Bingham plastic fluids are frequently found in both biological and industrial contexts, especially in situations requiring the movement of mucus, chyme, or blood that has unusual viscosity through microchannels. Inspired by the function of cilia-driven peristalsis in biological transport, this research presents a new mathematical model for the peristaltic motion of a Bingham plastic fluid that contains active microorganisms within an asymmetric microchannel incorporating slip boundary effect. The primary partial differential equations governing momentum, heat, concentration, and the transport of microorganisms are transformed into a non-dimensional format based on the assumptions of long wavelength and low Reynolds number. By utilizing suitable scaling parameters, the system is simplified to a pair of nonlinear ordinary differential equations. The slip effects are included along the channel walls, and the cilia-induced movement is represented through parameters relating to eccentricity and cilia length. The obtained equations, together with the relevant boundary conditions, are solved numerically using the bvp4c method in MATLAB. The findings indicate that slip increases the velocity near the walls of the channel, but decreases it in the core of the channel. A rise in the Bingham number diminishes fluid trapping, whereas a greater eccentricity enhances pumping efficiency by decreasing recirculating bolus regions. The temperature rises due to heat generation and Joule heating but is lowered by thermal radiation and heat sink effects. Concentration declines with an increase in Schmidt number and chemical reactions, while the density of microorganisms decreases with thermophoresis, bioconvection constant, and Peclet number. The novelty of this study lies in integrating the Bingham plastic rheology with cilia-induced wall motion, slip effects, and microorganism transport in an asymmetric channel. This fills a gap in the existing literature where such a combination has not been previously addressed, despite its strong relevance to physiological flows such as mucus clearance, chyme transport, and biomedical peristaltic pump design.

Purpose The shape factor of nanoparticles is a parameter of interest in the variation of the thermophysical properties of nanofluids, and it affects their fluid flow and temperature distribution. Hence, this study aims to focus on analysing the influence of the shape factor on the convective heat and mass transfer over a nonlinear stretching sheet under the influence of magnetohydronamics. Design/methodology/approach By using similarity transformations, the governing system of partial differential equations was simplified to a nonlinear ordinary differential equation system, which was solved numerically using an explicit finite difference method (Keller box method). The behaviour of the fluid velocity and thermal profile at the boundary, as a result of slip conditions, is studied through a comprehensive parameter exploration. Findings The behaviour of the fluid velocity and thermal profile at the boundary, as a result of slip conditions, is studied by a very extensive parameter exploration. The major findings reveal that increasing values of magnetic parameters promote Lorentz’s force, which slows down the velocity profile. Increasing the stretching rate parameter causes deformation reducing both the velocity and temperature profile. It is found that the temperature rise for elevated values of a thermophoretic parameter is greater for brick-shaped nanoparticles. It is also observed that the heat transfer (Nusselt number) for augmented values of Eckert number is lower in brick-shaped nanoparticles compared to platelet-shaped nanoparticles. Research limitations/implications The main limitation of this work has been the two-dimensional nature of the modelling, the analysis of a certain range of parameters that may not suit all the reader interests and the assumption of specific functions for the stretched sheet velocity and temperature, as well as the magnetic field. Also, regarding the nanofluid characteristics, it has been considered as single-phase, with Fe3O4 particles only and Newtonian. Originality/value This manuscript analyzes mathematically important aspects of the behaviour of a nanofluid with nanoparticles in magnetohydrodynamics of a non-linearly stretched sheet. This work is a detailed parametric exploration (magnetic parameter, stretching parameter, slip parameters, Brownian motion parameter, thermophoretic parameter, Ecker number, Lewis number and solid volume fraction) of the behaviour of two different nanoparticle shapes (brick and platelet), which sheds light on relevant aspects such as, skin friction, heat transfer and mass transfer. These are valuable results for the scientific community for either perform their numerical analysis upon these results and methodology, or perform experimental prototyping according to the behaviour described in this manuscript.

