A Refined JKR Model for Adhesion of a Rigid Sphere on a Soft Elastic Substrate

2019 ◽  
Vol 86 (5) ◽  
Author(s):  
Lei Zhang ◽  
C. Q. Ru
Keyword(s):  
Surface Energy ◽  
Contact Zone ◽  
Essential Role ◽  
Present Model ◽  
Recent Literature ◽  
Soft Materials ◽  
Detailed Comparison ◽  
Rigid Sphere ◽  
Elastic Substrate ◽  
Adhesion Mechanics

Surface energy outside the contact zone, which is ignored in the classical Johnson–Kendall–Roberts (JKR) model, can play an essential role in adhesion mechanics of soft bodies. In this work, based on a simple elastic foundation model for a soft elastic half space with constant surface tension, an explicit expression for the change of surface energy outside the contact zone is proposed for a soft elastic substrate indented by a rigid sphere in terms of two JKR-type variables (δ, a), where a is the radius of the contact zone and δ is the indentation depth of the rigid sphere. The derived expression is added to the classical JKR model to achieve two explicit equations for the determination of the two JKR variables (δ, a). The results given by the present model are demonstrated with detailed comparison with known results reported in recent literature, which verified the validity and robust accuracy of the present method. In particular, the present model confirms that the change of surface energy of the substrate can play an essential role in micro/nanoscale contact of soft materials (defined by W/(E*R)≥0.1, where W is the adhesive energy, E* is the substrate elasticity, and R is the rigid sphere radius). The present model offers a simpler analytical method for adhesion mechanics of a rigid sphere on a soft elastic substrate when compared with several existing methods proposed in recent literature that request more substantial numerical calculations.

An ellipsoidal cap model for adhesion of a soft particle on a rigid substrate

2018 ◽  
Vol 24 (4) ◽  
pp. 887-894
Author(s):  
CQ Ru
Keyword(s):  
Surface Energy ◽  
Explicit Expression ◽  
Contact Zone ◽  
Soft Particle ◽  
Rigid Substrate ◽  
Asymptotic Equations ◽  
Cap Model ◽  
Adhesion Mechanics ◽  
Elastic Particle ◽  
Good Agreement

Surface energy outside the contact zone, which is not accounted for in the classical Johnson–Kendall–Roberts (JKR) model, can play an essential role in adhesion mechanics of soft particles. An open problem in the adhesion mechanics of soft elastic particles is how to achieve an explicit expression for the surface energy outside the contact zone in terms of the two JKR-type variables ( a, δ), where a is the radius of the contact zone and δ is the relative approach of two bodies. The present work aims to develop an ellipsoidal cap model for the surface energy outside the contact zone of a soft elastic particle on a rigid substrate in terms of the two JKR-type variables ( a, δ). An explicit expression for the surface energy outside the contact zone is derived, and simple asymptotic equations are obtained to determine the two unknowns ( a, δ). The validity and accuracy of the derived expression and asymptotic equations are verified by good agreement with the Young–Dupre equation in the absence of an external applied force, and are also justified by good agreement of the predicted pull-off force with known results available in recent literature.

Examination of the lubricant storing and releasing ability of thermally sprayed surfaces

2011 ◽  
Vol 2 (2) ◽  
pp. 101-105
Author(s):  
L. Fazekas ◽  
Z. S. Tiba ◽  
G. Kalácska
Keyword(s):  
Free Energy ◽  
Surface Energy ◽  
Surface Free Energy ◽  
Essential Role ◽  
Index Number ◽  
Adhesion Ability ◽  
Thermally Sprayed ◽  
Proper Operation

Abstract The lubricant storing and releasing ability of the thermally sprayed surfaces plays an essential role in the proper operation of the components. In the case of porous sprayed surfaces the lubricant storing and releasing ability depends mainly on porosity and the surface energy (adhesion susceptibility). The adhesion ability can also be expressed indirectly with an index number that is by determining the surface free energy.

scholarly journals Effect of surface bending and stress on the transmission of line force to an elastic substrate

2018 ◽  
Vol 474 (2215) ◽  
pp. 20170775 ◽  
Author(s):  
Chung Yuen Hui ◽  
Zezhou Liu ◽  
Anand Jagota
Keyword(s):  
Elastic Modulus ◽  
Surface Stress ◽  
Broad Class ◽  
Local Stress ◽  
Soft Materials ◽  
Elastic Substrate ◽  
Capillary Length ◽  
Singular Stress ◽  
Line Load ◽  
Line Force

