Polymer based microfluidics, using polydimethylsiloxane (PDMS), are highly adaptable platforms for electrochemical studies commonly used for numerous applications. Deformations of these PDMS devices due to the flow pressure drop in microchannels have been widely documented in literature but cannot be prevented in all applications even though it is critical to measure quantitative data. In this work, we show that in electrochemical microfluidic devices used in energy conversion systems, the velocity profiles and channel deformations can be quantitatively measured based on spectro-electrochemistry and numerical simulations of Hagen-Poiseuille flows. PDMS deformations are found amplified in the case of large channel aspect ratios (i.e. close to 100), with deformation Δ h / h 0 > 100 % at 50 kPa, and start to be non-negligible > 10 % for channel internal pressure above 5 kPa. Finally, by considering these channel deformations in the Beer-Lambert law, we show that accurate absorbance and concentration measurements can be obtained using visible spectroscopy regardless the channel internal pressure.

The generalization of the Feynman modification of Landau's (1941) superfluid criterion, which gives the Reynolds number threshold condition Re>Reth≈1976 for the energetically favorable creation of small thin vortex rings in the boundary layer of the classical laminar Hagen–Poiseuille (HP) flow, is stated. This condition of the HP flow instability is not dependent on the infinitesimal perturbation energy, as usual in the linear instability theory, and is consistent with a sharp increase in the pipe drag coefficient and with the observational data for puff formation in the HP flow. The explicit analytical solutions for the pipe drag coefficient and for the viscous diffusion of vorticity in shear flows are obtained. The latter solution describes the dissipation and production rates of perturbation energy near the wall of the pipe and the characteristic time for the HP flow instability realization. That solution meets with the vortex burst periods observed in the boundary layer and with known observational data on the dissipation and production rates for the turbulent flow energy in the pipe and in the boundary layer.

A three-dimensional fractal permeability model for granular porous media incorporating pore roughness.

Abstract Stability analysis is a crucial tool for studying dynamical systems in mathematics, physics, and engineering. Lyapunov functions provide a framework for determining the stability of these systems, but constructing them is often challenging for non-linear systems. This paper focuses on using sum-of-squares (SOS) methods to construct quadratic Lyapunov functions for proving the local stability of finite-dimensional systems. These systems are designed to share certain properties of shear flows and are therefore described by second-order polynomials. Additionally, the system matrix of the linear part is non-normal, which presents challenges in constructing a Lyapunov function. Two established SOS-based algorithms from the literature (SOS1 and SOS2) are compared based on the size of the provable region of attraction (ROA), computational time, and the maximum allowable degrees of freedom of the system. Furthermore, this paper introduces a novel modification to the SOS2 algorithm, termed SOS2m, which aims to provide a larger ROA than the original SOS2 method with minimal additional computational cost. This new SOS2m method is shown to strike an effective balance between accuracy and computational efficiency. The presented methods, while demonstrated on shear flow models, are extendable to other dynamical systems described by polynomial functions. A further motivation for this research is to advance analysis methods for investigating subcritical laminar-turbulent transition and to develop methodologies for estimating permissible perturbation levels. To demonstrate their effectiveness, the three algorithms (SOS1, SOS2, and SOS2m) are applied to a simplified model of laminar-turbulent transition and truncated finite-dimensional reduced-order models of Poiseuille and Couette flows.

Data-driven bifurcation handling in physics-based reduced-order vascular hemodynamic models.

