## 1 Introduction
[10] established an improved sub-boundary lubrication (ISBL) adhesive contact model based on the Lennard-Jones surface force law [17], assuming that the lubricant did not influence the contact force and contact area. Their simulation results found the highest adhesion force for separations below 2 nm. [PERSON] et al. [8] extended the ISBL contact model to the dynamic analysis of the TFC slider-disk interface, and investigated influences of the TP geometry on the operation states of the slider. Despite the theoretical guidance of the above studies for the interpretation of contact characteristics of the HDI and the design of sliders, their usefulness is limited because all these models based on the Hamaker theory share the common assumption that the influence of neighboring atoms on the interaction between any pair of atoms can be ignored [13]. However, the effective polarizability of an atom changes when it is surrounded by other atoms, and the existence of multiple reflections and the extra force terms to which they give rise can make the simple additivity break down [13]. [PERSON] [18] pointed out that the nonretarded Hamaker constant in the Hamaker theory used to characterize the surface interaction can be qualitatively and quantitatively inaccurate. In addition, the multilayered constructions of the slider and the disk are not accounted for in the above studies based on the Hamaker theory. As is known, to prevent corrosion and damage from intermittent slider-disk contact, the disk surface is often deposited with a diamond-like carbon (DLC) layer and a strongly adhered molecularly thin lubricant layer, and the slider surface is also covered with a DLC layer [19]. The addition of a lubricant layer and a DLC layer can influence the adhesion energy and thus change the adhesion force [20; 21]. Therefore, predictions of the adhesive interaction at the HDI need a more accurate theory, which can consider the layered structures of the head and the disk. [PERSON] [22] proposed a theory based on the fluctuational electrodynamics for calculating the vdW force. This theory characterizes the contribution of the electromagnetic fluctuations of the media involved to the vdW force by the dielectric data, which can avoid problems introduced by additivity and thus can consider the interaction between adjacent molecules more precisely [13]. It has been reported, furthermore, that results obtained by the Lifshitz theory agree with the experimental data [18], suggesting that this theory is a more physically satisfying and rational approach. A model for predictions of the vdW force of layered materials using the Lifshitz theory was constructed as early as 1970 by [PERSON] et al. [23]. Following this model, [PERSON] et al. [24] established a Lifshitz-theory-based fully retarded vdW force model for the HDI system, and found that the multilayered structure of the disk made the Hamaker function strongly air gap-dependent and dramatically changed the magnitude of the vdW interaction. Subsequently, [PERSON] et al. [25] used the same model to HDI and clarified the role of vdW force on the flying characteristics under ultra-low _FH_. However, it should be pointed out that the above studies are for the traditional flat slider-disk interface, and the slider operates at the flying state. The possible recording states of the lube contact and the DLC contact are not taken into consideration. In addition, only the attractive portion of the molecular interaction is included. However, the repulsive interaction has significant effects on the properties of the HDI under ultra-low _FH_[15] and thus should be considered. This paper is undertaken to establish a steady-state numerical adhesive contact model for the TFC slider-disk interface based on the Lifshitz theory, capable of handling various recording status including the flying state, lubricant contact state and solid contact state. Numerical simulations are conducted, and the necessity of using the Lifshitz theory for the HDI is illustrated by comparing it with the Hamaker theory.