Maze Solving Using Fatty Acid Chemistry

Abstract

This study demonstrates that the Marangoni flow in a channel network can solve maze problems such as exploring and visualizing the shortest path and finding all possible solutions in a parallel fashion. The Marangoni flow is generated by the pH gradient in a maze filled with an alkaline solution of a fatty acid by introducing a hydrogel block soaked with an acid at the exit. The pH gradient changes the protonation rate of fatty acid molecules, which translates into the surface tension gradient at the liquid-air interface through the maze. Fluid flow maintained by the surface tension gradient (Marangoni flow) can drag water-soluble dye particles toward low pH (exit) at the liquid-air interface. Dye particles placed at the entrance of the maze dissolve during this motion, thus exhibiting and finding the shortest path and all possible paths in a maze.

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.…”

“…Chemical and electric potential wave propagation along a dendritic tube of a single cell organism is the most commonly employed setup for identifying the shortest path between two food sources in a biological system [1][2][3]. Finally, in chemical systems a chemical potential gradient created at the beginning of the experiment induces a flow of matter which highlights the shortest path in a maze in a number of distinct ways [8][9][10][11][12][13]. A silver ion gradient initiates the propagation of a chemical wave in the Belousov-Zhabotinsky solution along the paths of a maze with the fastest wave corresponding to the shortest path [8,9].…”

“…For the practical realization of such a chemical computer it is necessary to mention that we have to deal with a liquid chemistry environment [12,14].…”

Maze solving using temperature-induced Marangoni flow

“…In the last few decades several analogue computational techniques have been explored and used for maze solving, including finding the shortest path. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] These methods can be grouped as physical-, biological-, electronic-and chemical, depending on the phenomena utilized in obtaining the solution. Examples relevant for maze solving include applying a pressure difference in a channel network, 15 glow discharge in a microfluidic chip 14,27 or reconfiguration of an organism (slime mold) between two food sources within the maze.…”

“…13,19 Other successful approaches to "analog" maze solving have also been presented based on artificial chemotaxis in a liquid phase induced by the gradient of either pH or salt concentration. 16,23,26 Recently, we showed that a pH-induced Marangoni flow in a millimeter sized channel network filled with an alkaline solution of a fatty acid provides a method for identifying the shortest path and, importantly, all existing paths through a maze in a parallel fashion. 23 The Marangoni flow is established and maintained by the surface tension gradient at the liquid-air interface induced by pH.…”