The pseudopotential lattice Boltzmann method is a prominent approach for simulating multiphase flows, valued for its physical intuitiveness and computational tractability. However, existing immiscible pseudopotential methods for modeling dynamic multi-component immiscible fluid systems involving open boundaries face persistent challenges, notably the influence of spurious currents on interface formation and breakup, as well as the effects of inlet and outlet boundary configurations on simulation stability. Therefore, this paper proposes a corrected open boundary framework based on multiple-relaxation-time for the immiscible pseudopotential model. Our method includes three key improvements: (1) For the accurate recovery of macroscopic quantities at the inlet boundary, correction coefficients are introduced to reconstruct the distribution function; (2) Based on real-time mass flow rates at the inlet and outlet, the outlet boundary velocity is adjusted to ensure global mass conservation in the computational domain; (3) The relaxation coefficient related to numerical stability is adjusted based on the viscosity of two-phase fluids to reduce spurious currents. To validate the reliability of the proposed corrected method, four benchmark cases were simulated: Laplace tests and Taylor deformation, two-phase Poiseuille flow, migration of droplets in microchannels, as well as droplet generation in T-shaped and co-flow devices. The results demonstrate that the corrected method reduced the average spurious currents at the phase interface by 65.8% and controlled the average mass deviation of the fluid system at around 3.5%. In addition, the morphology of the droplets differs by less than 5% compared to the benchmark examples and experiments.

Abstract To enhance understanding of basket granulation, this study presents a custom‐built, instrumented radial extruder designed to evaluate how system parameters, including hole diameter, hole count, die thickness, and roller radius, affect extrusion force and extrusion rate. By adapting the Hagen–Poiseuille and orifice flow equations, semi‐empirical models were developed to predict extrusion rate and extrusion force, respectively. A novel composite solidity‐aspect ratio (CSAR) index was introduced to quantify extrudate quality by integrating both aspect ratio and solidity into a single metric. High CSAR values corresponded to elongated, compact extrudates, while low values indicated fractured, irregular morphologies. A physics‐informed neural network (PINN) was developed to predict extrusion force by integrating the developed extrusion force model into the machine learning framework. A proof‐of‐concept study experimentally validated that the PINN achieved better predictive accuracy for extrusion forces compared to conventional artificial neural networks (ANNs).

The inertial migration of a neutrally buoyant sphere in pipe Poiseuille flow is examined using numerical simulations. Three migration regimes are observed with increasing Reynolds number ( ${\textit{Re}}$ ): monotonic convergence to the equilibrium position, overshooting convergence and damped oscillations. The critical Reynolds numbers separating these regimes decrease with the sphere-to-pipe diameter ratio, $d/D$ . The axial entry length, $L_{p}$ , required for the sphere to reach equilibrium decreases with both ${\textit{Re}}$ and $d/D$ in the monotonic regime, but increases in the oscillatory regime. These results elucidate the dynamics of inertial migration and inform strategies for manipulating particles in confined, particle-laden flows.

We numerically investigate the lateral migration of deformable particles in rectangular-channel Poiseuille flow using a fictitious-domain method with distributed Lagrange multipliers. Compared with rigid particles, deformable particles experience significantly deformation-induced lift, driving them toward the channel corners. During migration, soft particles remain farther from the wall than stiff particles and, after reaching a corner, shift away from the corner along the bisector, whereas stiff particles attain stable equilibrium at the corner. In the case of cylindrical particles, migration is irregular and accompanied by stronger vorticity, enhanced cross-stream velocities, and continuous tumbling with pronounced deformation. By focusing on rectangular-channel geometry, this work reveals deformability-dependent corner migration and finite-offset equilibria that are absent in rigid-particle dynamics, and extends the analysis to deformable cylinders to expose shape-driven irregular migration and tumbling.

