TECHNICAL PAPER Deformation characteristics of ultra-thin liquid film considering temperature and film thickness dependence of surface tension Three-dimensional analyses by the unsteady and linearized long wave equation Hiroshige Matsuoka • Koji Oka • Yusuke Yamashita • Fumihiro Saeki • Shigehisa Fukui Received: 31 August 2010 / Accepted: 28 December 2010 / Published online: 18 January 2011 Ó Springer-Verlag 2011 Abstract Thermocapillary deformations of an ultra-thin liquid film caused by temperature distribution were three- dimensionally analyzed using the unsteady and linearized long wave equation considering the temperature and film thickness dependence of surface tension. The temperature and film thickness dependence equation for the surface tension of a liquid was firstly established. The temperature dependence of the surface tension was obtained experi- mentally using a surface tensiometer and the film thickness dependence was obtained theoretically from the corrected van der Waals pressure equation for a symmetric multi- layer system. Time evolutions of depression and groove of the ultra-thin liquid film caused by local heating were obtained quantitatively. 1 Introduction In current magnetic storage systems, the spacing between the flying head and the disk has been dramatically decreased to \ 10 nm in order to realize ultra-high density recording. When the flying height of the head is of the same order as the lubricant film thickness, lubricant deformation affects the static and dynamic flying charac- teristics of the slider. Therefore, it is very important to investigate the deformation and flow characteristics of the lubricant on the recording disk. In particular, in heat- assisted magnetic recording (HAMR), we need to consider heat conduction on the nanometer scale, the evaporation of the lubricant, the distribution of surface tension, and the distribution of viscosity by local laser heating, which may cause deformation of the lubricant film (Oka et al. 2009; Wu 2007). In the present paper, we focus on lubricant film defor- mation due to thermocapillary effects. We first establish the temperature and film thickness dependence equation for the surface tension. The temperature dependence was obtained by measuring the relationship between surface tension and temperature by means of a surface tensiometer, while the film thickness dependence was obtained based on the theoretical considerations of the van der Waals pressure equation for a symmetric multilayer system. Using the unsteady and linearized long wave equation considering the temperature and film thickness dependence of the sur- face tension, we analyzed the liquid film deformation caused by the temperature distribution three-dimensionally, and the basic characteristics of the liquid film deformation due to the thermocapillary effects are described. 2 Long wave equation for lubricant film deformation We assume that a thin liquid film is placed on a solid surface and that the liquid surface is exposed to a gas, as shown in Fig. 1. The film thickness is denoted by h L (x, y, t), where the x and y coordinates show the in-plane directions, and t denotes the time. Assuming that the liquid film satisfies the continuum hypothesis and that the char- acteristic length in the in-plane directions is much larger than the film thickness, the surface deformations caused by stresses acting on the liquid surface are described by the long wave equation (Oron et al. 1997; Fukui et al. 2007; Saeki et al. 2009). The equation for the unsteady state is written as follows: H. Matsuoka (&) K. Oka Y. Yamashita F. Saeki S. Fukui Department of Mechanical and Aerospace Engineering, Graduate School of Engineering, Tottori University, 4-101 Minami, Koyama, Tottori 680-8552, Japan e-mail: [email protected]123 Microsyst Technol (2011) 17:983–990 DOI 10.1007/s00542-011-1223-0
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TECHNICAL PAPER
Deformation characteristics of ultra-thin liquid film consideringtemperature and film thickness dependence of surface tension
Three-dimensional analyses by the unsteady and linearized long wave equation
Hiroshige Matsuoka • Koji Oka • Yusuke Yamashita •
Fumihiro Saeki • Shigehisa Fukui
Received: 31 August 2010 / Accepted: 28 December 2010 / Published online: 18 January 2011
� Springer-Verlag 2011
Abstract Thermocapillary deformations of an ultra-thin
liquid film caused by temperature distribution were three-
dimensionally analyzed using the unsteady and linearized
long wave equation considering the temperature and film
thickness dependence of surface tension. The temperature
and film thickness dependence equation for the surface
tension of a liquid was firstly established. The temperature
dependence of the surface tension was obtained experi-
mentally using a surface tensiometer and the film thickness
dependence was obtained theoretically from the corrected
van der Waals pressure equation for a symmetric multi-
layer system. Time evolutions of depression and groove of
the ultra-thin liquid film caused by local heating were
obtained quantitatively.
1 Introduction
In current magnetic storage systems, the spacing between
the flying head and the disk has been dramatically
decreased to \10 nm in order to realize ultra-high density
recording. When the flying height of the head is of the
same order as the lubricant film thickness, lubricant
deformation affects the static and dynamic flying charac-
teristics of the slider. Therefore, it is very important to
investigate the deformation and flow characteristics of the
lubricant on the recording disk. In particular, in heat-
assisted magnetic recording (HAMR), we need to consider
heat conduction on the nanometer scale, the evaporation of
the lubricant, the distribution of surface tension, and the
distribution of viscosity by local laser heating, which may
cause deformation of the lubricant film (Oka et al. 2009;
Wu 2007).
In the present paper, we focus on lubricant film defor-
mation due to thermocapillary effects. We first establish
the temperature and film thickness dependence equation for
the surface tension. The temperature dependence was
obtained by measuring the relationship between surface
tension and temperature by means of a surface tensiometer,
while the film thickness dependence was obtained based on
the theoretical considerations of the van der Waals pressure
equation for a symmetric multilayer system. Using the
unsteady and linearized long wave equation considering
the temperature and film thickness dependence of the sur-
face tension, we analyzed the liquid film deformation
caused by the temperature distribution three-dimensionally,
and the basic characteristics of the liquid film deformation
due to the thermocapillary effects are described.
2 Long wave equation for lubricant film deformation
We assume that a thin liquid film is placed on a solid
surface and that the liquid surface is exposed to a gas, as
shown in Fig. 1. The film thickness is denoted by
hL(x, y, t), where the x and y coordinates show the in-plane
directions, and t denotes the time. Assuming that the liquid
film satisfies the continuum hypothesis and that the char-
acteristic length in the in-plane directions is much larger
than the film thickness, the surface deformations caused by
stresses acting on the liquid surface are described by the
long wave equation (Oron et al. 1997; Fukui et al. 2007;
Saeki et al. 2009). The equation for the unsteady state is
written as follows:
H. Matsuoka (&) � K. Oka � Y. Yamashita � F. Saeki � S. Fukui
Department of Mechanical and Aerospace Engineering,
Graduate School of Engineering, Tottori University,