A nanomeniscus modeled as an equivalent mechanical oscillator meniscus spring constant

4 A nanomeniscus modeled as an equivalent mechanical oscillator meniscus spring constant 

In many applications, it will be useful to describe the nanomeniscus as an equivalent mechanical oscillator and thus to derive a meniscus spring constant. Here, we propose to determine this value in the simple case of a CL pinned on a fiber dipped in a liquid bath. Since the pressure inside the meniscus is zero, the capillary force is simply given by the tension term  

The associated spring constant that describes the elastic restoring force in response to a weak vertical displacement of the CL is  

For a forced vertical displacement along the z-axis, the corresponding variation of the contact wetting angle 9 is given by the derivative of Eq. 9.5  

Equation 9.9 is quite cumbersome and does not help to anal e the experimental data. In particular, the measurement of the spring constant k should allow deducing the contact angle 9 (see section 9.3.2.2). A first-order expansion of Eq. 9.9 gives a much tractable equation, still accurate enough to be used, in particular for small fibers, and small contact angles (Fig. 9.2)  

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