Flow differentiation within nanotube networks with symmetric bifurcations by local bending vibration: A theoretical study

Abstract

We present a theoretical scheme to produce oscillatory flows within fractal nanotube networks with simple Y-type bifurcations, via the exertion of bending motion at one tube in the network. To model the interaction of a vibrating tube within the fluid conveyed within, and its global effect on the flow obtained in the rest of the network, we depart from of a non-linear model that has been recently proposed to study the effect of tube’s elastic bending motion in the dynamics of a fluid subject to a constant external driving force. It is demonstrated that, even for a network where all the tubes are identical in geometrical and mechanical properties, the network develops a complex net and oscillatory flow, when a constant driving force is globally exerted along the network and one of the tubes is bent and develops an oscillatory motion. Even if the other tubes are static, oscillatory flow velocity is propagated to the rest of the network, but in such a fashion that the network exhibits a pattern of flow differentiation in the oscillatory-to-net flow rates quotient. Such a distribution of flow rates quotient at every portion of the network is described in terms of the physical properties of bent tube, network size, and location of bent tube within network. In addition, the role of flow slippage at the fluid/wall interface in flow differentiation is explored. The capability to obtain regions of high and low oscillatory-to-net flow rates quotient could be exploited as a strategy to mimic complex biological flow systems using symmetric networks, avoiding completely the typical issues concerning the design and preparation of tubes with differentiated specialized geometrical and mechanical properties along the network.