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.
Navier Slip Condition
Boundary Condition
Liquid flow across a solid wall follows the assumption of zero velocity at the interface in classical fluid dynamics. A navier slip condition allows for a non-zero velocity tangential to the boundary when the fluid is a non-Newtonian substance or a low-density gas at the microscale. It defines the relationship between the shear stress at the wall and the difference in velocity between the fluid layer and the stationary solid surface.
The model quantifies the slip velocity as proportional to the shear rate through a parameter known as the slip length. This length varies according to the surface chemistry and the physical texture of the wall material. Measurements of this parameter provide a correction for traditional flow equations when molecular effects become dominant.
Microfluidic Friction
Researchers apply this model to predict pressure drops in channels with dimensions smaller than ten micrometers where fluid molecules interact directly with the channel walls. Standard no-slip models fail to capture the pressure reduction observed in these narrow geometries because they ignore the slight movement of molecules against the surface. A navier slip condition bridges the gap between bulk flow behavior and molecular interactions.
It allows for the accurate calculation of velocity profiles in channels treated with hydrophobic coatings that repel fluid particles. These coatings reduce the overall resistance to flow by increasing the effective slip length. Experimental data validates that the degree of slip depends on the interaction potential between the liquid molecules and the solid substrate.
Surface Calibration
Material properties at the nanoscale determine the validity of the assumption in production environments like ink jet head manufacturing or lab on a chip devices. Fabrication processes that alter surface roughness or chemical composition force a recalibration of the slip parameters for the final component. Engineers evaluate the adhesion of liquids to the substrate to estimate the slip length required for performance modeling.
Variations in the contact angle of the working fluid act as a proxy for identifying the slip potential of a surface during the inspection phase. Correct calibration ensures that the predicted flow rates match the physical performance of the finished assembly. Predicting this slip behavior reduces the need for iterative prototyping of microfluidic paths.