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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]

In this paper we present a numerical scheme based on spectral collocation methods to investigate the flow of a piezo-viscous fluid, i.e., a fluid in which the rheological parameters depend on the pressure. In particular, we consider an incompressible Navier–Stokes fluid with pressure dependent viscosity flowing in: (i) a two-dimensional non-symmetric planar channel; (ii) a three-dimensional axisymmetric non-straight conduit. For both cases we impose the Navier slip boundary conditions that can be reduced to the classical no-slip condition for a proper choice of the slip parameter. We assume that the dependence of the viscosity on the pressure is of exponential type (Barus law), even though the model can be replaced by any other viscosity function. We write the mathematical problem (stress based formulation) and discretize the governing equations through a spectral collocation scheme. The advantage of this numerical procedure, which to the authors' knowledge has never been used before for this class of fluids, lies in in the ease of implementation and in the accuracy of the solution. To validate our model we compare the numerical solution with the one that can be obtained in the case of small aspect ratio, i.e., the leading order lubrication solution. We perform some numerical simulation to investigate the effects of the pressure-dependent viscosity on the flow. We consider different wall functions to gain insight also on the role played by the channel/duct geometry. In both cases (i), (ii) we find that the increase of the coefficient appearing in the viscosity function results in a global reduction of the flow, as physically expected. [ABSTRACT FROM AUTHOR]

This article is devoted to the mathematical analysis of a heat and mass transfer model for the pressure-induced flow of a viscous fluid through a plane channel subject to Navier's slip conditions on the channel walls. The important feature of our work is that the used model takes into account the effects of variable viscosity, thermal conductivity, and slip length, under the assumption that these quantities depend on temperature. Therefore, we arrive at a boundary value problem for strongly nonlinear ordinary differential equations. The existence and uniqueness of a solution to this problem is analyzed. Namely, using the Galerkin scheme, the generalized Borsuk theorem, and the compactness method, we proved the existence theorem for both weak and strong solutions in Sobolev spaces and derive some of their properties. Under extra conditions on the model data, the uniqueness of a solution is established. Moreover, we considered our model subject to some explicit formulae for temperature dependence of viscosity, which are applied in practice, and constructed corresponding exact solutions. Using these solutions, we successfully performed an extra verification of the algorithm for finding solutions that was applied by us to prove the existence theorem. [ABSTRACT FROM AUTHOR]

Measuring particles' three-dimensional (3D) positions using multi-camera images in fluid dynamics is critical for resolving spatiotemporally complex flows like turbulence and mixing. However, current methods are prone to errors due to camera noise, optical configuration and experimental setup limitations, and high seeding density, which compound to create fake measurements (ghost particles) and add noise and error to velocity estimations. We introduce a Bayesian volumetric reconstruction (BVR) method, addressing these challenges by using probability theory to estimate uncertainties in particle position predictions. Our method assumes a uniform distribution of particles within the reconstruction volume and employs a model mapping particle positions to observed camera images. We utilize variational inference with a modified loss function to determine the posterior distribution over particle positions. Key features include a penalty term to reduce ghost particles, provision of uncertainty bounds, and scalability through subsampling. In tests with synthetic data and four cameras, BVR achieved 95% accuracy with less than 3% ghost particles and an RMS error under 0.3 pixels at a density of 0.1 particles per pixel. In an experimental Poiseuille flow measurement, our method closely matched the theoretical solution. Additionally, in a complex cerebral aneurysm basilar tip geometry flow experiment, our reconstructions were dense and consistent with observed flow patterns. Our BVR method effectively reconstructs particle positions in complex 3D flows, particularly in situations with high particle image densities and camera distortions. It distinguishes itself by providing quantifiable uncertainty estimates and scaling efficiently for larger image dimensions, making it applicable across a range of fluid flow scenarios. [ABSTRACT FROM AUTHOR]

The article "Threshold transient growth as a criterion for turbulent mean profiles" in the Journal of Fluid Mechanics explores the role of transient growth in maintaining turbulence in wall-bounded shear flows. It examines the significance of short-term transient growth in comparison to long-term linear stability characteristics, challenging Malkus's classic hypothesis on turbulent mean profiles. The study uses numerical simulations to analyze optimal perturbation energy gain and streak breakdown mechanisms, emphasizing the importance of secondary growth exceeding a threshold of Gs = 50 for sustainable turbulence in minimal channels. The research suggests a nonlinear transient growth property of mean profiles and calls for further investigation into the synergy between different mechanisms and the impact of larger length scales on transient growth. [Extracted from the article]

The article delves into the use of patterned heating to minimize pressure losses in sloping channels by creating separation bubbles that reduce friction and induce fluid rotation. Factors like Reynolds number, heating wavelength, and channel inclination impact the effectiveness of heating in reducing pressure losses. While judicious heating can significantly decrease pressure losses, excessive heating may lead to increased energy costs. The study suggests that heating can be a viable method for drag reduction in specific channel orientations, emphasizing the potential for energy efficiency and flow rate optimization through patterned heating. [Extracted from the article]

The article examines the thermohydrodynamics of rarefied Poiseuille flow in a finite length channel, emphasizing the impact of dilatation and non-isochoric effects. Variations in pressure-driven and acceleration-driven Poiseuille flows are discussed, with a focus on the saturation of mass flow rate at high Knudsen numbers in pressure-driven flow. The study highlights the significance of dilatation in explaining differences in hydrodynamic fields, rheology, and flow-induced heat transfer between the two flows, as well as the implementation of boundary conditions and averaging procedures in the DSMC method. The research suggests that further exploration is needed to understand the implications of dilatation in various flow scenarios and discusses the challenges in solving the Boltzmann equation using the DSMC method. [Extracted from the article]