For a broad class of soft materials their surface stress can strongly influence mechanical behaviour. For example, a line force applied to the surface of an elastic substrate is locally supported by surface stress over an elasto-capillary length l c (surface stress/elastic modulus). Surface stress regularizes the otherwise highly singular stress and strain fields. However, surface such as lipid bilayer interfaces can also resist deformation by bending. This has not been studied either by experiments or theories. We analyse a theoretical model of the response of a half-space to a line force when the surface carries both a stress and resistance to bending. We find that surface bending further regularizes the singular fields. The local stress field near the line load can be separated into three regions. Region 1 occupies distances from the line load smaller than an elasto-capillary bending length l b (bending stiffness/elastic modulus to the 1/3 power) where surface bending dominates and the elastic stress and strains are continuous. Region 2 occupies intermediate distances between l b and l c   ( > l b ) where surface stress dominates. At distances larger than l c we retrieve the classical elasticity solution. The size of region 2 depends on κ = l c / l b and vanishes for small l c .

Lubricated steady sliding of a rigid sphere on a soft elastic substrate: hydrodynamic friction in the Hertz limit

Soft Matter ◽  
2020 ◽  
Vol 16 (11) ◽  
pp. 2760-2773 ◽  
Author(s):  
Haibin Wu ◽  
Nichole Moyle ◽  
Anand Jagota ◽  
Chung-Yuen Hui
Keyword(s):  
Rigid Sphere ◽  
Elastic Substrate ◽  
Hydrodynamic Friction ◽  
Elastic Substrates ◽  
Lubricated Sliding

Lubricated sliding on soft elastic substrates occurs in a variety of natural and technological settings.

Lubricated Soft Normal Elastic Contact of a Sphere: A New Numerical Method and Experiment

Soft Matter ◽  
2022 ◽  
Author(s):  
Zezhou Liu ◽  
Hao Dong ◽  
Anand Jagota ◽  
Chung-Yuen Hui
Keyword(s):  
Liquid Film ◽  
Numerical Solution ◽  
Numerical Method ◽  
Thin Liquid Film ◽  
Rigid Sphere ◽  
Elastic Contact ◽  
Elastic Substrate ◽  
Normal Contact

An important problem in lubrication is the squeezing of a thin liquid film between a rigid sphere and an elastic substrate under normal contact. Numerical solution of this problem typically...

Elastohydrodynamic Lubrication Analysis of Pure Squeeze Motion on an Elastic Coating/Elastic Substrate System

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Li-Ming Chu ◽  
Chi-Chen Yu ◽  
Qie-Da Chen ◽  
Wang-Long Li
Keyword(s):  
Young’S Modulus ◽  
Elastic Deformation ◽  
Maximum Stress ◽  
Young's Modulus ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Von Mises Stress ◽  
Rigid Sphere ◽  
Elastic Substrate ◽  
Asymptotic Value

A rigid sphere approaching a lubricated flat surface with a layer of elastic coating on the elastic substrate is explored under constant load conditions. The transient pressure profiles, film shapes, elastic deformation, von Mises stress (σvon) during the pure squeeze process under various operating conditions in the elastohydrodynamic lubrication (EHL) regime are discussed. The simulation results reveal that the greater the Young's modulus of coating is, the greater the pressure distribution is, the smaller the contact area is, and the greater the maximum stress (σvon) value is. As the Young’s modulus of coating decreases, the central elastic deformation at the surface (Z = 0) increases and the deformation at the interface of coating/substrate (Z = −1) decreases. For hard coating cases, the maximum central pressure increases to an asymptotic value and minimum film thickness decreases to an asymptotic value as the coating thickness increases. For soft coating cases, this phenomenon reverses. A thicker and stiffer coating leads to a higher maximum stress. At the deformation recovery stage, the positions of the maximum stress would begin to offset downwards and closer to the coating/substrate interface. Moreover, the position of maximum stress varies from the coating to the subsurface as the Young’s modulus of coating increases. The EHL with stress analysis can prevent the chance of fracture in coating or substrate. These characteristics are important for the lubrication design of mechanical elements with coatings.

