Fluid mechanics of flow in hydrophobic, rectangular microchannels with finite aspect ratios is of paramount importance. In such microchannels, not only the effect of the side walls should be taken into account, but also the classical assumption of no-slip boundary condition (BC) is no longer valid at the solid-liquid interface. Accordingly, slip flow can occur in microchannels fabricated from surfaces with low wetting conditions, hydrophobic surfaces. Determining the interactions of liquid molecules adjacent to solid surface is still a challenging issue, and it is especially important in small scale domains. Herein, the fluid mechanics of flow through rectangular hydrophobic microchannels has been reconsidered by taking into account the general Navier-slip BCs at the solid-liquid interface. For fully developed incompressible flow in microchannels at low Reynolds number, partial differential equation (PDE) of the momentum equation simplifies to the classical Poisson equation. Accordingly, by analytically solving the Poisson equations with general Navier-slip BCs, the most general forms of velocity distributions, flow rate, friction factor and Poiseuille number have been obtained.

We present an exact expression for the upscaled dynamic dispersion coefficient (D) for one-dimensional transport by Hagen-Poiseuille flow which is the basis for modeling transport in porous media idealized as capillary tubes. The theoretical model is validated by comparing the breakthrough curves (BTCs) from a 1D advection-dispersion model with dynamic D to that from direct numerical solutions utilizing a 2D advection-diffusion model. Both Taylor dispersion theory and our new theory are good predictors of D at lower Peclet Number (Pe) regime, but gradually fail to capture most parts of BTCs as Pe increases. However, our model generally predicts the mixing and spreading of solutes better than Taylor’s theory since it covers all transport regimes from molecular diffusion, through anomalous transport, and to Taylor dispersion. The model accurately predicts D based on the early part of BTCs even at relatively high Pe regime (~62) where the Taylor’s theory fails. Furthermore, the model allows for calculation of the time scale that separates Fickian from non-Fickian transport. Therefore, our model can readily be used to calculate dispersion through short tubes of arbitrary radii such as the pore throats in a pore network model.

The turbulent Poiseuille flow between two parallel plates is one of the simplest possible physical situations, and it has been studied intensively. In this paper, we propose a modified Prandtl-van Driest mixing length that satisfies both boundary conditions and wall damping effects. With our new formulations, we numerically solve the problem and, moreover, propose an approximate analytical solution of mean velocity. As applications of our solution, an approximate analytical friction coefficient of turbulent Poiseuille flow is proposed.

In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton evolving von Neumann neighbourhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

This study presents a new form of velocity distribution in laminar liquid flow in rectangular microchannels using the eigenfunction expansion technique. Darcy friction factor and Poiseuille number are also obtained analytically. Due to the symmetry of the solutions, the effects of changing the aspect ratio from 0 to ∞ are also discussed. Using finite element method (FEM), the obtained analytical results are further compared with the 3D numerical simulations for the rectangular microchannels with different range of aspect ratio and pressure gradient, and excellent agreements were found. These findings provide additional insights in interpreting the results of the pressure-driven flows in finite aspect ratio microchannels, in which very precise comparison with the macroscale theory is crucial.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.