"Dabiri and Leonard's article delves into the linear instability of viscous parallel shear flows, challenging the traditional no-slip condition by proposing alternative boundary models. By examining different boundary conditions, the authors aim to enhance our understanding of turbulence transition in fluid-solid interfaces. The research underscores the significance of diverse perspectives in fluid mechanics to refine predictions of turbulence transition, focusing on plane Couette flow, plane Poiseuille flow, and Hagen–Poiseuille pipe flow." [Extracted from the article]

The article delves into the computational analysis of deformable fluid particle migration in viscoelastic fluid within a square channel under pressure-driven flow. Factors such as particle deformability, fluid elasticity, shear thinning, and fluid inertia impact the migration dynamics. Varying shear thinning alters the direction of particle migration, with deformable particles moving towards the wall in shear-thinning fluids. The study also uncovers elastic flow instability, path instability, and secondary flow features induced by particle migration, shedding light on the intricate interplay between fluid properties and particle behavior in microfluidic systems. [Extracted from the article]

Direct numerical simulations of spiral Poiseuille flows in a narrow gap geometry are performed with the aim of identifying the mechanisms governing the dynamics of the axial friction coefficient. The investigation has explored a small portion of the Reynolds number–Taylor number phase space ($600 \leq Re \leq 5766$ and $1500 \leq Ta \leq 5000$), for which reference experimental results are available. The study is focused on the mechanism leading to the enhancement of the axial friction coefficient with the Taylor number when the Reynolds number is kept constant. The analysis of the spatial distribution of the Reynolds stress tensor and of the turbulent energy budget has evidenced the key role of the pressure–strain correlation in the energy transfer from the azimuthal to the axial component. The latter eventually determines the increase of the axial friction coefficient through the enhanced radial mixing of axial momentum. Data have also shown that the flow dynamics is heavily dependent on the $Ta/Re$ ratio, and different regimes develop (ranging from laminar to turbulent), each with peculiar behaviours. [ABSTRACT FROM AUTHOR]

The linear stability analysis of the onset of double-diffusive convection in a Poiseuille flow system is investigated. In addition, a volumetric uniform internal heat source is taken into account. In this problem, the horizontal fluid channel is bounded by two plates which are isothermal and isosolutal. The governing parameters are thermal Rayleigh number R a T , solutal Rayleigh number R a s , internal heat source parameter R a I , Prandtl number Pr, and Reynolds number Re. The eigenvalue problem arising from the linear perturbed system of equations is solved numerically using the Chebyshev–Tau method coupled with the QZ algorithm. It is found that the positive solutal Rayleigh number R a s destabilizes the system. Furthermore, it is observed that an increase in the Prandtl number Pr stabilizes the system. Additionally, at R a s = −60, the critical values of the thermal Rayleigh number R a c decreases with R = R e cos ϕ up 2; and increases with R beyond R = 2. [ABSTRACT FROM AUTHOR]

The compound droplet consists of the inner and outer droplets. The outer droplet's ability to isolate the inner contents from its surroundings makes applications such as drug delivery, cell encapsulation, and cell sorting possible. Here, we experimentally explore the transport of the compound droplet at different Reynolds numbers, viscosity ratios, and volume ratios. Compound droplets have a longer dimensionless transport distance along the X-axis than single-phase droplets at Reynolds numbers from 44 to 366. When the Reynolds number is increased from 81.2 to 243.7, the dimensionless maximum transport distance of the compound droplet along the X-axis becomes 2.04 times. As the Re increases, the compound droplet deflection rate decreases continuously. For a constant initial velocity of the compound droplet, an increase in the viscosity ratio leads to an increase in the dimensionless velocity along the x axis with the compound droplet during transport. The maximum transport distance along the x-axis increases, and the deflection rate decreases as the inertial and viscous forces increase with increasing viscosity and dimension ratios. The chemical droplets become more stable as a result. [ABSTRACT FROM AUTHOR]

The upstream motility of three microswimmer shapes (circular squirmer, squirmer rod, and elliptical squirmer) at the center of a Poiseuille flow is numerically investigated using the lattice Boltzmann method. Based on the stability and upstream ability, the swimming velocities and four motion states (stable motion, progressively unstable motion, unstable motion, and upstream failure) are summarized. The results show that the circular squirmer and squirmer rod are more stable than the elliptical squirmer; however, the elliptical squirmer has the greatest advantage in velocity and can swim up to twice as fast as the circular squirmer under the same conditions. The swimming type is also the key to influencing the motion state, which is reflected differently in the distinct microswimmer shapes. The increase in the Reynolds number (Re) and self-propelled strength (α) aggravates the motion instability; however, for elongated microswimmers, the aspect ratio (ε) plays a role in velocity rather than the motion state. Moreover, the upstream velocity of the pusher is always better than that of the puller, especially when Re increases. Notably, all microswimmers can maintain stable swimming when the preset velocity is twice the maximum velocity of the flow field. These findings can provide guidelines for the selection of design parameters and the appearance of microswimmers that resist complex incoming flows. [ABSTRACT FROM AUTHOR]

By combining the lattice Boltzmann model of fluid flow with the molecular dynamics model of copolymers, we investigate the inertial migration of cylindrical micelles, which is obtained by controlling the length ratios of hydrophilic and hydrophobic segments in a comb-like copolymer. Our results demonstrate that cylindrical micelles gradually deviate from the center of the nanochannel with increasing Reynolds number (Re). For the same Re, the larger the cylindrical micelle is, the closer it is to the center of the nanochannel. Importantly, we find that the change in the equilibrium position is particularly pronounced at Re less than 0.1, while the trend becomes smoother at Re greater than 0.1, which is because of the transition of micelles from cylindrical to disk-like shapes when Re is smaller than 0.1, and does not change as Re further increases. This work provides an understanding of cylindrical micelles' inertial migration, particularly in identifying the effect of morphological changes on the equilibrium position, which could lead to significant advancements in the inertial migration of polymer micelles. [ABSTRACT FROM AUTHOR]

