Dynamics of stain growth from sessile droplets on paper

The rate of stain growth of a sessile droplet deposited on paper has been previously studied (Kissa, 1981; Danino and Marmur, 1994; Kawase et al., 1986; Borhan and Rungta, 1993) but is not fully understood. In particular, the mechanism by which the abrupt decrease in growth rate occurs is unknown. This process is expected to follow a model where the disappearance of the droplet is represented by a change to the boundary condition at the droplet-paper interface when the volume of the fluid inside the paper is equal to the volume of the simulated droplet.

The stain size of sessile droplets on paper was monitored against time. A series of fluids varying in surface tension and viscosity was studied. The kinetics of stain growth was modelled and compared with experiments and existing models of stain growth.

The measured stain area formed by a sessile droplet deposited on paper follows a two regime mechanism (Danino and Marmur, 1994). In the initial regime, the dynamics are governed by the filling of pores. However, in the later stage, the process is influenced by the emptying/redistribution of fluid. Simulations show that experimental results are well described by a model that identifies the change in boundary conditions after the droplet is no longer present above the paper, coupled with the change to a redistribution dominated mechanism.