Squeeze flow modeling with the use of micropolar fluid theory

Abstract

Abstract. The aim of this paper is to study the applicability of micropolar fluid theory to modeling and to calculating tribological squeeze flow characteristics depending on the geometrical dimension of the flow field. Based on analytical solutions in the lubrication regime of squeeze flow between parallel plates, calculations of the load capacity and time required to squeeze the film are performed and compared -as a function of the distance between the plates -for both fluid models: the micropolar model and the Newtonian model. In particular, maximum distance between the plates for which the micropolar effects of the fluid become significant will be established. Values of rheological constants of the fluids, both those experimentally determined and predicted by means of using equilibrium molecular dynamics, have been used in the calculations. The same analysis was performed as a function of dimensionless microstructural parameters. MFT is being widely developed due to its potential use in tribology, microdevices, biotribology, and magnetorheology, to describe the flows in microchannels [10][11][12]. For the past twenty years, significant progress and results supporting the usefulness of MFT to model fluid flow in narrow gaps and passages have been developed. Based on the molecular dynamics method, it was confirmed that during the Poiseuille flow in very narrow channels, the microrotation velocity -not included in the classical continuum theory -does in fact exist and those results are sufficiently consistent with the results obtained based on the analytical solution of the micropolar fluid flow [13][14][15][16][17]. A new method has been developed by Hansen et al. [18] for designating the micropolar viscosity coefficients for real fluids using equilibrium molecular dynamics and values for water have been presented in the same work.Research on scale effect of MFT applicability to microflows modeling started in 2004. It showed that micropolar fluid equations of motion are being reduced to their counterparts in the classical continuum medium (Cauchy) theory, i.e. the Navier-Stokes equations, when the characteristic linear dimension of the flow field is sufficiently large [15,16]. As a result, questions concerning the size of the flow field arose as concerns the effective use of MFT in solving flow problems. HagenPoiseuille fluid flow in this context was studied in detail [16] and a microchannel maximum diameter value, above which the effect of micropolarity is negligibly small, was calculated for some real fluids, including water and blood, and expressed in dimensionless micropolar parameters. Hoffmann et al. (2007) compared the resistance force exerted on a sphere moving in micropolar fluids: water and blood, and showed that deviations are being observed only for small sphere radii.Lubrication-type analysis for squeezing flow is well established, and physical effects such as increased load capacity, etc., have been known since the 1970s, quoted e.g. in [3,4]. The increasing number of articles regarding squeez...

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…The numerous previous experimental studies on the scope of the influence of the phospholipid membrane on the hydrodynamic process of surface lubrication were mainly focused on non-stochastic the-ory and experiments in the field of chemistry, without taking into account random changes [8][9][10][11][12][13][14][15][16][17][18][19]. There has been no previous stochastic research concerning frictional forces and coefficients of friction based on experimental methods and analyticalnumerical hydrodynamics for lamellar and laminar biological flows [12,17,20,21].…”

“…ory and experiments in the field of chemistry, without taking into account random changes [8][9][10][11][12][13][14][15][16][17][18][19]. There has been no previous stochastic research concerning frictional forces and coefficients of friction based on experimental methods and analyticalnumerical hydrodynamics for lamellar and laminar biological flows [12,17,20,21].…”

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