Modeling Slip Velocity and Pressure Gradients across Smooth Copper Foils
Modelling slip velocity and pressure gradients across smooth copper foils prevents resin starvation and locks dielectric thickness tolerances during lamination.
Slip Length
Boundary Condition
A specific distance describes the theoretical point inside a solid surface where the velocity of a moving fluid would drop to zero. In micro-scale fluid channels, the slip length accounts for the fact that a liquid might slide along a smooth or hydrophobic wall instead of sticking to it. This measurement is necessary for predicting the flow rates in the tiny cooling paths used in advanced electronic packaging.
A larger value indicates that the fluid moves more easily with less friction at the boundary.
Flow Velocity
Hydrophobic coatings on the internal walls of a cooling channel increase the velocity of the liquid near the surface. Quantifying the slip length provides a way to quantify this effect in mathematical models of heat transfer. This reduction in drag allows for lower pump pressures in compact systems.
Surface Interaction
Surface roughness on the circuit board material can negate the benefits of a large slip length by creating mechanical anchors for the fluid. During the manufacturing of micro-channels, laser polishing or chemical treatments are used to achieve the necessary smoothness. If the slip length is ignored, the actual flow rate in the device will be much lower than the theoretical maximum.
Measuring the pressure drop across a known distance allows engineers to calculate the actual slip behavior. This data is essential for designing efficient thermal management solutions in high-density assemblies.