Nonuniform heating of a substrate in evaporative lithography

Abstract

The work is devoted to the study of one method connected with structured sediments formation, which belongs to the direction of evaporative lithography. A series of experiments were carried out with nonuniform evaporation of an isopropanol film containing polystyrene microspheres that occurred in an open cylindrical cell. The local inhomogeneity of the vapor flux density was achieved due to the temperature gradient. A copper rod was mounted in the central part of the bottom of the cell for further heating. The thermocapillary flow resulting from the surface tension gradient due to the temperature drop transfers the particles that were originally at rest along the bottom of the cell. The effect of the initial thickness of the liquid layer on the height and area of the sediment (cluster) formed in the central region of the cell is experimentally studied. The velocity of the particles was measured using particle image velocimetry. A mathematical model describing the process at the initial stage is developed. The equations of heat transfer and thermal conductivity were used to define the temperature distribution in the liquid and the cell. The fluid flow was simulated by the lubrication approximation. The particle distribution was modeled using the convection-diffusion equation. The evaporation flux density was calculated using the Hertz-Knudsen equation. The dependence of the liquid viscosity on the particle concentration was described by Mooney's formula. Numerical results showed that the liquid film gradually becomes thinner in the central region, as the surface tension decreases with increasing temperature. The liquid flow is directed to the heater near the substrate. It transfers the particles to the center of the cell. The volume fraction of the particles increases over time in this region. The work done allowed us to formulate the conclusion that the heat flow from the heater affects the geometry of the sediment for two reasons. First, the Marangoni flow velocity depends on the temperature gradient. Secondly, the decrease in film thickness near the heater depends on the temperature.