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

Biological systems are influenced by fluid mechanics at nearly all spatiotemporal scales. This broad relevance of fluid mechanics to biology has been increasingly appreciated by engineers and biologists alike, leading to continued expansion of research in the field of biological fluid dynamics. While this growth is exciting, it can present a barrier to researchers seeking a concise introduction to key challenges and opportunities for progress in the field. Rather than attempt...

We use a one dimensional symmetric exclusion model to study pressure and osmosis driven flows through molecular-sized channels, such as biological membrane channels and zeolite pores. Analytic expressions are found for the steady-state flow which show rich nonlinear behavior. We find a maximum in the flow rates depending upon pore radius, pore energetics, reservoir temperature, and driving force. We also present exact mean-field results of transport through pores with interna...

Stokes' equations model microscale fluid flows including the flows of nanoliter-sized fluid samples in lab-on-a-chip systems. Helmholtz's dissipation theorem guarantees that the solution of Stokes' equations in a given domain minimizes viscous dissipation among all incompressible vector fields that are compatible with the velocities imposed at the domain boundaries. Helmholtz's dissipation theorem directly guarantees the uniqueness of solutions of Stokes flow, and provides a ...

Transport networks are typically optimized, either by evolutionary pressures in biological systems or by human design in engineered structures. In the case of systems such as the animal vasculature, the transport of fluids is hindered by the inherent viscous resistance to flow while being kept in a dynamic state by the pulsatile nature of the heart and elastic properties of the vessel walls. While this imparted pulsatility necessarily increases the dissipation of energy cause...

Non-linear effects of the Navier-Stokes equations disappear under the Stokes regime of Newtonian fluid flows disallowing the fluid flow rectification. Here we show mathematically and experimentally that passive flow rectification of Newtonian fluids is obtainable under the Stokes regime of both compressible and incompressible flows by introducing nonlinearity into the otherwise linear Stokes equations. Asymmetric flow resistances arise in shallow nozzle/diffuser microchannels...

Immersed nonlinear elements are prevalent in biological systems that require a preferential flow direction, such as the venous and the lymphatic system. We investigate here a certain class of models where the fluid is driven by peristaltic pumping and the nonlinear elements are ideal valves that completely suppress backflow. This highly nonlinear system produces discontinuous solutions that are difficult to study. We show that as the density of valves increases, the pressure ...

Of concern in this paper is an investigation of peristaltic transport of a physiological fluid in an asymmetric channel under long wave length and low-Reynolds number assumptions. The flow is assumed to be incompressible, viscous, electrically conducting micropolar fluid and the effect of induced magnetic field is taken into account. Exact analytical solutions obtained for the axial velocity, microrotation component, stream line pattern, magnetic force function, axial-induced...

The paper deals with a theoretical investigation of the peristaltic transport of a physiological fluid in a porous asymmetric channel under the action of a magnetic field. The stream function, pressure gradient and axial velocity are studied by using appropriate analytical and numerical techniques. Effects of different physical parameters such as permeability, phase difference, wave amplitude and magnetic parameter on the velocity, pumping characteristics, streamline pattern ...

Pumping at low Reynolds number is a ubiquitously encountered feature, both in biological organisms and engineered devices. Generating net flow requires the presence of an asymmetry in the system, which traditionally comes from geometric flow rectifiers. Here, we study a valveless system of $N$ oscillating pumps in series, where the asymmetry comes not from the geometry but from time, that is the phase shifts between the pumps. Experimental and theoretical results are in very ...

In Nature, liquids often circulate in channels textured with leaflets, cilia or porous walls that deform with the flow. These soft structures are optimized to passively control flows and inspire the design of novel microfluidic and soft robotic devices. Yet so far the relationship between the geometry of the soft structures and the properties of the flow remains poorly understood. Here, taking inspiration from the lymphatic system, we devise millimetric scale fluidic channels...