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

The present paper deals with a theoretical investigation of the peristaltic transport of a couple stress fluid in a porous channel. The study is motivated towards the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The velocity, pressure gradient, stream function and frictional force of blood are investigated, when the Reynolds number is small and the wavelength is large, by using appropriate analytical and numerical...

Recent simulations indicate that streamwise-preferential porous materials have the potential to reduce drag in wall-bounded turbulent flows(Gomez-de-Segura & Garcia-Mayoral 2019). This paper extends the resolvent formulation to study the effect of such anisotropic permeable substrates on turbulent channel flow. Under the resolvent formulation, the Fourier-transformed Navier-Stokes equations are interpreted as a linear forcing-response system. The nonlinear terms are considere...

Fluid-structure interactions are ubiquitous in nature and technology. However, the systems are often so complex that numerical simulations or ad hoc assumptions must be used to gain insight into the details of the complex interactions between the fluid and solid mechanics. In this paper, we present experiments and theory on viscous flow in a simple bioinspired soft valve which illustrate essential features of interactions between hydrodynamic and elastic forces at low Reynold...

Recent studies have advocated using the total dissipation rate under topology optimization to realize material designs involving the flow of fluids through porous media. However, these studies decided how to pose the design problem, such as maximizing the total dissipation rate for some situations while minimizing for others, by solving one-dimensional problems and justifying their choices using numerical experiments. The rigor is lacking -- a bottleneck for further scientifi...

Many microfluidic devices use macroscopic pressure differentials to overcome viscous friction and generate flows in microchannels. In this work, we investigate how the chemical and geometric properties of the channel walls can drive a net flow by exploiting the autophoretic slip flows induced along active walls by local concentration gradients of a solute species. We show that chemical patterning of the wall is not required to generate and control a net flux within the channe...

Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by many local extrema. In general, finding the global, or nearly global optimum is difficult. In biological systems, it is believed that natural selection slowly guides the network towards an optimized state. However, general coarse grained model...

Topology optimization (TopOpt) is a mathematical-driven design procedure to realize optimal material architectures. This procedure is often used to automate the design of devices involving flow through porous media, such as micro-fluidic devices. TopOpt offers material layouts that control the flow of fluids through porous materials, providing desired functionalities. Many prior studies in this application area have used Darcy equations for primal analysis and the minimum pow...

An ion-exchange-resin-based microfluidic pump is introduced that utilizes trace amounts of ions to generate fluid flows. We show experimentally that our pump operates in almost deionized water for periods exceeding 24h and induces fluid flows of um/s over hundreds of um. This flow displays a far-field, power-law decay which is characteristic of two-dimensional (2D) flow when the system is strongly confined and of three-dimensional (3D) flow when it is not. Using theory and nu...

In this paper, we derive upscaled equations for modelling biofilm growth in porous media. The resulting macro-scale mathematical models consider permeable multi-species biofilm including water flow, transport, detachment and reactions. The biofilm is composed of extracellular polymeric substances (EPS), water, active bacteria and dead bacteria. The free flow is described by the Stokes and continuity equations and the water flux inside the biofilm by the Brinkman and continuit...

We study the effect of isotropic porous walls on a plane Couette flow laden with spherical and rigid particles. We perform a parametric study varying the volume fraction between $0$ and $30\%$, the porosity between $0.3$ and $0.9$ and the non-dimensional permeability between $0$ and $7.9 \times 10^{-3}$ We find that the porous walls induce a progressive decrease in the suspension effective viscosity as the wall permeability increases. This behavior is explained by the weakeni...