Predictive Hydrodynamic Modeling of High-Viscosity Epoxy Flow in Ultra-Heavy Copper Cavities
Predictive non-Newtonian flow modeling prevents micro-voiding in ultra-heavy copper cavities by matching prepreg viscosity minimums to press force ramps.
Cross Carreau Model
Rheological Function
Mathematical equations describing fluid viscosity changes over wide ranges of shear rate provide the numerical foundation for simulating fluid flow in microelectronics assembly. The Cross Carreau model captures non-Newtonian shear-thinning behavior across both low-shear zero shear viscosity plateaus and high-shear infinite shear viscosity limits. In printed circuit board manufacturing, solder paste formulations, underfill encapsulants and conductive adhesives exhibit pseudoplastic behavior that cannot be predicted by simple power-law equations.
Acceptable parameter fitting against rotational rheometer test data requires measuring shear stress across four orders of magnitude of strain rate. The validity of this formulation stops at the threshold of solid phase separation or particle jamming, where continuum fluid mechanics ceases to apply.
Viscosity Curve
Computational modeling of liquid dispense operations relies on accurate curve fitting to prevent nozzle clogging and yield loss during high speed surface mount component attachment. Under constant pressure, solder pastes and polymer fluids modeled by the Cross Carreau model undergo rapid viscosity drop as extrusion forces increase inside narrow needle tips. This shear-thinning response enables high volumetric flow through small apertures without requiring extreme pump pressures that damage delicate mechanical dispense valves.
Once fluid leaves the nozzle tip, shear forces drop to zero, allowing the material to recover viscosity and maintain dot geometry on the substrate surface. Failure to model the low-shear viscosity region accurately leads to miscalculated slumping behavior, causing solder bridging between adjacent fine pitch pads during thermal reflow.
Dispense Behavior
Viscous behavior at high strain rates dictates needle backpressure requirements during automated dispensing. Mechanical shear stress inside automated dispensing heads alters polymer chain orientation, driving temporary structural breakdown in complex paste matrices. Rheological testing verifies that model parameter fitting matches real material extrusion profiles across temperature ranges encountered during production line operation.