The electrohydrodynamic stability of a two-layer plane Poiseuille flow has been examined under the influence of an electric field acting normally to the unperturbed interface of two viscous immiscible fluids. The presence of insoluble surfactant at the interface is considered to achieve passive control over the instability that naturally comes into play in such flows. The fluids considered here for the asymptotic and numerical stability analyses are treated as leaky dielectrics, which are allowed to have different viscosities, densities, permittivities, and conductivities. An asymptotic analysis shows that the two opposite influences from the electrical stresses and the Marangoni stresses in competition at the interface give rise to remarkably different patterns of neutral curves depending upon the ratios of viscosities and thicknesses of the fluid layers. A linear stability analysis utilizing the Chebyshev spectral collocation method for disturbances of all wave numbers is employed numerically to obtain various types of dispersion curves and neutral stability diagrams originating from the associated Orr–Sommerfeld eigenvalue problem. Our results suggest that increasing the electrical conductivity ratio leads to an increase in the growth rate of disturbances, whereas an increase in the electrical permittivity ratio stabilizes the flow as the interfacial surface tension resists the growth of perturbations that are otherwise promoted by electrical stresses. The energy budget calculations show that the presence of the insoluble surfactant is primarily responsible for the viscosity-induced instability triggered by the modified interface deformation. The comparisons with pertinent studies are performed to enhance the quantitative reliability of the present work. [ABSTRACT FROM AUTHOR]

Although the Boltzmann equation is instrumental in capturing the dynamics of rarefied gases, finding its solutions in engineering problems is challenging. Therefore, over the past century and a half, numerous partial differential equations based on a few macroscopic variables have been introduced. However, they not only have complicated forms but also cannot make satisfactory prediction when the Knudsen number is large. Here, we propose a non-localized spatial–temporal (NiST) constitutive relation for rarefied gas dynamics, where the stress/heat flux at time t and position x is determined by the velocity/temperature gradient in the nearby spatial–temporal coordinates, via convolution operators. Utilizing solutions of the Boltzmann equation for the Couette/Fourier/Poiseuille flow and the spontaneous Rayleigh–Brillouin scattering, we extract the universal parameters of non-locality as functions of the spatial and temporal Knudsen numbers. Subsequent validation through sound propagation and backward-facing step flow demonstrates that the NiST constitutive relation is capable of accurately forecasting rarefied gas flows across a broad spectrum of Knudsen numbers. [ABSTRACT FROM AUTHOR]

Context: In a very small surface separation, the fluid flow is actually multiscale consisting of both the molecular scale non-continuum adsorbed layer flow and the intermediate macroscopic continuum fluid flow. Classical simulation of this flow often takes over large computational source and is not affordable owing to using molecular dynamics simulation (MDS) to model the adsorbed layer flow, if the flow field size is on the engineering size scale such as of 0.01–10 mm or even bigger like occurring in micro or macro hydrodynamic bearings. The present paper uses full MDS to validate Zhang's multiscale flow model, which yields the closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate continuum fluid flow. Here, full MDS was carried out for the pressure-driven flow of methane in the nano slit pore made of silicon respectively with the channel heights 5.79 nm, 11.57 nm, and 17.36 nm. According to the number density distribution, the flow areas were respectively discriminated as the adsorbed layer zone and the intermediate fluid zone. The values of the characteristic parameters for Zhang's multiscale scheme were extracted from full MDS and input to Zhang's multiscale flow equations respectively for calculating the flow velocity profile and the volume flow rates of the adsorbed layers and the intermediate fluid. It was found that for these three channel heights, the flow velocity profiles calculated from Zhang's model approximate those calculated from full MDS, while the total flow rates through the channel calculated from Zhang's model are close to those calculated from full MDS. The accuracy of Zhang's multiscale flow model is improved with the increase of the channel height. Method: The recent modification of the optimized potential for liquid simulation (MOPLS) model was used to calculate the interaction force between two methane molecules. In order to calculate the interaction force between the wall atoms and the methane molecules accurately, our previous non-equilibrium multiscale MDS was used. The interaction forces between the methane molecule and the wall atom were obtained from the coupled potential function by the L-B mixing rule when the fluid molecules arrived at near wall. The methane molecule diameter was obtained from the radial distribution function by using equilibrium MDS under the same initial conditions. The local viscosities across the adsorbed layer were obtained from the local velocity profile by using the Poiseuille flow method. The motion equation of the methane molecule was solved by the leapfrog method. The temperature of the simulation system was checked by Bhadauria's method, i.e., the system temperature was rectified by the velocities in the y- and z-directions. The flow velocity distributions across the channel height and the volume flow rates through the channel were also calculated from Zhang's closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate fluid flow. The results respectively obtained from full MDS and Zhang's multiscale flow equations were then compared. [ABSTRACT FROM AUTHOR]

We consider the effect of a shear flow which has, without loss of generality, a zero mean flow rate, on a Kolmogorov–Petrovskii–Piscounov (KPP)‐type model in the presence of a discontinuous cutoff at concentration u=uc$u = u_c$. In the long‐time limit, a permanent‐form traveling wave solution is established which, for fixed uc>0$u_c>0$, is unique. Its structure and speed of propagation depends on A$A$ (the strength of the flow relative to the propagation speed in the absence of advection) and B$B$ (the square of the front thickness relative to the channel width). We use matched asymptotic expansions to approximate the propagation speed in the three natural cases A→∞$A\rightarrow \infty$, A→0$A\rightarrow 0$, and A=O(1)$A=O(1)$, with particular associated orderings on B$B$, while uc∈(0,1)$u_c\in (0,1)$ remains fixed. In all the cases that we consider, the shear flow enhances the speed of propagation in a manner that is similar to the case without cutoff (uc=0$u_c=0$). We illustrate the theory by evaluating expressions (either directly or through numerical integration) for the particular cases of the plane Couette and Poiseuille flows. [ABSTRACT FROM AUTHOR]

