A predictive model for frictional pressure loss reduction in laminar pipe flow based on surface wettability and slip length

Abstract

The classical no-slip boundary condition is widely adopted in internal flow analyses, although hydrophobic surfaces can induce measurable slip at the fluid–solid interface. This study presents a computational investigation and predictive modeling of frictional pressure loss reduction in laminar pipe flow as a function of surface wettability. A three-dimensional circular pipe (D = 4 mm, L/D = 100) is analyzed for Reynolds numbers between 400 and 1600. Partial slip boundary conditions are implemented via a user-defined function, where slip length is systematically varied in relation to the contact angle. The results show that increasing slip length leads to a consistent decrease in pressure drop, with a maximum reduction of approximately 1.1% at the highest slip condition. Although the magnitude is modest, the trend is systematic across all Reynolds numbers. A dimensionless analysis demonstrates that the normalized pressure drop exhibits an excellent collapse onto a nearly single curve when expressed as a function of the slip length-to-diameter ratio, indicating that the dominant governing parameter is the dimensionless slip length. Based on the numerical data, an empirical correlation is proposed to predict pressure-drop reduction, exhibiting an almost linear dependence on the slip-length ratio. In addition, an exponential relationship between the contact angle and the slip length is established. By combining these relationships, a design-oriented parametric framework is developed that estimates frictional pressure loss through a prescribed contact angle-dependent slip-length approximation. The proposed framework provides a rapid parametric engineering estimate of hydrophobic slip effects in internal flows within the investigated parameter range.