•The apparent contact angle is influenced by nano-bubbles at the bottom of the porous coating. As heat flux density increases, these nano-bubbles gradually form thickening vapor films.•This study proposes a CHF prediction model applicable to biphilic surfaces based on the two-dimensional distribution of Helmholtz instability at the interface.•This study presents a CHF prediction model tailored for biphilic surfaces based on the influence of Taylor instability on the formation location of mushroom bubbles and the impact of Helmholtz instability on the liquid layer beneath the bubbles. This study demonstrated that combination hydrophilic copper and hydrophobic nano-silver surfaces simultaneously enhanced the critical heat flux (CHF) and heat transfer coefficient (HTC) in pool boiling heat transfer (BHT) with deionized water as the employed working fluid. To further investigate the influence of geometric factors on heat transfer, this study designed three patterns denoted as squares/stripes/networks, ranging from 50 μm to 3000 μm. The effects of pattern size d, spacing p, and pitch ratio p/d on heat transfer results were obtained. Based on bubble visualization, the study further analyzed the reasons for inflection points in the boiling curve and the mechanisms caused by porous hydrophobic coating. Finally, the study proposed a numerical model suitable for predicting CHF of biphilic surfaces based on Helmholtz instability and Taylor instability. The model began with vapor columns escaping toward far-field and the fluid supplied to the heating surface. Concrete model derivation and adjustments are categorized according to the relationship between pattern size and bubble detachment diameter. For surfaces where the bubble detachment diameter exceeds the pattern size, this study originated from the perspective of Helmholtz instability on the vapor column surface. The resulting model is anticipated to quantitatively solve for the former and modulate the wavelength of Taylor instability on biphilic surfaces. Regarding surfaces with bubble detachment diameters smaller than the pattern size, this research begins with the existence time of the micro-liquid layer. The derived model validates the predominant role of p/d in the CHF values on micron-scale biphilic surfaces. Display omitted