In addition to solar water heating and transformers, these applications of research include heat exchangers and braking fluids, as well as acoustics and microelectronics. The mathematical model of Poiseuille hybrid nanofluid flow through a microchannel is considered with differing thermal conductivity and viscosity parameters. This mathematical model has mainly been developed to cater to the diversity of the hybrid nanofluid properties, which contains oxide and metal nanoparticles, for example, Cu and Al2O3 immersed in water (H2O) and Ethylene glycol (EG) as the base liquid. The substructure for hybrid nanofluid abides by the mixture of 20% water while the rest is filled with EG. Moreover, the perception of entropy is analyzed. The dimensional form of the current problem is deformed into a non-dimensional form using the appropriate choice of similarity transformation. Thence, the Runge–Kutta-Fehlberg method is being used to treat the numerical solution for the problem. The graphs spectacle the entropy, Bejan numbers, and physical behavior of the contributing factors to the flow phenomena. The numerical results of the rate coefficients for these parameters are shown in the table below. Furthermore, a comparison analysis is conducted to confirm the current result with prior work demonstrating a higher degree of concordance. [ABSTRACT FROM AUTHOR]

Murray’s law, as the best-known optimal relationship between bifurcation calibers, is obtained based on the assumption of steady-state Poiseuille blood flow and is mostly accurate in small vessels. In middle sized and large vessels such as the aorta and coronary arteries, the pulsatile nature of the flow is dominant and deviations from Murray law have been observed. In the present study, a general scaling law is proposed, which describes the optimum relationship between the characteristics of bifurcations and pulsatile flow. This scaling law takes into account the deviations from Murray law in large vessels, and proposes optimal flow (i.e. less flow resistance) for the full range of the vascular system, from the small vessels to large ones such aorta. As a general scaling law, it covers both symmetrical and asymmetrical bifurcations. One of the merits of this scaling law is that bifurcation characteristics solely depend on the Womersley number of parent vessels. The diameter ratios suggested by this scaling law are in acceptable agreement with available clinical morphometric data such as those reported for coronary arteries and aortoiliac bifurcations. A numerical simulation of pulsatile flow for several Womersley numbers in bifurcation models according to the proposed scaling law and Murray law has been performed, which suggests that the general scaling law provides less flow resistance and more efficiency than Murray law in pulsatile flow. [ABSTRACT FROM AUTHOR]

We present a numerical study for Poiseuille and Couette as well as Taylor- Couette swirling flows. The governing equations of momentum and energy are transformed into coupled and nonlinear ordinary differential equations using similarity transformation and then solved numerically. We critically evaluate the effect of dimensionless pressure gradients on fluid velocity and observed that the velocity increases as the dimensionless pressure gradient increases. Couette flows are simulated in different scenarios, including top plate moving, bottom plate moving, and top plate moving in adverse pressure gradient conditions. In a third scenario, the flow velocity profile revealed a backflow regime (BFR). A simple schematic model is, therefore, proposed to explain the presence of BFR in the flow’s profile. Numerical and analytical solutions around the circular cylinder are presented. The marginal discrepancy between the analytical and numerical profiles is maximum at ~ 900 and 2700 degrees, which indicates that the chosen method is suitable and capable of reproducing engineering problems. Velocity magnitude and vector diagrams show that the cylinder shape was found to have a significant effect on the flow field. The velocity at the top and bottom of the cylinder is twice the velocity that seen away from the cylinder.

The document delves into the linear stability analysis of generalized Couette-Poiseuille (GCP) flow between moving parallel plates under various conditions. It examines the neutral surface in (Re, α, β) space, the mapping to plane Couette-Poiseuille flow stability, and the global critical properties of GCP flow. The research articles included discuss the stability of different fluid flows, exploring topics like energy budget analysis, slip effects, and the impact of non-ideal fluids on flow stability. Researchers have explored modal and non-modal approaches to understanding the behavior of viscous and viscoelastic liquids in diverse flow scenarios. [Extracted from the article]

Recently, subcritical transition to turbulence in the quasi-two-dimensional (quasi-2-D) shear flow with strong linear friction (Camobreco et al. , J. Fluid Mech. , vol. 963, 2023, R2) has been demonstrated by the 2-D mechanism at $Re = 71\,211$ , and the nonlinear Tollmien–Schlichting (TS) waves related to the edge state were approached independently of initial optimal disturbances. For 2-D plane Poiseuille flow, transition to the fully developed turbulence requires that the Reynolds number is several times larger than the critical Reynolds number $Re_c$ (Markeviciute & Kerswell, J. Fluid Mech. , vol. 917, 2021, A57). In this paper, we observed the subcritical transitional flow in 2-D plane Poiseuille flow driven by the nonlinear TS waves by both linear and nonlinear optimal disturbances ($Re) with different quantitative edge states. The nonlinear optimal disturbances could trigger the sustained subcritical transitional flow for $Re \geqslant 2400$. The initial energy for nonlinear optimal disturbance is more efficient than the linear optimal disturbance in reaching the subcritical transitional flow for $2400 \leqslant Re \leqslant 5000$. Moreover, the initial energy of linear optimal disturbance is larger than the energy of its edge state. The nonlinear TS waves along the edge state are formed by the nonlinear optimal disturbances to trigger transitional flow, which agrees well with the main conclusions of Camobreco et al. (J. Fluid Mech. , vol. 963, 2023, R2), while the required $Re$ of 2-D plane Poiseuille flow is much smaller. [ABSTRACT FROM AUTHOR]

