are replaced by their exponential forms and (2) the number of these contributions can be chosen arbitrary. In practice, post-collision moments of our exponential formulation are enforced through an iterative moment-matching approach to recover any macroscopic physics of interest, with or without external forces. This methodology directly flows from the extended framework on numerical equilibria [J. Latt et al., Philos. Trans. R. Soc. A 378, 20190559 (2020)] and goes one step further by allowing for the independent relaxation of hydrodynamic and high-order modes in a given moment space, notably, making the Prandtl number freely adjustable. The model is supplemented by a shock-capturing technique, based on the deviation of non-equilibrium moments from their equilibrium counterparts, to ensure good numerical properties of the model in inviscid and under-resolved conditions. A second exponential distribution accounts for extra degrees of freedom of molecules and allows for the simulation of polyatomic gases. To validate this novel approach and to quantify the accuracy of different lattices and moment closures, several 2D benchmark tests of increasing complexity are considered: double shear layer, linear wave decay, Poiseuille flow, Riemann problem, compressible Blasius flow over a flat plate, and supersonic flow past an airfoil. Corresponding results confirm the accuracy and stability properties of our approach for the simulation of compressible flows with LBMs. Eventually, the performance analysis further highlights its efficiency on general purpose graphical processing units. [ABSTRACT FROM AUTHOR]

The temporal nonmodal stability of the Poiseuille flow in a pipe of axially uniform elliptic cross section is numerically studied. In particular, it is shown that the maximum amplification of kinetic energy of disturbances depends significantly on the pipe aspect ratio, and this dependence is non-monotonic. It agrees with the corresponding dependence of the energy critical Reynolds number, which is the lower limit of the Reynolds numbers enabling the growth of disturbance kinetic energy. In other words, changing the aspect ratio similarly affects both nonmodal and monotonic stability of the flow. The optimal disturbances displaying the maximum amplification are streamwise counter-rotating vortices. These disturbances are streamwise uniform at sufficiently large Reynolds numbers and may become streamwise harmonic as the Reynolds number decreases. In addition, their symmetry with respect to the cross section axes varies with the aspect ratio. Thus, the obtained results suggest that changing the aspect ratio may be a perspective tool for the passive control of the subcritical laminar-turbulent transition in pipe flows. In other words, this factor is worth considering when designing various devices (e.g., heat exchangers or ventilation systems) containing pipes to enhance their efficiency. [ABSTRACT FROM AUTHOR]

The manipulation and control of particles in microfluidic devices through non-intrusive methods is pivotal in many application fields, e.g., cell focusing and sorting. Inertial microfluidics is rapidly gaining attention in the scientific community because of the considerable advantages in terms of throughput. In addition to inertia, other factors can trigger the cross-stream migration of particles in liquids undergoing pressure-driven channel flows, such as the deformability of the particles themselves and/or the viscoelasticity of the carrier fluid. For this reason, the dynamics of an initially spherical elastic particle suspended in a viscoelastic liquid subjected to pressure-driven flow in a cylindrical channel at non-negligible inertia is studied through three-dimensional arbitrary Lagrangian–Eulerian finite-element numerical simulations. The mechanical behavior of the particle is described through the neo-Hookean hyper-elastic constitutive equation, whereas the rheological behavior of the carrier liquid is described through the Giesekus model. The Reynolds number Re, measuring the relative importance of inertial and viscous forces in the tube, the elastic capillary number Ca e , measuring the relative importance of liquid viscous stress and solid elastic stress, and the Deborah number De, measuring the ratio of the liquid relaxation time and the flow characteristic time, are varied. The particle migrates transversally to the flow direction until reaching a radial equilibrium position depending on Re, Ca e , and De. Different dynamics are observed depending on the interplay among inertia and elasticity of both the liquid and the solid phase: one, two, or even three stable equilibrium positions can be found along the tube radius. [ABSTRACT FROM AUTHOR]

Direct numerical simulations of viscoelastic, subdiffusive, and plane Poiseuille flow, representing thick polymer solutions including polymer melts, flows of liquid crystals, as well as biological flow such as mucus, are reported. The stress strain equation is fundamentally derived by relating the timescale exponent at the microscale ( t α , with 0 < α ≤ 1) with the fractional order of the time derivative, α, of the corresponding non-linear equation in the continuum. The resultant stress constitutive equation is the fractional variant of the well-known upper convected Maxwell equation. In order to quantify the formation of spatiotemporal macrostructures (or the non-homogeneous regions of high viscosity at moderate to high fluid inertia), the space of symmetric positive definite polymer conformation tensors is visualized using a Riemannian metric along with its three scalar invariants. Numerical simulations of the channel flow, in the regime of low to moderate Reynolds number and low Weissenberg number, effectively capture these flow-structures by providing (i) a better resolution of the instantaneous regions of elastic shocks (which are the alternating regions of expanded and compressed polymer volume, in comparison with the volume of the mean conformation tensor), and (ii) a better resolution to detect neighborhoods where the mean conformation tensor tends to be significantly different in comparison to the instantaneous conformation tensor, thereby corroborating the experimentally observed flow-instability transition of subdiffusive flows. Finally, the strength of the subdiffusive flow model and the invariant theory is highlighted through an application of an electrohydrodynamic micropump. [ABSTRACT FROM AUTHOR]