Wall slip refers to the phenomenon where particles in a suspension move away from the boundary wall, creating a thin liquid-rich layer nearby. This occurrence can significantly affect rheological measurements, notably viscosity, shear stress, and shear rate. Suspensions find widespread use in various industries such as food processing, personal care products, pharmaceuticals, paints, medicine, and agrochemicals. Predicting the actual shear rate traditionally proves challenging, time-consuming, and cost-intensive. Hence, there's a pressing need for a computational model to perform this task with acceptable accuracy. Leveraging the precise input-output mapping capability of recurrent neural network (RNN), it was employed to develop a model for the actual shear rate prediction. Evaluation of these models through statistical analyses reveals that RNN model III outperforms others, boasting the highest coefficient of determination (0.9998), lowest mean squared error (0.000721), root mean squared error (0.001361), most negative Akaike information criterion (-18646.3), Bayesian information criterion (-18635.9), and the smallest percentage error (15%). This developed model provides an alternative means to predict suspension shear rate under experimental constraints.

This study analytically explores the peristaltic flow and heat transfer of a couple-stress fluid in the annular space between coaxial inclined tubes, where the outer wall exhibits sinusoidal motion. The governing equations, simplified under long-wavelength and low Reynolds number assumptions, are solved using the Adomian decomposition method. Key effects of magnetic field strength, wall slip, porous media permeability, peristaltic amplitude, and internal heat generation are examined. Results show that wall slip reduces near-wall shear, while magnetic fields enhance pressure gradients and dampen flow via Lorentz forces. Our results quantify several critical interactions. For instance, applying a magnetic field was found to increase the pressure gradient required to drive the flow by approximately 50%, while also dampening the axial velocity by about one-third. Conversely, introducing slip at the boundary reduced near-wall shear stress by 17%, and the use of a porous medium enhanced the axial flow speed by 35% while reducing friction. These findings offer insights into optimizing biomedical and industrial peristaltic systems, such as drug delivery and endoscopy, by balancing flow efficiency, shear control, and energy demands. Future work may involve experimental validation and Multiphysics optimization for practical applications.

Wall slip sensitivity and non-sphericity and orientation effects are investigated for a moving no-slip solid body immersed in a fluid above a plane slip wall with a Navier slip. The wall–particle interactions are examined for the body motion in a quiescent fluid (resistance problem) or when freely suspended in a prescribed ‘linear’ or quadratic ambient shear flow. This is achieved, assuming Stokes flows, by using a boundary method which reduces the task to the treatment of six boundary-integral equations on the body surface. For a wall slip length $\lambda$ small compared with the wall–particle gap $d$ a ‘recipe’ connecting, at $O((\lambda /d)^2),$ the results for the slip wall and another no-slip wall with gap $d+\lambda$ is established. A numerical analysis is performed for a family of inclined non-spheroidal ellipsoids, having the volume of a sphere with radius $a,$ to quantity the particle behaviour sensitivity to the normalised wall slip length $\overline {\lambda }=\lambda /a,$ the normalised wall–particle gap ${\overline {d}}=d/a$ and the particle shape and orientation (here one angle $\beta ).$ The friction coefficients for the resistance problem exhibit quite different behaviours versus the particle shape and $({\overline {d}}, \overline {\lambda },\beta ).$ Some coefficients increase in magnitude with the wall slip. The migration of the freely suspended particle can also strongly depend on $({\overline {d}}, \overline {\lambda },\beta )$ and in a non-trivial way. For sufficiently small $\overline {d}$ a non-spherical particle can move faster than in the absence of a wall for a large enough wall slip for the ambient ‘linear’ shear flow and whatever the wall slip for the ambient quadratic shear flow.

When wall slip wins over shear flow: A temperature-dependent Eyring slip law and a thermal multiscale model for diamond-like carbon lubricated by a polyalphaolefin oil

On dispersion of solute in a hydromagnetic flow through a channel subject to asymmetric wall temperature and slip velocity

Thermotropic liquid crystal polymers comprise rigid chain segments called mesogens. This study presents a modeling approach to simulate the orientation of these mesogens in a flow channel with a rectangular cross section under no slip and wall slip boundary conditions. Rigid rods with finite length and an initial orientation are proposed. The interactions between the velocity field in the flow channel and these rods are modeled to simulate orientation. Moreover, a highly oriented boundary layer can be simulated. Orientation occurs in the flow direction close to the die wall under the no slip condition due to the high shear rate. As the distance from the die wall increases, the orientation decreases. Wall slip effectuates a more uniform orientation and causes a delay in the development of the highly oriented boundary layer. The thickness profile of this layer exhibits a shape that is analogous to that of a root function. To ensure products with high mechanical properties, it is essential to orient the mesogens at a high level in the die during manufacturing. The presented model enables the prediction of orientation in the flow channel. Therefore, this model is a useful tool to design the process in the right way to reach this goal.

