Biomedical Engineering Reference
In-Depth Information
the model here the tip comes to rest asymptotically on the surface at zero
separation. In reality, there is a repulsive interaction that determines a
non-zero separation (this will be considered in the next section). If the
temperature is low enough the vibration of the tip about the stable
equilibrium position may be insignificant and the critical equilibrium
condition s = s 0 may be reached at which F = k = 0 . Infinitesimal motion
of the indenter such that s
<
s 0 is imposed leads to F
<
0 for all z and the
tip irreversibly snaps on to the surface as before.
In summary, adhesion between the two bodies under consideration
here, the probe and the surface, occurred when the probe position
imposed by the environment, in this case the indentation apparatus,
reached a snap-on point. This point characterized a critical equilibrium
configuration in which both the force and stiffness fields of the combined
surface attraction and probe spring restoring influence were balanced.
Mechanical perturbation of the system (by further imposed motion of
the probe towards the surface) or thermal perturbation (by oscillation
of the probe tip) led to a dominance of the surface attraction over
the spring resistance and irreversible motion of the tip to the surface
such that the two bodies were adhered. The imposed probe position
at the onset of the snap-on process was determined by the ratio
of the parameters characterizing the surface attraction and spring
constant, s = s 0 = 2( A / k S ) 1/2 , and the snap-on force was determined
by the product of these parameters, F S ( s
( Ak S ) 1/2 . These simple
expressions are a consequence of the simple system chosen here
to illustrate the snap-on instability phenomenon. Greater analytic
complication will result for systems with less analytically-tractable
surface potentials and for which both the probe and the surface are
deformable (and maybe non-linearly or irreversibly) but the physics will
remain the same: A critical length scale in the system is determined by a
vanishing stiffness that depends on a competition between surface
attraction and elastic restoring forces. The next section will illustrate this
principle for the de-adhesion or separation process in which the adhered
bond is fractured.
=
s 0 )
=
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