Gas lubrication theory

Historically, gas lubrication theory was developed from the classical liquid lubrication equation—Re5molds equation [4]. The first gas lubrication equation was derived by Harrison [5] in 1913, taking the compressibility of gases into account. Because the classical gas lubrication equation is based on the Navier-Stokes equation, it does not incorporate some gas flow characteristics rooted in the rarefaction effects of dilute gases. As early as 1959, Brunner s experiment [6] showed that the classical gas lubrication equation was... 

The last category is the pressure-driven gas flows, which are typical in micro gas fluidic and micro heat transfer systems. Because the channel diameter or width in micro gas fluidic systems is in the scale of sub-micrometer or less, ultra-thin gas lubrication theory plays an important role in... 

S.-C. Kang, R. M. Crone, and M. S. Jhon, A new molecular gas lubrication theory suitable for head-disk interface modeling, J. Appl. Phys. 85(8), 5594-5596 (1999). 

As described above, the magnitude of Knudsen number, Kn, or inverse Knudsen number, D, is of great significance for gas lubrication. From the definition of Kn in Eq (2), the local Knudsen number depends on the local mean free path of gas molecules,, and the local characteristic length, L, which is usually taken as the local gap width, h, in analysis of gas lubrication problems. From basic kinetic theory we know that the mean free path represents the average travel distance of a particle between two successive collisions, and if the gas is assumed to be consisted of hard sphere particles, the mean free path can be expressed as... 

The flow of a long bubble in a capillary is a classical problem in fluid mechanics. Bubbles have been used as tracers in capillaries filled with liquid in order to determine liquid velocity. This application led to the discovery that when a wetting viscous liquid is displaced by a gas bubble in a capillary a liquid film is deposited on the wall. Initial experimental findings that the thickness of the film was proportional to Ca / were confirmed and extended to Ca= 10 [3]. In his pioneering approach, Brether-ton [1] assumed creeping flow in the liquid and used lubrication theory for the region of the film between the end of the spherical bubble cap and the flat film behind it to calculate the thickness of the film, the pressure drop and... 

In 1959, Burgdorfer [39] first introduced a concept of the kinetic theory to the field of gas film lubrication. This was to derive an approximation equation, called the modified Reynolds equation, using a slip flow velocity boundary con-... 

Thus, fundamentally the interest is in testing the limits and theory of polymer behavior in end-tethered systems, e.g., viscoelastic behavior, wetting and surface energies, adhesion, shear forces relevant to tribology, etc. It should be noted that relevant surfaces and interfaces can also refer to polymers adsorbed in liquid-liquid, liquid-gas, solid-gas, and solid-liquid interfaces, which makes these polymer systems also of prime importance in interfacial science and colloidal phenomena (Fig. 2). Correspondingly, a wide number of potential applications can be enumerated ranging from lubrication and microelectronics to bioimplant surfaces. 

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