Optimal reservoir conditions for fluid extraction through permeable walls in the viscous limit

The method of matched asymptotic expansions is used to study the canonical problem of steady laminar flow through a narrow two-dimensional channel blocked by a tight-fitting finite-length highly permeable porous obstacle. We investigate the behaviour of the local flow close to the interface between the single-phase and porous regions (governed by the incompressible Navier--Stokes and Darcy flow equations, respectively). We solve for the flow in these inner regions in the limi...

We derive a limit on energy savings in controlled channel flow. For flow in a channel driven by pressure, shear, or any combination of the two, and controlled via wall transpiration or spanwise wall motion, the uncontrolled laminar state requires the least net energy (accounting for the energetic cost of control). Thus, the optimal control solution is to laminarize the flow. Additionally, we raise the possibility of beating this limit. By simultaneously applying wall transpir...

The paper deals with a theoretical study of the transport of a fluid in a channel, which takes place by the phenomenon of peristalsis. A mathematical analysis of the said problem has been presented. The analysis involves the application of a suitable perturbation technique. The velocity profile and the critical pressure for the occurrence of reflux are investigated with particular emphasis by using appropriate numerical methods. The effects of various parameters, such as Reyn...

The dynamics of flow within a material transport network is dependent upon the dynamics of its power source. Responding to a change of these dynamics is critical for the fitness of living flow networks, e.g. the animal vasculature, which are subject to frequent and sudden shifts when the pump (the heart) transitions between different steady states. The combination of flow resistance, fluid inertia, and elasticity of the vessel walls causes the flow and pressure of the fluid t...

Air-permeable porous media hosts air within their pores. Upon removal from the material's interior, these porous media have the tendency to replenish the air, effectively acting as a suction pump. Therefore, the technique used to convert a porous media into a pump, consists of degassing the material to remove their air inside. The suction property when recovering the air, can be used to move a liquid through a microfluidic channel, studying the dynamics of the liquid-air fron...

The separation of measured arterial pressure into a reservoir pressure and an excess pressure was introduced nearly 20 years ago as an heuristic hypothesis. We demonstrate that a two-time asymptotic analysis of the 1-D conservation equations in each artery coupled with the separation of the smaller arteries into inviscid and resistance arteries, based on their resistance coefficients, results, for the first time, in a formal derivation of the reservoir pressure. The key to th...

Viscous flows in hyperelastic chambers are relevant to many biological phenomena such as inhalation into the lung's acinar region and medical applications such as the inflation of a small chamber in minimally invasive procedures. In this work, we analytically study the viscous flow and elastic deformation created due to inflation of such spherical chambers from one or two inlets. Our investigation considers the shell's constitutive hyperelastic law coupled with the flow dynam...

Salt transport in bulk electrolytes is limited by diffusion and convection, but in microstructures with charged surfaces (e.g. microfluidic devices, porous media, soils, or biological tissues) surface conduction and electro-osmotic flow also contribute to ionic fluxes. For small applied voltages, these effects lead to well known linear electrokinetic phenomena. In this paper, we predict some surprising nonlinear dynamics that can result from the competition between bulk and i...

In this paper, we consider the homogenization of evolutionary incompressible purely viscous non-Newtonian flows of Carreau-Yasuda type in porous media with small perforation parameter $0< \varepsilon \ll 1$, where the small holes are periodically distributed. Darcy's law is recovered in the homogenization limit. Applying Poincar\'e type inequality in porous media allows us to derive the uniform estimates on velocity field, of which the gradient is small of size $\varepsilon$ ...

The calculus of variations is employed to find steady divergence-free velocity fields that maximize transport of a tracer between two parallel walls held at fixed concentration for one of two constraints on flow strength: a fixed value of the kinetic energy or a fixed value of the enstrophy. The optimizing flows consist of an array of (convection) cells of a particular aspect ratio Gamma. We solve the nonlinear Euler-Lagrange equations analytically for weak flows and numerica...