The flow of electrically conducting fluids in rotating porous channels is of significant importance in various engineering and industrial applications, including the cooling of rotating electrical machines, magnetohydrodynamic generators, biomedical devices involving rotational blood flow, and filtration systems in chemical reactors. Motivated by these applications, this paper investigates the flow through a rotating porous channel bounded by two impermeable horizontal plates, where the lower plate is stationary and the upper plate moves at a constant velocity. The system is subjected to a uniform inclined magnetic field, incorporates wall slip effects, and accounts for viscous dissipation. The channel rotates with a constant angular velocity, inducing a secondary flow due to Coriolis effects. Analytical expressions for the velocity profiles and flow rates in both directions are derived, while the temperature distribution is computed numerically using the Runge–Kutta method via MATLAB's built-in solver. A parametric study is conducted to analyze the influence of the Hartmann number, Taylor number, slip parameter, inclination angle of the magnetic field, and Eckert number. A contour plot between the Hartmann number and Taylor number is also analyzed. Furthermore, asymptotic analysis is performed to understand the limiting behavior of the solution with respect to key parameters. Future studies may extend this work to non-Newtonian fluids, transient flow, or geometrically more complex domains.

An asymptotic solution for the planar Poiseuille flow of a power-law fluid with pressure-dependent wall slip

The complex transport behavior of hydrocarbons in micro/nanochannels leads to inaccuracies in identifying hydrocarbon accumulation zones, as well as to hydrocarbon leakage. Hydrocarbon movement through confined channels is difficult to characterize and understand in detail because it involves complex hydrodynamic behaviors of hydrocarbon under the joint effects of various physical and chemical effects. Microfluidic platforms provide a powerful means to directly visualize and quantify these confined transport behaviors. In this work, we summarize recent theoretical and experimental advances enabled by microfluidic approaches and highlight five dominant mechanisms governing hydrocarbon transport in micro/nanochannels: (1) molecular sieving and adsorption jointly control the lower transport limit; (2) asphaltene aggregation induces pore blockage; (3) wall slip triggers ultrafast flow; (4) strong confinement shifts the hydrocarbon phase envelope; (5) wettability and roughness modulate capillary retention and flow resistance. Integrating these insights into reservoir simulation frameworks will improve the accuracy of hydrocarbon flow prediction.

Abstract This study investigates the peristaltic transport of Herschel–Bulkley fluids through a porous, uniform cylindrical tube under the influence of wall slip and variable wall porosity. Such fluid behavior is particularly relevant in biomedical and industrial applications, where the non-Newtonian nature of fluids—like blood and mucus—plays a vital role in transport mechanisms. The governing equations are derived under the assumptions of long wavelength and low Reynolds number, with appropriate boundary conditions including a non-zero slip velocity and porous wall interactions. Analytical expressions for velocity, stream function, pressure gradient, volumetric flow rate, and axial frictional force are obtained. The analysis explores the effects of key physical parameters such as the Darcy number (Da), slip parameter (α), porous wall thickness (ϵ), and power-law index (n) on flow behavior. The results reveal that increased wall permeability (higher Da) and wall slip significantly reduce pressure drop and enhance volumetric flux, while higher yield stress and power-law indices increase flow resistance. The novelty of this work lies in integrating wall slip and porous structure effects with Herschel–Bulkley fluid characteristics in a peristaltic setup—an area that has been limited in existing literature. These insights contribute to the design of efficient peristaltic pumps and biomedical flow devices, especially where fluid rheology and wall interactions critically affect performance.

Neutron reflectometry is a technique for measuring structure near planar interfaces that has been previously used to non-destructively characterize the polymer density of hydrated, dilute, and soft materials. Previous investigations have conducted neutron reflectometry measurements of liquids, gels, emulsion, and polymer solutions at rest, in compression, and subject to shear stress. However, correlating structure with tribological properties of soft materials presents significant experimental challenges for prior instruments due to wall slip, sample thickness, and structural heterogeneity (e.g., depth-wise gradients). A linear reciprocating tribometer offers several advantages for in situ neutron reflectometry studies, including uniform velocity profiles, constant shear stress over large regions of interest, and independent control of normal force and sliding velocity during measurements. This work outlines basic considerations for the design of a custom linear reciprocating tribometer that operates in a neutron beamline and includes commissioning measurements. The tribometer is designed to compress soft and hydrated materials against linearly reciprocating silicon disks. The three key design considerations for this tribometer are (1) safety, (2) neutron transmission, and (3) sample positioning. This instrument design will enable in situ studies of soft matter and illuminate the role of interfacial structure on tribological phenomena.

