Nanomedicine, Volume I: Basic Capabilities

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

9.2.7.6 Nanoplumbing and Fluidic Circuits

In fluid distribution systems that minimize total energy dissipation in laminar nonpulsatile flow, space-filling fractal networks of branching tubes are most efficient.3242 At each branch point in such a network, where a single large tube of radius R bifurcates into N branches with each branch tube having radii r1, r2,..., rN, Murray1220 found that shear stresses are equalized and flow impedance is minimized when:

{Eqn. 9.41}

In the special case where r = r1 = r2 = ... = rN, which is quite common in biological systems, Murray's law reduces to R3 = N r3. For example, the human bronchial system typically has N = 2, so the ideal fractal network has R/r ~ N1/3 = 1.26; from Table 8.7, the actual value from trachea (generation 0) through the terminal bronchiole in generation 16 (after which alveoli begin to appear irregularly) is R/r = 1.24, in good agreement with Murray's law. In turbulent flow regimes, the exponent on Murray's law becomes 2.33, rather than 3.1615 And in pulsatile flow through elastic tubes, which dominates the aorta and major arteries in the human circulatory system, the energy minimization principle requires area-preserving branching, or R2 = N r2 for the ideal network.698

Complex nanoscale fluidic logic devices are readily imagined. While fractal geometries are likely, for simplicity consider a three-dimensional fluidic circuit of volume Vcircuit. A volume fraction ftube consists of Ntube independent fluidic pathways each of length ltube and radius rtube, and a second volume fraction fvalve consists of Nvalve fluidic gates each of volume Lvalve3. If each independent fluidic pathway is gated, on average, by a single valve, then Ntube = Nvalve = N = fvalve Vcircuit / Lvalve3 and ltube = (ftube / p fvalve) (Lvalve3 / rtube2). Ignoring reservoirs, inlet and outlet manifolds and support mechanisms, and taking Vcircuit = 1 micron3, ftube = 0.9, fvalve = 0.1, Lvalve = 20 nm, rtube = 10 nm, and h = 0.6915 x 10-3 kg/m-sec for water at 310 K, then the fluidic circuit includes Nvalve = 12,500 fluidic gates and Ntube = 12,500 independent fluidic pathways each of length ltube = 230 nm. If typical flow velocity vflow = 1 mm/sec,1228 then from Section 9.2.5 the total volume flow rate through the circuit is N 'VHP ~ 4000 micron3/sec at a pressure differential Dp = 0.1 atm. Circuit power dissipation (ignoring valve dissipation) is N Pflow ~50 pW and tflow ~0.2 millisec assuming fully parallel operation (e.g., a path length ltube), allowing a circuit operating frequency of tflow-1 ~ 5000 Hz.

Capillary networks are readily gated by applying appropriate voltages, allowing valveless switching of liquid flow among various fluidic pathways. Purely electrical valving of fluid flows has been common practice in neurobiological research for decades. For example, the flow of acetylcholine from the open end of a micronsized pipette (as it is inserted into tissue) is prevented by applying a negative bias or braking current of 3 nanoamps at the tip; flow resumes when the braking current is removed.803 Constant-discharge flow-control valves using opposing polymer brushes with ~25 chains of ~40 monomers each2902 and micron-scale electrorheological diodes498 have been investigated. Macroscale fluidic NOR logic elements that can be used to construct arbitrary Boolean logic circuits* (for controlling materials flow) are widely available commercially,1227 although these often employ the Coanda effect, vortices, or turbulence effects, which generally don't scale well to micron and submicron devices. In 1997, a microfluidic chip-based system for the integration of high-throughput drug discovery efforts was demonstrated by SmithKline Beecham and Orchid Biocomputer.1222 This microfluidic chip incorporated microfabricated components for valving and pumping of organic solvents using electrokinetic transport within a three-dimensional fluidic network. The pumping and valving mechanisms had no moving parts, "making large scale integration feasible and inherently reliable." The study of microfluidic networks1228,2697,2698 using hundreds of micron-wide channels was an active research area in 1998, and integrated chemical systems were being widely discussed.121

* In the 1950s, Marvin Minsky and Rollo Silver289 built a "hydroflip computer" using hydraulic logic elements consisting of millimeter-wide grooves and holes in multiple layers of plastic sheets with small rods and balls inserted in some of the grooves. When the assembly was pressed together and connected to a water supply, it became a hydraulic computer powered by a 3-inch high column of water, operating at ~30 Hz.

Last updated on 20 February 2003