We report on a simple method to improve bondline formation kinetics by means of a hierarchical set of channels patterned into one of the surfaces. The channel arrays are used to improve the gap squeezing and cooling of single and multiple flip-chip electronic modules with highly viscous fluids and thermal pastes or greases. They allow a fast formation of thin gaps or bond lines by reducing the pressure gradient in the thermal interface material as it moves in and out of the gap. Models describing the dynamics of Newtonian fluids in these "hierarchically nested channel" interfaces combine squeeze flow and Hagen-Poiseuille theories. Rapid bond-line formation is demonstrated for Newtonian fluids and selected particle-filled pastes. Modeling of particle-laden polymeric pastes includes Bingham and Hershel-Bulkley fluid properties. Bond-line formation and thermal resistance are improved particularly for high-viscosity high-thermal-conductivity interface materials created from higher-volumetric particle loadings or for thermal interface materials with smaller filler-particle diameters.Index Terms-Bondline thickness (BLT), fluid flow, interface, interface aging, microchannel, packaging, thermal interface material (TIM), thermal management, thermal resistance, viscosity.