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Distributed roughness occurs on aerodynamic surfaces like wind/gas turbine blades and aircraft wings causing early boundary layer transition resulting in a reduction of the lift-to-drag ratio/power production. Despite being a recurring…
When a fluid flows over a solid surface, it creates a thin boundary layer where the flow velocity is influenced by the surface through viscosity, and can transition from laminar to turbulent at sufficiently high speeds. Understanding and…
This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two…
A new OpenFOAM application to simulate multiphase flows in porous media is formulated and tested. The proposed solver combines the Eulerian multi-fluid formulation for a system of phase fractions with Darcy's law for flows through porous…
We describe a method to address efficiently problems of two-phase flow in the regime of low particle Reynolds number and negligible Brownian motion. One of the phases is an incompressible continuous fluid and the other a discrete…
In this work, we consider a certain multilayered (thick layer) wave--(thin layer) wave--heat (fluid) interactive PDE system. Such coupled PDE systems have been used in the literature to describe the blood transport process in mammalian…
This paper reviews theories, experimental data, and modeling methods for pre-Darcy flow in low-permeability porous media, where Darcy velocity shows nonlinear dependence on pressure gradients at sufficiently low pressures, a deviation from…
Boundary layer flow over a realistic porous wall might contain both the effects of wall-permeability and wall-roughness. These two effects are typically examined in the context of a rough-wall flow, i.e., by defining a ``roughness'' length…
This study investigates the coupled deformation and flow behavior of thin, hyper-elastic, porous membranes subjected to pressure loading. Using bulge test experiments, optical deformation measurements, and flow rate characterization, we…
Numerical analysis of a shear layer between a cool liquid n-decane hydrocarbon and a hot oxygen gas at supercritical pressures shows that a well-defined phase equilibrium can be established. Variable properties are considered with the…
This work investigates the effects of the choice of momentum diffusion operator on the evolution of multiphase fluid systems resolved with Meshless Lagrangian Methods (MLM). Specifically, the effects of a non-zero viscosity gradient at…
In this paper, we consider the flow of an incompressible fluid in a deformable porous solid. We present a mathematical model using the framework offered by the theory of interacting continua. In its most general form, this framework…
We used the discrete element method (DEM) to study the flow dynamics of a mixture of dumbbells and discs for two silo cases: 1. orifice situated on the lateral wall and 2. multiple orifices placed on the base of a two-dimensional silo. The…
In this paper we present the two-level homogenization of the flow in a deformable double-porous structure described at two characteristic scales. The higher level porosity associated with the mesoscopic structure is constituted by channels…
Three different porous substrates (with different pore sizes, s, and permeabilities, K) are used to examine their effect on the structure of boundary layer flow over them. The flow is characterised with single-point hot-wire measurements as…
We discuss two doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results…
We present a mathematical approach to optimize the material distribution for fluid transport in unsaturated porous media. Our benchmark problem is a simplified diaper model as an exemplary liquid absorber. Our model has up to three…
We study average flow properties in porous media using a two-dimensional network simulator. It models the dynamics of two-phase immiscible bulk flow where film flow can be neglected. The boundary conditions are biperiodic which provide a…
In this work we study a degenerate pseudo-parabolic system with cross diffusion describing the evolution of the densities of an unsaturated two-phase flow mixture with dynamic capillary pressure in porous medium with saturation-dependent…
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…