A popular equation that is often employed to represent the relationship between the pressure loss and the fluid flow in fluidized or packed granular beds is the Ergun equation, which is an extension of Darcy’s law. In this paper, the method of Smoothed Particle Hydrodynamics (SPH) is used to numerically study the flow field across a rectangular channel partially filled with a porous layer both at the Representative Elementary Volume (REV) scale using the Ergun equation and at the pore scale. Since the flow field can be estimated at the REV scale with a much lower cost compared to the pore scale, it is important to evaluate how accurately the pore-scale results can be reproduced at the REV scale. The comparison between both scales is made in terms of the velocity profiles at the outlet of the rectangular channel and the pressure losses across the clear and porous zones for three different arrays of solid grains at the pore scale. The results show that minimum differences in the flow structure and velocity profiles between the REV and the pore scale always occur at intermediate values of the porosity ($\varphi =0.44$ and 0.55). As the porosity increases, the differences between the REV and the pore scale also increase. The details of the pressure losses are affected by the geometry of the porous medium. In particular, we find that the pressure profiles at the REV scale match those at the pore scale almost independently of the porosity only when the grains are uniformly distributed in a non-staggered square array.

Smoothed particle hydrodynamics (SPH) is a grid-free numerical method that relies on a Lagrangian description of the fluid. It has been used in a variety of multiphysics applications, including applications to free surface flow problems where surface tension plays a pivotal role. Accurate simulations of surface tension are crucial for a realistic description of multiphase flows and small-scale fluid systems, such as drops and bubbles. This article describes a novel approach based on a pair potential force within the SPH framework that simulates surface tension in a physically consistent manner. The Young–Laplace equation is used to calibrate the force term associated with the cohesive action so that there is a close correspondence between the calculated surface tension and the minimization of the surface area. The performance of the model has been assessed against a number of benchmark tests, including the spherization of cubic drops, the spreading of a drop impacting on a solid surface, and the drop oscillation in a gas environment. A comparison of experimentally obtained pendant drop images with the simulation results for distilled water, ethylene glycol and ethanol drops is also provided as a further validation test. The proposed approach has been shown to be accurate enough to simulate surface tension effects in liquid drops under a variety of dynamical conditions irrespective of the length scale, implying that it is particularly suitable for simulating microfluidic systems.

Smoothed Particle Hydrodynamics (SPH) has become a promising tool for the simulation of fluids. Although too much research has been addressed to improve the method over the years, a comparison of the errors and consistency evolution when trying different approaches are still necessary to define the best scheme for practical applications. Here, a two-dimensional Poiseuille flow test benchmark is employed to enforce comparisons when varying the kernel, the definition of the sound speed inthe pressure term, the viscosity and the Reynolds number.