The important problem of the flow through a star-shaped crack is studied. Both clear and porous medium-filled ducts are solved for the first time. An accurate modified Ritz method is used to accommodate concave sharp corners. Flow rates and Poiseuille numbers are determined for star ducts with 2–6 pointy branches. Asymptotic approximations and corner singularities are discussed. [ABSTRACT FROM AUTHOR]

Application of two-dimensional lattice Boltzmann equations of various orders on standard lattices to the description of slow isothermal rarefied flows is considered. A two-dimensional Poiseuille flow at different Knudsen numbers is used as a test problem. This problem is solved numerically using several lattice Boltzmann equations of low and high orders that have from nine to 53 discrete velocities. The results are compared with the solutions to the linearized Boltzmann and Bhatnagar–Gross–Crook equations, which are used as test ones. Numerical experiments showed that increasing the order of the lattice Boltzmann equation (i.e., the number of first moments of the local Maxwell distribution reproduced by the discrete local equilibrium of the lattice Boltzmann equation) does not always lead to improved accuracy. In particular, a new low-order LB model with 16 velocities which reproduces diffuse reflection boundary conditions at a qualitative level is proposed. It is shown that for this model it is possible to obtain accurate values of the volumetric flow rate slip velocities for a wide range of Knudsen numbers in comparison with other models under consideration. [ABSTRACT FROM AUTHOR]

The Kelvin–Helmholtz (K–H) interfacial instability induced by an infinitely fast bimolecular chemical reaction (A + B → C) is studied numerically by considering that the depth of the boundary layer and the reaction front develop simultaneously in the channel flow. In a flow of one reactant fluid (A) to another reactant fluid (B), the generation of a more viscous or less viscous product (C) induces a viscosity gradient at the reaction front, resulting in instability motions of different types. According to the redefinition of the log viscosity ratio, R Chem and R Phys , which is used to describe the viscosity ratio between the product and non-iso-viscous reactants, the growth of K–H instability is identified chemically and hydrodynamically. Instability with roll-ups occurs along the reaction front near the wall for a less viscous product compared to that with two reactants; i.e., R Chem > 0 , and the number of roll-ups increases with an increase in R Chem . For a system with R Chem < 0 , the growth of instabilities is greatly delayed and incomplete roll-ups (billows) arise along the reaction front. This instability motion is determined by the complex contribution of the diffusive flow effect, which delocalizes the vorticity source/sink, and the vorticity effect, which is localized according to the viscosity gradient. Interestingly, for a small Re, the system instead becomes destabilized by a strong wall effect within the boundary layer, showing the active growth of roll-ups at the reaction front near the wall. The wall critically impedes the unstable motion in the entrance region, resulting in the instability becoming localized within the boundary layer, δ ∼ xRe − 1 / 2 , especially for a positive R Chem system. This study suggests that the boundary layer thickness plays an important role in the development of instability motion. This wall effect is not profound for a negative R Chem system showing billow-type instability motion. [ABSTRACT FROM AUTHOR]

In rarefied gas dynamics, the Cercignani-Lampis (CL) scattering kernel, containing two accommodation coefficients (ACs), namely the tangential momentum and normal energy ones, is widely employed to characterize gas-surface interaction, particularly in non-isothermal setups, where both momentum and energy may simultaneously be exchanged. Here, a formal and detailed sensitivity analysis of the effect of the CL ACs on the main output quantities of several prototype problems, namely the cylindrical Poiseuille, thermal creep and thermomolecular pressure difference (TPD) flows, as well as the plane Couette flow and heat transfer (Fourier flow), is performed. In each problem, some uncertainties are randomly introduced in the ACs (input parameters) and via a Monte Carlo propagation analysis, the deduced uncertainty of the corresponding main output quantity is computed. The output uncertainties are compared to each other to determine the flow configuration and the gas rarefaction range, where a high sensitivity of the output quantities with respect to the CL ACs is observed. The flow setups and rarefaction regimes with high sensitivities are the most suitable ones for the estimations of the ACs, since larger modeling and experimental errors may be acceptable. In the Poiseuille and Couette flows, the uncertainties of the flow rate and shear stress respectively are several times larger than the input uncertainty in the tangential momentum AC and much smaller than the uncertainty in the normal energy AC in a wide range of gas rarefaction. In the thermal creep flow, the uncertainty of the flow rate depends on the input ones of both ACs, but, in general, it remains smaller than the input uncertainties. A similar behavior with the thermal creep flow is obtained in the TPD flow. On the contrary, in the Fourier flow, the uncertainty of the heat flux may be about the same or even larger than the input ones of both ACs in a wide range of gas rarefaction. It is deduced that in order to characterize the gas-surface interaction via the CL ACs by matching computations with measurements, it is more suitable to combine the Poiseuille (or Couette) and Fourier configurations, rather than, as it is commonly done, the Poiseuille and thermal creep ones. For example, in order to estimate the normal energy AC within an accuracy of 10 %, experimental uncertainties should be less than 4 % in the thermal creep or TPD flows, while may be about 10 % in the Fourier flow. [ABSTRACT FROM AUTHOR]

Large-scale slot die coating technology is crucial for producing perovskite films in perovskite solar cells. Producing high-quality perovskite films requires a stable coating window to ensure that the thickness of the films is uniform and free of defects. This research delves into the production of high-quality perovskite films via slot die coating. It employs a combined approach of theoretical analysis and numerical simulation to define coating limits. Furthermore, it examines the influence of the geometric structure within the internal flow field and the transformation of fluid flow patterns in the external flow field on the overall film quality. We demonstrate that the removal of the edge geometry to the transverse fluid channel in the coating head significantly improves the stability of the internal flow field and enhances the consistency of fluid discharge. Additionally, uniform and stable coating of a perovskite solution can be achieved when the speed of the coating substrate in the downstream coating gap exceeds 0.7 times the maximum velocity of the Poiseuille component of the flow, and the coating flow pattern in the downstream coating gap remains consistent with Couette flow. [ABSTRACT FROM AUTHOR]

