Contact quasi-static

Basire and Frctigny [72J to determine the sample modulus quasi-statically for viscous contacts. 

Far from a wellbore, the velocity of reservoir fluids is about one linear foot per day. Near a wellbore, the velocity can increase one-hundred fold. A static or quasi-static test such as the sessile drop (contact angle) test may not represent the dynamic behavior of the fluids in the field. The dynamic Wilhelmy device gives results which are comparable in interface velocity to the field displacement rate. The interface in the Wilhelmy test described here moved at a steady rate of 0.127 mm/sec or 36 ft/day. The wetting cycle for a hybrid-wetting crude oil system was not affected by moving at a rate less than 1 ft/day. 

The effect has been observed for a variety of combustible materials, but no variations in charge to combustible mass, charge type, structure volume, or degree of venting have been tested. The implications of the data accumulated so far are that quasi-static loading calculations should include estimates of contributions from the burning of combustible materials whenever such materials are expected to be in intimate contact with HI sources. 

The quasi-static acquisition and interpretation of the force-distance curves is straightforward for elastic materials. The information is generally incomplete and less reproducible for polymers which demonstrate viscoelastic contact, plastic deformation, and ploughing type friction. Moreover, they exhibit a wide spectrum of relaxation times from 105 to 109 Hz [121]. 

In this chapter, two simple cases of stereomechanical collision of spheres are analyzed. The fundamentals of contact mechanics of solids are introduced to illustrate the interrelationship between the collisional forces and deformations of solids. Specifically, the general theories of stresses and strains inside a solid medium under the application of an external force are described. The intrinsic relations between the contact force and the corresponding elastic deformations of contacting bodies are discussed. In this connection, it is assumed that the deformations are processed at an infinitely small impact velocity and for an infinitely long period of contact. The normal impact of elastic bodies is modeled by the Hertzian theory [Hertz, 1881], and the oblique impact is delineated by Mindlin s theory [Mindlin, 1949]. In order to link the contact theories to collisional mechanics, it is assumed that the process of a dynamic impact of two solids can be regarded as quasi-static. This quasi-static approach is valid when the impact velocity is small compared to the speed of the elastic... 

The basic theories of elastic deformations associated with various contact forces under static contact conditions have been introduced in the last section. Assuming that an impact process of two solids can be regarded as quasi-static, the theories given in 2.3 are used directly to link the dynamic deformations of the colliding solids with the impact forces. In this section, the collisions of elastic spheres are described. 

Collisions between particles with smooth surfaces may be reasonably approximated as elastic impact of frictionless spheres. Assume that the deformation process during a collision is quasi-static so that the Hertzian contact theory can be applied to establish the relations among impact velocities, material properties, impact duration, elastic deformation, and impact force. 

We consider an arbitrary adiabatically isolated system consisting of two parts in thermal contact. The system is at a uniform temperature t, and we assume that the equilibrium states of each of the parts can be characterized by t and one other parameter. Thus, for a quasi-static process,... 

The dc-mode or topography mode with quasi-static probe contact [5] is the most used, in which the AFM tip is in intimate repulsive contact with a smface, as shown in Figure 9.2. The contact mode is typically used for scanning hard samples and when a resolution of greater than 20 nm is required. The cantilevers are usually silicon (Si) or sUicon nitride (SiaN4), with typical resonant frequencies of 50 kHz and force constants below 1 N m . ... 

Figure 7.35. Quasi-static advancing and receding contact angles versus the fibre surface coverage of AKD sizing agents (given as the relative C/-to total carbon ratio minus that measured for the non-sized reference, as described below). The Cl value represents aliphatic carbons (see Section 8)...

For a wide variety of systems, quasi-static distortions of the contact line have been localized at the micrometer scale as they retreat because of the inability of the surfactant to completely re-self-assemble at localized positions along the contact line. 

Since the surfactant molecules re-self-assemble into their relaxed structure over most of the contact line, a steadily moving contact line is generated due to a uniform SV surface tension. During this stage, the more hydrophilic structure pins the contact line locally, causing a quasi-statical distortion as the substrate is continuously pulled out of the solution. 

The recorded force first increases, then decreases. The maximum value, termed the tack force, is a measure of the adherence under this particular experimental condition and has no clear physical significance. The area under the curve, termed the tack energy, is equal to the work jGda of the cohesive stress at the crack tip. Tackiness refers to the ability of an elastomer to adhere instantaneously to a solid surface, or to itself, after a brief time of contact under low pressure. Probe tack testing can be analyzed by Eq. (54), and tack curves obtained by computer integration almost coincide with experimental ones. S) Figure 8 pertains to a spherical probe and shows that even at a very low cross-head velocity the viscoelastic effects considerably increase the adherence force compared to the elastic (or quasi-static) adherence force at fixed displacement (point D). 

For quasi-static process, if one ignores the gravity, the pressure on each side of an interface is a constant at any time. This implies that the curvature of the interface is constant (from the Young-Laplace equation). Thus, the interface is a circular arc. From (4.16), it is easy to show that the contact point X is related to 6 as. 

We consider a rigid spherical contaminant particle of radius and density initially resting on a substrate smface and interacting with a liquid droplet under quasi-static conditions (see Figme 5.4). Four forces are involved in this interaction particle weight F, contact line force hydrostatic force F, and buoyancy force F, defined as follows ... 

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