This study develops a weighted-residual model for Oldroyd-B films on slippery substrates at moderate Reynolds number and large slippery length. Linear stability analysis reveals that wall slip promotes perturbation growth rates, increases cut-off wave numbers, and accelerates long-wave propagation speed, demonstrating a destabilizing effect. Two distinct families of traveling waves are sought, which demonstrate that varying the slippery length can alter the bifurcation type of traveling wave families. Particularly, large slippery length can cause the transition of drag-gravity regime into the drag-inertia regime. In the drag-gravity regime, slippery effect promotes the wave speed and height. However, in the drag-inertia regime, slippery effect can suppress the wave height even though the wave propagates faster. Interestingly, plateau-type waves are found in the Oldroyd-B film flow at large slippery length, which has not been reported previously.

Due to rich rheological properties, dispersions of attractive colloidal particles are ubiquitous in industries. Specifically, upon experiencing a sudden reduction in the shear rate, these dispersions may exhibit transient behaviors such as thixotropy—where viscosity increases over time—and its antonym, antithixotropy, characterized by an initial viscosity decrease before reaching a steady state. While thixotropy has been described as a competition between structure buildup and disruption, the mechanisms of antithixotropy remain poorly understood. Here, we investigate the antithixotropic dynamics of carbon black particles dispersed in oil—a system known for exhibiting antithixotropy—through flow step-down experiments. Using a multitechnique approach combining rheology with velocimetry and structural characterizations, we show that viscosity decrease results from a decrease in wall slip concomitant to shear-induced structural rearrangements, indicating a transition from a dynamical network of fractal clusters into a network of loosely connected dense agglomerates. Additionally, after a characteristic antithixotropic time τ, a steady flow is reached. This time τ diverges with increasing shear rates at a critical value corresponding to a Mason number of one, indicating that antithixotropy occurs only when colloidal attraction outweighs viscous forces. More precisely, we show that the structural rearrangement underpinning the viscosity decrease is mediated by initial elastic stresses σe, such that τ∝σe−3. Finally, on long time scales, the steady state is linked to a microstructure with nearly zero yield stress, indicating a loss of flow memory. These findings clarify the mechanics of antithixotropy and its distinction from thixotropy, providing a better understanding of both processes in attractive colloidal dispersions.

This research investigates the effects of thermal emission, temperature-dependent thermal energy generation/absorption under the application of an inclined magnetic force field on a 3-D micropolar Darcy-Forchheimer stream resting on a convectively heated and nonlinearly elongated sheet with wall slip. The study aims to understand how these factors influence fluid dynamics and heat transfer characteristics in this complex system. To accomplish this, adapting scaling analysis, the set of partial differential equations (PDEs) representing the physics of the problem is altered into a system of ordinary nonlinear differential equations (ODEs). The consequential ODEs are solved utilizing the shooting mechanism in conjunction with the Runge-Kutta Fehlberg algorithm. The visualization of results is discussed eliciting the impact of different parameters emerged in the analysis. It is perceived that the velocity distribution across the fluid is enhanced by the material parameter (β) and the thermal Grashof number (Gr). Augmentation of Forchheimer number ( Fr ) and porosity parameter ( K ) has a declining influence on velocities and the x and y components of drag coefficient. The temperature distribution across the fluid region is boosted with radiation parameter and Biot number. The heat transfer rate is positively correlated with the Prandtl number (Pr), while a contrasting effect is observed with the temperature-dependent heat source/sink (Q).

ABSTRACT To address challenges in modeling inclined two-phase flow in deep-sea gas-lift mining operations, we propose a modified drift-flux model that integrates void-fraction dynamics, a dimensionless pipe-diameter parameter, and the non-Newtonian rheology of deep-sea muds. The model accurately captures flow-regime transitions, predicts void-fraction distributions, and accounts for varying diameters under both unsteady and steady-state conditions. Validation against experimental data demonstrates close agreement in apparent velocities, void fractions, and pressure drop at the outlet. Numerical simulations further explore the effects of pipe inclination on wall shear stress, gas holdup, slip velocity, mixture velocities, and drift velocities. Results reveal that increasing inclination significantly alters flow structure and drift characteristics, informing optimized gas-injection strategies. The integrated model offers enhanced predictive accuracy and economic feasibility for gas-lift operations in inclined pipelines, providing a robust design tool to improve operational efficiency and guide parameter selection in deep-sea mining.

