IEEE TRANSACTIONS ON MAGNETICS, VOL. 39, NO. 5, SEPTEMBER 2003 2447 A Model for Lubricant Flow From Disk to Slider Bruno Marchon, Tom Karis, Qing Dai, and Remmelt Pit Abstract—A model is presented that calculates the equilibrium lubricant thickness on a slider, resulting from a steady state where net inflow from disk evaporation equals net outflow from evaporation back to the disk, and flow to the slider back end from air shear. Based on experimental vapor pressure and viscosity data, and using surface viscosity enhancement factor and disjoining pressure values available in the literature, this model predicts a transition from a flooded regime for molecular weight below 1.5 kDaltons to a starved regime where slider lubricant thickness drops to a value close to zero. At the same time, lubricant accumulation to the slider back end is expected to decrease exponentially. Index Terms—Head/disk interface, lubrication, tribology. I. INTRODUCTION A S HEAD/MEDIA magnetic spacing in disk drives is fast approaching the 10 nm mark, the need to understand the spacing contribution of the disk lubricant becomes more pressing. Earlier studies have attempted to indirectly measure the effect of lubricant thickness on the actual head/media spacing, using the readback signal [1]. A moderately quan- titative correlation was observed. In addition to its effect on physical spacing, disk lubricant has been shown to exhibit slider-assisted redistribution [2]. In the more distant past, issues such as fly/stiction [3], [4] have been studied, and a reasonable assumption for the presence of lubricant on the slider is that the low molecular weight part of the perfluoropolyether (PFPE) from the disk somehow transfers to the slider through an evaporation/condensation process. In this paper, a model of lubricant transfer between disk and slider surface is presented that takes into account evaporation/condensation driven by thin-film vapor pressure, as well as shear toward the back of the slider. II. MODEL DESCRIPTION A simplified slider/disk system with zero pitch and zero skew is depicted in Fig. 1. The lubricant flow to/from the slider air- bearing surface (ABS) has three components. One is the inflow coming from the disk surface, and it is assumed that it is equal to the outflow from the disk surface (no edge effect). Considering that slider/disk spacing is less than the air mean free path, the evaporation mass flux from the disk will be approximated by the kinetic rate given by the Langmuir equation for the bulk liquid [first term in (1)], adjusted for surface effects, as the disjoining Manuscript received December 31, 2002. B. Marchon, Q. Dai, and T. Karis are with Almaden Research Center, IBM, San Jose, CA 95120 USA (e-mail: bmarchon@almaden.ibm.com; karis@ almaden.ibm.com; qingdai@almaden.ibm.com). R. Pit is with the Storage Technology Division, IBM, San Jose, CA 95193 USA (e-mail: remmelt@us.ibm.com). Digital Object Identifier 10.1109/TMAG.2003.816433 Fig. 1. Lubricant head/disk mass transfer model. pressure tends to retain lubricant on the disk (second term). The condensation mass flux can, therefore, be expressed as (1) where is the bulk vapor pressure, is the molecular weight, is the gas constant, is the absolute temperature, and is the lubricant density. is the disjoining pressure for disk lubricant thickness [5]. The expression for the dispersive (or Van der Waals) part of is as follows: (2) with being the effective Hamaker constant for the lubri- cant/overcoat system, and the distance of closest approach between the lubricant molecule and the carbon sur- face [6]. For a functional lubricant such as Zdol, a polar com- ponent of the disjoining pressure also needs to be taken into account [7]. This part is important, as it reflects the propensity of Zdol to spontaneously dewet beyond a critical thickness (autophobocity), where the overall disjoining pressure changes sign [8], [9]. The same physics limits the adsorption to thick- nesses below this critical value. To simulate the periodic nature of the polar interaction [10], a sinusoidal functional expression for will be used as follows: (3) where is estimated at 4 MPa [8]. It should be pointed out that this value is expected to vary with molecular weight, but due to the lack of solid experimental data, it will be considered constant in this study. For Zdol, the dewetting thickness was shown to vary fairly linearly with molecular weight as follows: (kDaltons) [7]. An example of the variation of with lubricant thickness is shown in Fig. 2, for kDaltons. Equations (1)–(3) can be similarly derived for the evapora- tion flux from the slider ABS surface (outflow), using the 0018-9464/03$17.00 © 2003 IEEE