Dynamic Squeeze Flow Hydrodynamics across Ultra Smooth Circuit Foil Interfaces
Dynamic resin squeeze flow across ultra smooth copper foils demands precise thermal press ramping to prevent micro-voiding and hold tightly controlled plane spacing.
Stefan Dynamic Equation
Viscous Formula
Fluid dynamics formulations describe the transient force required to compress a thin layer of viscous liquid between two parallel disks. The stefan dynamic equation models the relation between the fluid viscosity and the changing gap height during lamination. It provides the analytical basis for predicting the flow of resin sheets as they fill the gaps between copper tracks.
This relation shows that the resistance to compression increases rapidly as the distance between the plates decreases.
Mathematical Solution
Mathematical derivations of this relation assume that the fluid is Newtonian and incompressible, with the flow dominated by viscous shear forces rather than inertia. The formulation calculates the squeezing force as a function of the disk radius and the rate of change of the gap height. Because the force varies inversely with the cube of the gap height, a massive increase in pressure is required to maintain a constant compression rate as the layer thins.
This strong non-linear dependency explains why thin prepreg layers are highly resistant to further compression during the final stages of the lamination cycle.
Application Boundary
Non-Newtonian fluid behaviors, such as shear thinning or yield stress, violate the assumptions of the classic formulation and require correction factors. For highly filled resins or cross-linking prepregs, the viscosity changes dynamically with both the shear rate and the temperature. Under these conditions, the simple equation must be modified to prevent underestimating the required lamination pressure.