Aiming at the compliant end face gas film seal structure, based on the linearized Boltzmann equation, the Poiseuille flow coefficient is introduced, and the generalized Reynolds equation and the sealing performance parameter solution formula considering the boundary slip flow effect are established. Through Newton–Raphson iterative calculation, the degree of influence of the slip flow effect under different working conditions is analyzed, and the internal relationship between structural parameters and sealing performance is compared. The results show that the slip flow effect can have a large impact on the pressure distribution in the fluid field close to the low-pressure side. Due to the existence of the step phenomenon of boundary velocity, it is not conducive to increasing the gas film opening force and controlling the mass leakage rate, but it can play a positive role in reducing the viscous friction power consumption. In the case of a smaller sealing gas film thickness and lower medium pressure, the slip flow effect is significant, which will have a greater impact on the sealing performance, and at this time, the slip flow effect can not be ignored. In addition, the change in seal structure parameters will also have a large impact on the sealing performance. With an increase in the wave foil thickness, the compliant end face evolves towards the rigid end face, the fluid wedge effect is weakened, and the gas film opening force and mass leakage rate are reduced. The stiffness-to-leakage ratio shows a strong nonlinear decreasing trend with an increase in the wave foil chord length and pitch, which eventually tends to a stable value. The results of this paper provide a theoretical basis for the matching design of the structural parameters of compliant end-face gas film seals under different service conditions. [ABSTRACT FROM AUTHOR]

We study the energy stability of pressure‐driven laminar magnetohydrodynamic flow in a rectangular duct in the presence of a transverse homogeneous magnetic field. The walls of the duct are electrically insulating. The quasistatic approximation of the induction equation is used. For sufficiently strong fields, the laminar velocity distribution has a uniform core and convex Hartmann and Shercliff boundary layers on the walls perpendicular and parallel to the magnetic field. The linear eigenvalue problem for the energy Reynolds number depends on the streamwise wavenumber, the Hartmann number, and the aspect ratio. We focus on duct geometries with small aspect ratios in order to compare with stability results from one‐dimensional channel flow. The lift‐up mechanism dominates in the limit of zero streamwise wavenumber and provides a linear dependence between the critical Reynolds and Hartmann number in the duct. For finite streamwise wavenumbers and decreasing aspect ratio, the duct results converge to Orr's original energy stability result for spanwise uniform perturbations to the plane Poiseuille base flow. [ABSTRACT FROM AUTHOR]

Shear thickening fluids are liquids that stiffen as the applied stress increases. If many of these types of fluids follow a monotonic rheological curve, some experimental and numerical studies suggest that certain fluids, like cornstarch, may exhibit a non-monotonic, S-shaped rheology. Such non-monotonic behavior has however proved very difficult to observe experimentally in classical rheometer. To explain such difficulties, the possible presence of vorticity banding in the rheometer has been considered. To prevent such instabilities, we use a capillary rheometer, which is a cylindrical tube, measuring the flow rate versus the applied pressure drop. With this setup, we indeed observe a non-monotonic behavior: the flow rate increases monotonically at low pressure drops up to a maximum, after which it abruptly decreases to an almost constant flow rate regardless of further increases in pressure drop. This maximum-jump–plateau behavior occurs over a wide range of concentrations and is reproducible without hysteresis, which is in agreement with an S-shaped rheology. However, the obtained flow versus pressure difference function Q (Δ P) does not agree with the classical Wyart–Cates rheological model, which predicts an S-shaped non-monotonic function, but with neither a jump nor a plateau. To understand this jump–plateau behavior, we remark that any rheological model would establish a relationship between the flow rate and the local pressure gradient, but not the total pressure drop. We thus discuss and analyze the implications of having an S-shaped non-monotonic flow rate-pressure gradient in Poiseuille flow. In particular, we discuss the possibility of a non-uniform pressure gradient in the direction of the flow, i.e., a kind of streamwise banding. The key issue is then the selection of the gradient pressure distribution along the tube. One solution could arise from an analogy of this problem with the spinodal decomposition. It, however, leads to an increase in flow rate with ∂ x P up to a plateau between two values of ∂ x P as determined by the Maxwell construction. To account for the bump–jump behavior, we have implemented a simple dynamical stochastic version of the Wyart–Cates model, where the thickening occurs with a characteristic time. As a result, with increasing the total pressure drop, the flow rate increases monotonically up to a maximum value. Beyond this point, the flow rate drops abruptly to a lower value, forming a slowly decreasing plateau. This behavior is likely to account for the maximum-jump–plateau observed in the experiments. We also show that in such a system, the final state is quite sensitive to the initial state of the fluid, especially its homogeneity. Our results then demonstrate that the mere presence of a non-monotonic rheological curve is sufficient to predict the occurrence of stress banding in the streamwise direction and a plateau flow rate, even if the suspension remains homogeneous. [ABSTRACT FROM AUTHOR]

We present a 3D discrete‐continuum model to simulate blood pressure in large microvascular tissues in the absence of known capillary network architecture. Our hybrid approach combines a 1D Poiseuille flow description for large, discrete arteriolar and venular networks coupled to a continuum‐based Darcy model, point sources of flux, for transport in the capillary bed. We evaluate our hybrid approach using a vascular network imaged from the mouse brain medulla/pons using multi‐fluorescence high‐resolution episcopic microscopy (MF‐HREM). We use the fully‐resolved vascular network to predict the hydraulic conductivity of the capillary network and generate a fully‐discrete pressure solution to benchmark against. Our results demonstrate that the discrete‐continuum methodology is a computationally feasible and effective tool for predicting blood pressure in real‐world microvascular tissues when capillary microvessels are poorly defined. [ABSTRACT FROM AUTHOR]