Control of the Cobalt Surface Layer Formation on Cemented Carbides

2015 ◽  
Vol 825-826 ◽  
pp. 1009-1015
Author(s):  
Alan Pasquazzi ◽  
Wolf Dieter Schubert ◽  
Ronald Weissenbacher
Keyword(s):  
Surface Layer ◽  
Essential Role ◽  
Recent Literature ◽  
Cemented Carbide ◽  
Cemented Carbides ◽  
Layer Formation ◽  
Grain Sizes ◽  
Cooling Conditions ◽  
Microstructure Of The Material ◽  
Surface Layer Formation

The formation of a surface layer of cobalt on cemented carbides which occurs on cooling during sintering is an often observed phenomenon which has been discussed in the recent literature. The presented work shows different factors which influence the formation of the layer and proposes factor-related mechanisms. For this purpose cemented carbide samples with different compositions, WC grain sizes and carbon contents were produced and studied. The results reveal that besides the cooling conditions also the variations in composition and microstructure of the material play an essential role for the formation of a surface layer.

scholarly journals Steady streaming of a viscoelastic fluid within a periodically rotating sphere

2014 ◽  
Vol 761 ◽  
pp. 329-347 ◽  
Author(s):  
Rodolfo Repetto ◽  
Jennifer H. Siggers ◽  
Julia Meskauskas
Keyword(s):  
Viscoelastic Fluid ◽  
Present Model ◽  
Transport Processes ◽  
Rigid Sphere ◽  
Steady Streaming ◽  
Circulation Cell ◽  
Different Types ◽  
Parameter Values ◽  
Streaming Flow ◽  
Axis Passing

AbstractMotivated by understanding mass transport processes occurring in the vitreous chamber of the eye, we consider the steady streaming component of the flow generated in a viscoelastic fluid contained within a hollow, rigid sphere performing small-amplitude, periodic, torsional oscillations about an axis passing through its centre. The problem is solved semi-analytically, assuming that the amplitude of the oscillations is small. The paper extends the work by Repetto et al. (J. Fluid Mech., vol. 608, 2008, pp. 71–80), in which the case of a purely viscous fluid was analysed. However, in reality, in young and healthy subjects, the vitreous humour has complex rheological properties, and so here we model it as a viscoelastic fluid. A similar problem was studied by Nikolakis (Eine Theorie für stationäre Drifterscheinungen viskoelastischer Flüssigkeiten, 1992, VDI). In the present model, the steady streaming flow is governed by four dimensionless parameters. We show that, when we account for the viscoelasticity of the fluid, there is a considerably more complex set of possible flow regimes than was found in the purely viscous case, and the flows can be classified into five qualitatively different types. Whereas there was only one circulation cell in each hemisphere in the viscous case, accounting for viscoelasticity it is possible have either one, two or three circulation cells, with different senses of rotation, depending on the parameter values.

scholarly journals Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion

2015 ◽  
Vol 471 (2175) ◽  
pp. 20140727 ◽  
Author(s):  
Chung-Yuen Hui ◽  
Tianshu Liu ◽  
Thomas Salez ◽  
Elie Raphael ◽  
Anand Jagota
Keyword(s):  
Surface Tension ◽  
Small Strain ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Rigid Sphere ◽  
Elastic Substrate ◽  
Indentation Force ◽  
Resistance To Deformation ◽  
Sphere Radius ◽  
Force Displacement

The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that owing to elasticity. This paper studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The relation between indentation force (displacement) and contact radius is found to depend on a single dimensionless parameter: ω = σ ( μR ) −2/3 ((9 π /4) W ad ) −1/3 , where σ and μ are the surface tension and shear modulus of the substrate, R is the sphere radius and W ad is the interfacial work of adhesion. Our theory reduces to the Johnson–Kendall–Roberts (JKR) theory and Young–Dupre equation in the limits of small and large ω , respectively, and compares well with existing experimental data. Our results show that, although surface tension can significantly affect the indentation force, the magnitude of the pull-off load in the partial wetting liquid-like limit is reduced only by one-third compared with the JKR limit and the pull-off behaviour is completely determined by ω .

Role of microRNAs in haemopoiesis, heart hypertrophy and cancer

2008 ◽  
Vol 36 (6) ◽  
pp. 1206-1210 ◽  
Author(s):  
Laura Fontana ◽  
Antonio Sorrentino ◽  
Gianluigi Condorelli ◽  
Cesare Peschle
Keyword(s):  
Gene Expression ◽  
Essential Role ◽  
Recent Literature ◽  
Human Diseases ◽  
Present Review ◽  
Heart Hypertrophy ◽  
Control Gene ◽  
Research Areas ◽  
Control Gene Expression

miRNAs (microRNAs) are important regulatory molecules that control gene expression in all eukaryotes. miRNAs play an essential role in basic cellular activities such as proliferation, differentiation, morphogenesis and apoptosis. In haemopoiesis, several miRNA-based pathways have been identified. Importantly, miRNA mutations or mis-expression correlate with various human diseases. In cancer, deregulated miRNAs can function as tumour suppressors or oncogenes. The present review focuses on the recent literature concerning the role of miRNAs in three different research areas: haematology, cardiology and oncology, with particular focus on the results obtained by our group.

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