Hard-disk fluid

Computer simulations also constitute an important basis for the development of the molecular theory of fluids. They could be regarded as quasiexpeiimental procedures to obtain datasets that connect the fluid s microscopic parameters (related mainly to the structure of the system and the molecular interactions) to its macroscopic properties (such as equation of state, dynamic coefficients, etc.). In particular, some of the first historical simulations were performed using two-dimensional fluids to test adaptations of commonly used computer simulation methods [14,22] Monte Carlo (MC) and molecular dynamics (MD). In fact, the first reliable simulation results were obtained by Metropolis et al. [315], who applied the MC method to the study of hard-sphere and hard-disk fluids. 

TFL is an important sub-discipline of nano tribology. TFL in an ultra-thin clearance exists extensively in micro/nano components, integrated circuit (IC), micro-electromechanical system (MEMS), computer hard disks, etc. The impressive developments of these techniques present a challenge to develop a theory of TFL with an ordered structure at nano scale. In TFL modeling, two factors to be addressed are the microstructure of the fluids and the surface effects due to the very small clearance between two solid walls in relative motion [40]. 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

Molecularly thin lubricant film is an important application of nanoscale confined polymeric fluids, and is the focus of this chapter. Ultrathin lubricant films are necessary in high-density data storage to increase the reliability and performance of hard-disk drive (HDD) systems [2-4]. Spinoff and intermittent contact between the slider (or head) and the lubricated disk [ultrathin perfluoropolyether (PFPE) films are applied to the disk s carbon-overcoated surface, as shown in Fig. 1.1] cause loss and reflow of the lubricant film. The relevant HDD technology is summarized briefly in the end-of-chapter Appendix Section A.I, which provides an overview of how certain information technology devices are controlled by nanoscale chemistry. 

Our presentation here has been limited to the 3D case of a hard-sphere fluid. However, the GPRG method is equally successful in predicting the compressibility factor for a two-dimensional (2D) fluid of hard disks [29]. 

Figure 1. Equations of state for hard rod, hard disk, and hard sphere fluids [2,4,5,6].

We will now use dimensional interpolation to proceed from the known results, namely those at low n, at low B, and at high B, to the desired results at higher n and at D = 2 or D = 3. The interpolation will actually be performed on the cluster integral ratios p nk] D), since these quantities had finite but non-zero dimensional limits. Given interpolated ratios, one can simply step up from the known integrals for hard points or rods to those for hard disks or spheres (or even higher-dimensional fluids), since... 

Finally, we mention the fact that the molecular dynamics calculation of Po t) for a gas of hard disks exhibited a vortex type of velocity correlation between the tagged molecule and the surrounding molecules that is very similar to the hydrodynamic flow field surrounding a moving volume element in a fluid initially at rest. This vortex pattern, illustrated in Fig. 26, suggests that a fraction of the momentum transferred by the tagged particle to the particles in front of it is eventually returned to it from behind. This process causes the velocity autocorrelation function to be larger than it would be if these vortices did not occur, and it is connected with the slow decay of the velocity autocorrelation function. 

Magnetic recording media, such as computer hard disk drives, rotate at high frequencies (5-15 kHz) and need lubricants to maintain opertation. Phosphazenes are of interest in this application due to their ability to form fluids with little to no volatility and, due to their phosphorus eontent, they do not support combustion. Two differing phosphazene fluid additives have been developed based on fluorine ehemistry." Structure (8) was an early... 

These machine calculations provide what is essentially exact information on the consequences of a given intermolecular force law. Application has been made to hard spheres and hard disks, to particles interacting through a Lenard-Jones 12-6 potential function and other continuous potentials of interest in the study of simple fluids, and to systems of charged particles [123]. 

Another important advance was represented by the work of Sokolowski and Steele [187, 188], who used the density functional formalism to study the fi eezing of strictly 2D fluids on an exposed crystal face of a chemically inert solid. In particular, numerical calculations were presented for the freezing of hard disks on a periodic surface chosen to model the graphite structure [187]. They also presented a more detailed application to the freezing of krypton monolayers on graphite. The Kr-Kr interaction was modeled by a L-J potential. This theory... 

The temperature instability of a two-dimensional reactive fluid of N hard disks bounded by heat conducting walls has been studied by molecular dynamics simulation. The collision of two hard disks is either elastic or inelastic (exothermic reaction), depending on whether the relative kinetic energy at impact exceeds a prescribed activation barrier. Heat removal is accomplished by using a wall boundary condition involving diffuse and specular reflection of the incident particles. Critical conditions for ignition have been obtained and the observations compared with continuum theory results. Other quantities which can be studied include temperature profiles, ignition times, and the effects of local fluctuations. 

Figure 3.19 shows the fluid flow regimes prevalent in different MEMS devices. It clearly demonstrates the limitation of the N-S equation for microscale flow modeling. It can be seen that most of the microsystems with gaseous flow works in the slip flow regime. Some flows inside microchannel, micropump, micronozzle, and microvalve operate in transitional regime. Free molecular flow is observed for Couette flow between hard disk and read-write head with a gap of about 100 nm. 

Valve Trim Various alloys are available for valve parts such as seats, disks, and stems which must retain smooth finish For successful operation. The problem in seat materials is fivefold (1) resistance to corrosion by the fluid handled and to oxidation at high temperatures, (2) resistance to erosion by suspended solids in the fluid, (3) prevention of galling (seizure at point of contact) by differences in material or hardness or Both, (4) maintenance of high strength at high temperature, and (5) avoidance of distortion. 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

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