An original numerical matrix algorithm aimed at solving the optimal control problems for linear systems of ordinary differential equations with constant coefficients is proposed. The work of the algorithm is demonstrated with the problem, which consists in generating a given small disturbance of the Poiseuille flow in an infinite duct by blowing and suction through the walls. The costs of creating the leading modes and optimal disturbances are compared, which is of independent interest. [ABSTRACT FROM AUTHOR]

Viscoelastic flows play an important role in numerous engineering fields, and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids. However, traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time, and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids. In this paper, a universal multiscale method coupling an improved smoothed particle hydrodynamics (SPH) and multiscale universal interface (MUI) library is presented for viscoelastic flows. The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain. We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows. In the first example, the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions. The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain. In the second example, the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics (DPD) method. The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain. Moreover, transferring different physical quantities has an important effect on the numerical results. [ABSTRACT FROM AUTHOR]

Flows of solid particles in suspension are ubiquitous in both nature and industry. Compared to a spherical particle, the dynamics of a non-spherical particle in flow is much less understood, especially its interaction with a micro-confined environment. We consider an elliptical particle because its different aspect ratios can represent a large family of non-spherical shapes. To capture the complex dynamic interface between the particle and the flow, we employ the smoothed particle hydrodynamics method and benefit from its Lagrangian property. In particular, we consider an elliptical cylinder in confined Poiseuille flow and systematically study the effects of five factors: the confinement strengths, the particle Reynolds numbers between 0.1 and 10, particle initial positions/orientations, and the particle aspect ratios, respectively. We identify three types of periodic motion at steady state and they are tumbling, oscillation with either major or mini axis along the flow. In weakly confined channels, the particle always tumbles and has determined focusing positions off the centerlines, which depend mainly on the competition between the shear gradient lift and wall-induced force in the transverse direction. In strongly confined channels, the particle has steady oscillations at the centerlines, and its actual state depends on the Reynolds number, initial states, and aspect ratios of the particle. Our study provides a valuable insight into the dynamics of non-spherical particles in microfluidic systems. [ABSTRACT FROM AUTHOR]

In this paper, we study the linear stability of a planar Poiseuille flow of a De-Kée–Turcotte fluid. After a suitable scaling of the governing equations, we explicitly determine the base one-dimensional (1D) flow by exploiting the Lambert function. We show that the problem admits two steady-state solutions, one for each branch of the Lambert function. We perturb the base flow with a disturbance in the form of longitudinal wave of unknown amplitude. We derive the modified Orr–Sommerfeld equation for the second component of the perturbed velocity. The relative eigenvalue problem is solved through a spectral collocation scheme based on Chebyshev polynomials. We prove that the solution corresponding to the secondary branch of the Lambert function is unconditionally unstable, whereas the one relative to the principal branch may exhibit two critical Reynolds numbers: one marking the onset of instability and the other its cessation. [ABSTRACT FROM AUTHOR]

The investigation focuses on the hydrodynamic instability of a fully developed pressure-driven flow within a bidisperse porous medium containing an electrically conducting fluid. The study explores this phenomenon using the Darcy theory for micropores and the Brinkman theory for macropores. The system involves an incompressible fluid under isothermal conditions confined in an infinite channel with a constant pressure gradient along its length. The fluid moves in a laminar fashion along the pressure gradient, resulting in a time-independent parabolic velocity profile. Two Chebyshev collocation techniques are employed to address the eigenvalue system, producing numerical results for evaluating instability. Our findings indicate that enhancing the values of the Hartmann numbers, permeability ratio, porous parameter, and interaction parameter contributes to an enhanced stability of the system. The spectral behavior of eigenvalues in the Orr-Sommerfeld problem for Poiseuille flow demonstrates noteworthy sensitivity, influenced by various factors, including the mathematical characteristics of the problem and the specific numerical techniques employed for approximation. [ABSTRACT FROM AUTHOR]

The unsteady Poiseuille flow of Carreau‐Yasuda fluid in a pipe, caused by a variable pressure gradient, is studied theoretically. As a special case, the steady flow is considered separately. It is proved that at some values of the viscosity model parameters, the problem has a generalized solution, while at others ‐ a classical solution. For the latter, a necessary and sufficient condition is found, which depends on the maximum pressure gradient and the Carreau‐Yasuda model parameters. [ABSTRACT FROM AUTHOR]

We present a numerical study for Poiseuille and Couette as well as Taylor- Couette swirling flows. The governing equations of momentum and energy are transformed into coupled and nonlinear ordinary differential equations using similarity transformation and then solved numerically. We critically evaluate the effect of dimensionless pressure gradients on fluid velocity and observed that the velocity increases as the dimensionless pressure gradient increases. Couette flows are simulated in different scenarios, including top plate moving, bottom plate moving, and top plate moving in adverse pressure gradient conditions. In a third scenario, the flow velocity profile revealed a backflow regime (BFR). A simple schematic model is, therefore, proposed to explain the presence of BFR in the flow's profile. Numerical and analytical solutions around the circular cylinder are presented. The marginal discrepancy between the analytical and numerical profiles is maximum at ~ 900 and 270° degrees, which indicates that the chosen method is suitable and capable of reproducing engineering problems. Velocity magnitude and vector diagrams show that the cylinder shape was found to have a significant effect on the flow field. The velocity at the top and bottom of the cylinder is twice the velocity that seen away from the cylinder. [ABSTRACT FROM AUTHOR]

