When two silicon wafers approach each other for bonding, the air between them has nowhere to go. The thin film of trapped air creates a pressure field through Reynolds lubrication — viscous squeeze-out that resists the wafers' approach. Simultaneously, the wafers deform under their own weight and the interfacial attraction pulling them together. The air pressure depends on the gap geometry. The gap geometry depends on the wafer deformation. The wafer deformation depends on the air pressure.
This coupled fluid-structure problem produces bonding-front kinetics with nonlinear, and in some cases non-monotonic, sensitivities to initial gap spacing, air viscosity, and interfacial energy. Increase the gap and the bonding may speed up, then slow down, then speed up again. The Reynolds pressure acts as an effective contact reaction at the bond front — not a fixed resistance but a dynamic one that reshapes itself as the geometry evolves.
The non-monotonicity is the interesting part. In a simpler system, wider gap means slower bonding (more air to squeeze out) or faster bonding (less viscous resistance per unit area). The coupled system generates both behaviors at different parameter ranges because the wafer's flexibility introduces a geometric feedback: a wider gap allows more bending, which concentrates the bonding front, which changes the air channel's shape, which changes the squeeze-out rate.
Manufacturing optimization for wafer-to-wafer bonding can't assume that improving one parameter improves the outcome. The coupling makes the landscape folded, not monotone.