Formulation of the tangential velocity slip problem in terms of variational inequalities

Strozzi, Antonio; Giacopini, Matteo; Bertocchi, Enrico; Dini, Daniele

doi:10.1177/1350650114530680

Cited by 5 publications

(7 citation statements)

References 33 publications

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“…[3,4]). Therefore, a facility to control the normal pressure on the confined sample applied at the wall within a molecular dynamics context is desirable.…”

mentioning

confidence: 99%

Boundary-controlled barostats for slab geometries in molecular dynamics simulations

et al. 2014

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Molecular dynamics simulation barostat schemes are derived for achieving a given normal pressure for a thin liquid or solid layer confined between two parallel walls. This work builds on the boundary-controlled barostat scheme of Lupkowski and van Swol [J. Chem. Phys. 93, 737 (1990)]. Two classes of barostat are explored, one in which the external load is applied to a virtual regular lattice to which the wall atoms are bound using a tethering potential. The other type of barostat applies the external force directly to the wall atoms, which are not tethered. The extent to which the wall separation distribution is Gaussian is shown to be an effective measure of the quality of the barostat. The first class of barostat can suffer from anomalous dynamical signatures, even resonances, which are sensitive to the effective mass of the virtual lattice, whose value lacks any rigorous definition. The second type of barostat performs much better under equilibrium and wall-sliding nonequilibrium conditions and in not being so prone to resonance instabilities in the wall separation and does not require so many largely arbitrary parameters. The results of exploratory simulations which characterize the dynamical response of the model systems for both dry and wet or lubricated systems using the different barostats are presented. The barostats which have an inherent damping mechanism, such as the ones analogous to a damped harmonic oscillator, reduce the occurrence of large fluctuations and resonances in the separation between the two walls, and they also achieve a new target pressure more quickly. Near a nonequilibrium phase boundary the attributes of the barostat can have a marked influence on the observed behavior.

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“…[3,4]). Therefore, a facility to control the normal pressure on the confined sample applied at the wall within a molecular dynamics context is desirable.…”

mentioning

confidence: 99%

Boundary-controlled barostats for slab geometries in molecular dynamics simulations

et al. 2014

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“…In the following a brief description of the numerical method employed is presented. The reader is referred to [35,36,34] to have more details about these numerical methods.…”

Section: Methodsmentioning

confidence: 99%

“…The developed algorithm is based on the concept of complementarity. This technique was first applied to deal with unilateral contacts in structural mechanics [32] and then applied to individually describe slip at the wall [33,34] and cavitation [35,36]. The flexibility of the complementary algorithm is fundamental to predict the behaviour of contact with extreme thickness gradients, typical of textured surfaces (such as dimple or pockets, for instance).…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…In this paper we focus on the case of the possible slippage just in the positive streamwise direction as in the preliminary work of Strozzi [33]. However, an algorithm based on variational inequalities which naturally incorporates the possibility of slippage in the two opposite directions can be developed since it is relatively easy to consider a finite interval for the values assumed by the shear stress at the slippage surface, τ , see [34].…”

Section: Slippagementioning

confidence: 99%

“…The extension to negative threshold for the shear stress is straightforward and the reader is referred to Ref. [34] for further details.…”

Section: Slippagementioning

confidence: 99%

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Interplay between wall slip and cavitation: A complementary variable approach

Biancofiore

Giacopini

Dini

2019

Tribology International

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In this work a stable and reliable numerical model based on complementary variables is developed to study lubricated contacts characterised by slip at one or both surfaces and in the presence of cavitation. This model can be used to predict surface behaviour when cavitation induced by e.g. the presence of surface texture, slip, or a combination of the two is encountered, with varying surface parameters. For this purpose, two different algorithms are coupled to predict the formation of cavitation, through a mass-conserving formulation, and the presence of slip at the wall. The possible slippage is described by a limiting shear criterion formulated using a Tresca model. To show the flexibility of our model, several bearing geometries have been analysed, such as a twin parabolic slider, a cosine profile used to mimic a bearing, and a pocketed slider bearing employed to study the effect of surface texture. We observe that the lubrication performance (i.e. low friction coefficient) can be improved by using materials that promote slippage at the moving wall. The location of the slippage region can be optimised to find the lowest value of friction coefficient. Our theoretical developments and numerical implementation are shown to produce useful guidelines to improve and optimise the design of textured superoleophobic surfaces in the presence of lubricated contacts.

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