Solving Mazes Using Microfluidic Networks

Abstract

This work demonstrates that pressure-driven flow in a microfluidic network can solve mazelike problems by exploring all possible solutions in a parallel fashion. Microfluidic networks can be fabricated easily by soft lithography and rapid prototyping. To find the best path between the inlet and the outlet of these networks, the channels are filled with a fluid, and the path of a second, dyed fluid moving under pressuredriven flow is traced from the inlet to the outlet. Varying the viscosities of these fluids allows the behavior of the system to be tailored. For example, filling the channels with immiscible fluids of different viscosities enhances the resolution of paths of different fluidic resistances.

System-Theoretic Analysis and Least-Squares Design of Microfluidic Channels for Flow-Induced Molecular Communication

“…Furthermore, in microfluidic channels the inertial effects such as gravity, and turbulence are negligible [24]- [26]. The laminar flow and the absence of turbulence are essential to minimize unsteady-state flows at turning channels and connection nodes in microfluidic channels [27]. Moreover, when the distance from the inlet of a channel with radius satisfies the condition , the laminar flow can be taken as fully-developed, and analysis of infinite channels can be used to analyze flows in finite length channels [21], [22].…”

“…Fourier transform of (23) is found by converting the derivative in time domain to multiplication with in frequency domain as (27) where is the concentration spectral density, which is found by Fourier transform of concentration, i.e., . Using boundary conditions and , the transfer function is obtained as (28) where the temporal frequency is converted to angular frequency using identity .…”

Chemical robotics — chemotactic drug carriers

“…Solving maze problems using adaptive systems is not only relevant to the everyday issues of urban transportation and to experimental psychology, but is also one of the model problems of network and graph theory as well as robotics [41]. Several groups have thus explored the possibility of maze solving by physical, chemical or even biological systems: microfluidic networks [42], chemical waves [43] or plasmas [44], or microorganisms growing in response to nutrition gradients within the maze [45]. Recently, we designed a new adaptive system, in which an inanimate/chemical construct (a small fatty acid droplet suspended in basic water) can self-propel and solve mazes in response to chemical stimuli [46] (Figure 1).…”

Marangoni Flow Driven Maze Solving

“…It is thus not surprising that the geometric and topological complexity of a maze and its solutions (i.e., one or more paths leading from the entrance to the exit) serves as a model configuration in many areas of science and technology (e.g., logistics, robot control, neuroscience, etc.). It has been shown that besides humans, animals, and computer algorithms, some amoeboid organisms [1][2][3], and even nonliving, synthetic constructs are 'able' to solve mazes [1][2][3][4][5][6][7][8][9][10][11][12]. Such chemical, physical or biological systems are initially in a non-equilibrium thermodynamic state with a spatial gradient of some thermodynamic variable, e.g., temperature, chemical potential, pressure, electric or magnetic field, which induces a flow of matter (momentum) or energy within the system to reach its equilibrium state.…”

“…Some of the most prominent approaches are briefly mentioned next. Microfluidic networks are often solved by imposing a pressure gradient across the corresponding maze [4] between the entrance and the exit so that the pressure-induced flow has the largest amplitude along the shortest path. An electric field gradient was used to induce a glow discharge in gas-filled microchannels and to identify the shortest path in mazes or urban city maps [5,6]; in a medium conducting electric current the shortest path is characterized by the largest gradient of the electric field which ionizes a gas and induces a plasma glow.…”