The electroosmotic flow (EOF) of non-Newtonian fluids plays a significant role in microfluidic systems. The EOF of Powell–Eyring fluid within a parallel-plate microchannel, under the influence of both electric field and pressure gradient, is investigated. Navier’s boundary condition is adopted. The velocity distribution’s approximate solution is derived via the homotopy perturbation technique (HPM). Optimized initial guesses enable accurate second-order approximations, dramatically lowering computational complexity. The numerical solution is acquired via the modified spectral local linearization method (SLLM), exhibiting both high accuracy and computational efficiency. Visualizations reveal how the pressure gradient/electric field, the electric double layer (EDL) width, and slip length affect velocity. The ratio of pressure gradient to electric field exhibits a nonlinear modulating effect on the velocity. The EDL is a nanoscale charge layer at solid–liquid interfaces. A thinner EDL thickness diminishes the slip flow phenomenon. The shear-thinning characteristics of the Powell–Eyring fluid are particularly pronounced in the central region under high pressure gradients and in the boundary layer region when wall slip is present. These findings establish a theoretical base for the development of microfluidic devices and the improvement of pharmaceutical carrier strategies.

This paper primarily focuses on areas within non-Newtonian fluid mechanics that remain underexplored or inadequately investigated. It highlights research domains that have not received sufficient attention or detailed study, while also considering the emergence of new areas unexplored by recent scientific and technological advancements. For example, this study explores research directions and innovative modeling and theoretical strategies for understanding fluid dynamics in complex, deformable, and branched flow systems across multiple scales. The elastoviscoplastic behavior of fluids under external forcing is used to model droplet spreading, coalescence, and filtering over porous and soft substrates. Wall slip and junction resistance effects of the flow are in a tree-like structure. The study also highlights and explores research directions in the flow physics of non-Newtonian fluids that exhibit odd viscosity and odd elasticity, focusing on their unconventional stress–strain responses and the resulting unique flow behaviors. The objective of this paper is to raise awareness about these relatively neglected or unexplored areas of research, encouraging researchers to put efforts toward these promising domains. By doing so, they can contribute to advancing the field in ways that diverge from which have already been sufficiently explored and may lead to breakthroughs and novel discoveries by generalizing the existing laws or creating new models and laws. Moreover, addressing these under-explored areas could have far-reaching implications for both theoretical and practical applications in non-Newtonian fluid mechanics. Investigating these areas more deeply could uncover new insights, enhance existing models, and drive forward technological advancements that were previously overlooked. In addition, this paper will briefly discuss the potential introduction of novel tools, techniques, and methodologies that could be applied to these research areas, as well as to the broader field of non-Newtonian fluid mechanics. Furthermore, we also discuss the current and upcoming applications using non-Newtonian fluids. These innovations could open up new avenues of exploration and help overcome some of the existing limitations in past and current research.

ABSTRACTUnderstanding the flow characteristics of materials in complex flow channels is crucial for key dimension control and process optimization in precision forming manufacturing of multi‐cavity tubes. Conventional reverse compensation design methods for extrusion die outlets based on polymer material swell deformation are not applicable to polytetrafluoroethylene (PTFE) paste extrusion. This study proposes a rheology‐structure co‐optimization method for reverse design of an eight‐cavity PTFE tube extrusion die. By coupling the Carreau model with wall slip characteristics, we established quantitative relationships between geometric parameters of the flow channel (mandrel compression zone profile, mandrel compression ratio, and flow channel entrance angle) and the exit velocity field. Combining with the Kriging surrogate model optimization method and using the minimum flow balance coefficient as the objective function, local optimization of the eight‐cavity PTFE tube die flow channel was achieved. The results indicate that after optimization, the die exit velocity decreased from 14.58 to 9.72 mm/s, accompanied by a 67.1% reduction in the maximum velocity gradient and a 92.8% decrease in the flow balance coefficient. This research provides a theoretical foundation and technical support for precision multi‐cavity extrusion die design of high‐viscosity PTFE paste materials.