This study investigates the complex behavior of Jeffrey nanofluid flow in a porous oscillating microchannel under the influence of magnetohydrodynamic (MHD) effects. The research explores how magnetic field distortions lead to diverse accumulation patterns of nanofluid particles, a phenomenon attributed to homogeneous magnetization in fluid dynamics. Nanoparticles ranging from 0.25 % to 0.5 % (low and inexpensive concentrations) are remarkably consistent for best results in most machining procedures. Different concentrations of various nanomaterial's is utilized (φ1 = φ2 = 0.01, 0.02, 0.03, 0.04) to make the simple nanfluid and hybrid nanofluid suspensions. By employing fractal-fractional derivatives governed by power law, a mathematical model developed to describe the time-varying, compressible MHD flow of Jeffrey nanofluid. The model incorporates the effects of heat transfer, pressure, and magnetic fields on the fluid dynamics. A novel fractional approach utilizing the Laplace transform is applied to solve the fractal MHD hybrid-fluid model integrated into a porous medium. The study reveals velocity flow decrease with increasing Reynolds numbers but increase with channel inclination. Additionally, both the Darcy number and magnetic field orientation enhance heat transfer rates. In addition, the velocity profile enhanced by the hybrid nanofluid suspension as compared to simple nanofluid flow. The research validates its findings by demonstrating the convergence of fractional and numerical solution methods. Furthermore, the study compares the performance of different hybrid nanofluids, concluding that water-based (H2O + GO + MoS2) hybrid fluids exhibit slightly superior characteristics compared to (CMC + GO + MoS2) hybrid nanofluids.

Although the roll-streak (R-S) is fundamentally involved in the dynamics of wall turbulence, the physical mechanism responsible for its formation and maintenance remains controversial. In this work we investigate the dynamics maintaining the R-S in turbulent Poiseuille flow at R = 1650. Spanwise collocation is used to remove spanwise displacement of the streaks and associated flow components, which isolates the streamwise-mean flow R-S component and the second-order statistics of the streamwise-varying fluctuations that are collocated with the R-S. This partition of the dynamics into streamwise-mean and fluctuation components facilitates exploiting insights gained from the analytic characterization of turbulence in the second-order statistical state dynamics (SSD), referred to as S3T, and its closely associated restricted nonlinear dynamics (RNL) approximation. Symmetry of the statistics about the streak centreline permits separation of the fluctuations into sinuous and varicose components. The Reynolds stress forcing induced by the sinuous and varicose fluctuations acting on the R-S is shown to reinforce low- and high-speed streaks, respectively. This targeted reinforcement of streaks by the Reynolds stresses occurs continuously as the fluctuation field is strained by the streamwise-mean streak and not intermittently as would be associated with streak-breakdown events. The Reynolds stresses maintaining the streamwise-mean roll arise primarily from the dominant proper orthogonal decomposition (POD) modes of the fluctuations, which can be identified with the time average structure of optimal perturbations growing on the streak. These results are consistent with a universal process of R-S growth and maintenance in turbulent shear flow arising from roll forcing generated by straining turbulent fluctuations, which was identified using the S3T SSD. [ABSTRACT FROM AUTHOR]

Poiseuille flows are considered as flows of Newtonian fluids through stationary pipes, with applications ranging from the pharmaceutical industries to manufacturing companies. These flows have been extensively studied in several works of literature due to their relevance in many spheres of life. However, the Poiseuille flow for non-Newtonian flows has not gained much attention, even though most fluids are non-Newtonian. Based on this, this study investigates the Poiseuille flow of the second-grade fluid. Second-grade fluids are viscoelastic non-Newtonian fluids that exhibit both shear-thinning and shear-thickening with applications found in several industrial applications such as pharmaceutical, cosmetics and polymer processing. The Poiseuille flow of second-grade fluid is formulated from the underlying Navier-Stokes' equations and the general assumptions of Poiseuille flow are invoked to reduce the equations to the regular ordinary differential equations. An analytical solution for the flow problem is sought using the method of separation of variables and the results are graphed to show the response of velocity and flow rate to the parameters of the flow. The outcomes show that velocity distribution reduces as the pipe radius increases and second-grade fluid has lower velocity than the Newtonian fluid. [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]

We present a numerical study, using the vortex filament model, of vortex tangles in a flow of pure superfluid 4 He in the T = 0 limit through a channel of width D = 1 mm for various applied velocities V. The flat channel walls are assumed to be microscopically rough such that vortices terminating at the walls are permanently pinned; vortices are liberated from their pinned ends exclusively through self-reconnection with their images. Sustained tangles were observed, for a period of 80 s, above the critical velocity V c ∼ 0.20 cm s - 1 = 20 κ D . The coarse-grained velocity profile was akin to a classical parabolic profile of the laminar Poiseuille flow, albeit with a nonzero slip velocity ∼ 0.20 cm s - 1 at the walls. The friction force was found to be proportional to the applied velocity. The effective kinematic viscosity was ν ′ ∼ 0.1 κ , and effective Reynolds numbers within Re ′ < 200 . The fraction of the polarised vortex length varied between zero in the middle of the channel and ∼ 60% within the shear flow regions ∼ D / 4 from the walls. Therefore, we studied a state of statically polarised ultraquantum (Vinen) turbulence fuelled at short length scales by vortex reconnections, including those with vortex images due to the relative motion between the vortex tangle and the pinning rough surface. [ABSTRACT FROM AUTHOR]

This paper reviews the latest findings on instability and subcritical transition to turbulence in wall-bounded flows (i.e., pipe Poiseuille flow, plane channel flow, and plane Couette flow). The main focus was on the early stage of transitional flow and the appearance of coherent structures. The scaling of threshold disturbance amplitude for the onset of natural transition was discussed. Generally, the scaling proved to be in the form of Ac = O(Reγ ) for Newtonian fluids where Re is the Reynolds number, γ ≤ -1, and Ac is the critical perturbation amplitude. It was noted that exploration of perturbations like vortices, streaks, and traveling waves together with their amplitudes could clarify the instability and transition process. Hence, this paper focused on physical behavior and realizations of the transitional flow. Finally, a summary of consequential implications and some open issues for future works were presented and discussed. [ABSTRACT FROM AUTHOR]