The present study investigates the stability of viscoelastic Poiseuille flow of Walters' liquid B, placed within a transverse magnetic field and restricted between two infinite parallel plates. Stability is performed within the framework of modal and non-modal analyses to discuss the impact of the Reynolds number, fluid elasticity, and magnetic field strength. The governing fourth-order linearized disturbance equation, modified by the transverse magnetic field and the viscoelasticity of the fluid, is solved numerically using the Chebyshev spectral and shooting methods. A modal analysis examines the eigenspectrum, continuous spectrum, and neutral stability curves to characterize long-term stability behavior, revealing that increased fluid elasticity destabilizes the flow, whereas the transverse magnetic field tends to stabilize it. Analysis of ε-pseudospectrum and transient energy growth for optimal two-dimensional perturbations involving the non-normal Orr–Sommerfeld operator is investigated using a non-modal analysis. The ε-pseudospectral contours protrude into the unstable region, signaling flow instability, while the transient growth function shows that disturbances initially surge exponentially before decaying and subsequently evolving into sustained growth or further decay based on the magnetic effect and the elasticity number. Energy budget analysis of the perturbations further elucidates these dynamics by identifying regions of negative energy production due to Reynolds stress, alongside positive contributions from viscous dissipation and transverse magnetic field effects. The study provides a detailed discussion of these complex flow phenomena and their implications for flow stability.

Influence of spanwise domain constraint on flow statistics and heat transfer in spanwise rotating plane Poiseuille flows

Accurately modeling immiscible fluid flow in disordered media remains a significant challenge due to the interference of spurious currents. Using the multiple-relaxation-time (MRT) multicomponent pseudopotential lattice Boltzmann method as an exemplar, we perform a Helmholtz decomposition on the anisotropic residual of discrete interaction forces to elucidate its coupling to viscosity pathways. The solenoidal component dissipates through shear viscosity (μ), while the irrotational component engages bulk viscosity (ζ), establishing distinct routes for suppressing spurious currents. Numerical experiments show that employing a 10th-order interaction force markedly reduces the solenoidal share of the residual—by three to four orders of magnitude compared to fourth-order schemes—thereby activating bulk-viscosity control via the energy-mode relaxation parameter (se, sϵ). This approach attains spurious capillary numbers as low as 10−5 and maintains stability at high viscosity ratios, representing up to two orders of magnitude improvement over MRT color-gradient models. The methodology is validated through Laplace pressure tests, two-component Poiseuille flow, Taylor–Bretherton bubble dynamics, and applications in digitized porous media under challenging wettability conditions and high viscosity ratios. From analysis to implementation, the present framework advances high-fidelity multiphase simulations in complex geometries at high viscosity ratios.

Hydrothermal and entropy generation analysis of mixed convection heat transfer in Couette–Poiseuille flow of a trihybrid nanofluid over a backward-facing step

Four-dimensional (4D) Flow MRI can noninvasively measure cerebrovascular hemodynamics but remains underused clinically because current workflows rely on manual vessel segmentation and yield velocity fields sensitive to noise, artifacts, and phase aliasing. We present VAST (Vascular Flow Analysis and Segmentation), an automated, unsupervised pipeline for intracranial 4D Flow MRI that couples vessel segmentation with physics-informed velocity reconstruction. VAST derives vessel masks directly from complex 4D Flow data by iteratively fusing magnitude- and phase-based background statistics. It then reconstructs velocities via continuity-constrained phase unwrapping, outlier correction, and low-rank denoising to reduce noise and aliasing while promoting mass-consistent flow fields, with processing completing in minutes per case on a standard CPU. We validate VAST on synthetic data from an internal carotid artery aneurysm model across SNR = 2-20 and severe phase wrapping (up to five-fold), on in vitro Poiseuille flow, and on an in vivo internal carotid aneurysm dataset. In synthetic benchmarks, VAST maintains near quarter-voxel surface accuracy and reduces velocity root-mean-square error by up to fourfold under the most degraded conditions. In vitro, it segments the channel within approximately half a voxel of expert annotations and reduces velocity error by 39% (unwrapped) and 77% (aliased). In vivo, VAST closely matches expert time-of-flight masks and lowers divergence residuals by about 30%, indicating a more self-consistent intracranial flow field. By automating processing and enforcing basic flow physics, VAST helps move intracranial 4D Flow MRI toward routine quantitative use in cerebrovascular assessment.

