Optimal counter-current exchange networks

The structure of pipe networks minimizing the total energy dissipation rate is studied analytically. Among all the possible pipe networks that can be built with a given total pipe volume (or pipe lateral surface area), the network which minimizes the dissipation rate is shown to be loopless. Furthermore, such an optimal network is shown to contain at most N-2 nodes in addition to the N sources plus sinks that it connects. These results are valid whether the possible locations...

We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape of channels in such optimal networks and show that they must be straight with uniform cross-sectional areas. Then, we establish a relation between the cross-sectional areas of adjoining channels at each junction. Indeed, this relation is a g...

Flow networks efficiently transport nutrients and other solutes in many physical systems, such as plant and animal vasculature. In the case of the animal circulatory system, an adequate oxygen and nutrient supply is not guaranteed everywhere: as nutrients travel through the microcirculation and get absorbed, they become less available at the venous side of the vascular network. Ensuring that the nutrient distribution is homogeneous provides a fitness advantage, as all tissue ...

Heat exchangers are devices that typically transfer heat between two fluids. The performance of a heat exchanger such as heat transfer rate and pressure loss strongly depends on the flow regime in the heat transfer system. In this paper, we present a density-based topology optimization method for a two-fluid heat exchange system, which achieves a maximum heat transfer rate under fixed pressure loss. We propose a representation model accounting for three states, i.e., two flui...

In biological transport mechanisms such as insect respiration and renal filtration, fluid travels along a leaky channel allowing exchange with systems exterior the the channel. The channels in these systems may undergo peristaltic pumping which is thought to enhance the material exchange. To date, little analytic work has been done to study the effect of pumping on material extraction across the channel walls. In this paper, we examine a fluid extraction model in which fluid ...

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...

A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with prefractal geometries show that, within very good approximation, the flux depends only on a few characteristic features of the interface geometry: the lower and higher cut-offs and the fractal dimension. Although the active zones are different for...

Integrated micro-nanochannel networks in fluidic devices are desirable in a number of applications ranging from self-healing/cooling materials to bioengineering. The conventional micro-manufacturing techniques are capable of either producing microchannel or nanochannel networks for a fluidic application but lack proficiency in the production of an integrated micro-nanochannel network with a smooth transition from micro-to-nano scale dimension. In addition, these techniques po...

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...

Life and functioning of higher organisms depends on the continuous supply of metabolites to tissues and organs. What are the requirements on the transport network pervading a tissue to provide a uniform supply of nutrients, minerals, or hormones? To theoretically answer this question, we present an analytical scaling argument and numerical simulations on how flow dynamics and network architecture control active spread and uniform supply of metabolites by studying the example ...