Hydrodynamics of Writing with Ink

Jungchul Kim, Myoung-Woon Moon, Kwang-Ryeol Lee, L. Mahadevan, and Ho-Young Kim
 

Writing with ink involves the supply of liquid from a pen on to a porous hydrophilic solid surface, paper. The resulting line width depends on the pen speed and the physicochemical properties of the ink and of paper. Here we quantify the dynamics of this process using a combination of experiment and theory. Our experiments are carried out using a minimal pen: a long narrow tube that serves as a reservoir of liquid, which can write on a model of paper: a hydrophilic micropillar array. A minimal theory for the rate of wicking or spreading of the liquid is given by balancing capillary forces that drive the liquid flow and viscous forces exerted by the substrate. This allows us to quantitatively predict the shape of the front and the width of the line laid out by the pen, the results corroborated by experiments.