This work investigates the role of an active Navier–Stokes angular term, inherent in micropolar theory, in characterizing small-scale turbulence behavior. By incorporating the micropolar viscosity ratio m, a modified Navier–Stokes equation is derived that allows for fine-tuning of small-scale turbulence intensity without changing the bulk flow properties. Direct numerical simulations of turbulent micropolar Poiseuille flow show that increased m intensifies the near-wall turbulence and enhances dissipation of turbulent kinetic energy, particularly within the viscous sublayer. The decisive role of small-scale structures in micropolar flows is further enhanced here by the analysis of helicity, where acceleration of velocity–vorticity alignment is observed. The outcome underlines the potential of a micropolar model in advancing studies and modeling of turbulence.

In this paper, we propose a complete formulation of the Lattice Boltzmann Method adapted for quantum computing. The classical collision, based on linear equilibrium distribution functions and streaming steps, are reformulated as linear algebraic operations. The inherently non-unitary collision operator is decomposed using Singular Value Decomposition and the Linear Combination of Unitaries technique. Bounce-back boundary conditions are incorporated directly into the collision matrix, while the streaming step is realized through conditional unitary shift operations on spatial registers, controlled by lattice velocity indices encoded in the distribution function register. This formulation ensures that the streaming step remains purely unitary. The resulting quantum circuit is implemented using Qiskit and validated against Couette flow and Poiseuille flow benchmarks. The simulation accurately reproduces the expected velocity profile, with relative errors below 1 0 − 4 . This work establishes a foundational framework for quantum fluid solvers and provides a pathway toward quantum computational fluid dynamics.

Poiseuille flow of hyperbolic Ericksen-Leslie system in dimension two

Graphene-based materials, with their exceptional physicochemical properties, have demonstrated great potential in desalination. However, conventional graphene membranes face a trade-off between water permeability (WP) and salt rejection, which imposes certain limitations on their overall water treatment performance. In this study, we employ molecular dynamics simulations to demonstrate a strategically engineered intercalated-graphene channel that synergistically combines ultra-high water transport capacity with exceptional ion rejection (IR) capabilities. An interesting phenomenon we observed is that as the intercalation position changes, the salt rejection of the device exhibits a pronounced peak behavior. For small-sized channels, this can be primarily attributed to the high energy barrier for ion transport caused by the dehydration-reassociation process, which effectively blocks ions. For large-sized channels, where the dehydration process is weak, the primary barrier to ion diffusion arises from changes in the water layer structures, because water and ions are coupled, moving together as a co-transport system. Additionally, both water and ion flux exhibit a linear increase with pressure difference (ΔP), aligning with the predictions of the ideal Hagen-Poiseuille equation. Overall, in the best-performing system, the IR remains above 93.1% even as the ΔPincreases, while maintaining high WP, effectively achieving a balance between both factors. Our findings highlight how sub-nanometer geometric structure control can fundamentally alter transport physics in desalination meters.

When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a novel numerical formulation for simulating incompressible viscous flows at low Reynolds numbers in the presence of deformable interfaces. Our method employs a vorticity-stream vector formulation that significantly simplifies the fluid solver, transforming it into a set of coupled Poisson problems. The body–fluid interface is modeled using a phase field, allowing for the incorporation of various free-energy models to account for membrane bending and surface tension. In contrast to existing three-dimensional approaches, such as lattice Boltzmann methods or boundary-integral techniques, our formulation is lightweight and grounded in classical fluid mechanics principles, making it implementable with standard finite-difference techniques. We demonstrate the capabilities of our method by simulating the evolution of a single vesicle or droplet in Newtonian Poiseuille and Couette flows under different free-energy models, successfully recovering canonical axisymmetric shapes and stress profiles. Although this work primarily focuses on single-body dynamics in Newtonian suspending fluids, the framework can be extended to include body forces, inertial effects, and viscoelastic media.

Role of insoluble surfactant on electrohydrodynamic stability of a two-layer plane Poiseuille flow: An asymptotic analysis