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--- lmn:isr [30/12/2013 18:07] – davide.orsi
+++ lmn:isr [30/12/2013 18:09] (versione attuale) – davide.orsi
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+====== Oscillating needle technique ======
+{{ lmn:isr:isr_photo.jpg|ISR - photo of the instrument}}
+The instrument is designed to measure the mechanical response of a Langmuir monolayer to an external shear deformation.
+The instrument is a custom-made apparatus analogous to the one recently
+developed by the group of Gerald Fuller [@Brooks1999 @Reynaert2008].
+The stress exerted by the needle on the film is equal to the shear
+oscillating force (with amplitude $F$), divided by two times the length
+$L$ of the magnetic needle. The resulting shear strain $\gamma$ is equal
+to the needle oscillation amplitude $X$, divided by the distance $W$
+between the needle and the channel that delimits the investigated
+portion of the film. The oscillations of $\gamma$ and $\sigma$ are
+separated by a phase lag $\delta$. The dynamic modulus is then given by:
+$$G(\omega)=\frac{\sigma(\omega)}{\gamma(\omega)}= \frac{W}{2L}\frac{F(\omega)}{X(\omega)}e^{i\delta}$$
+This experimental technique presents some limitations, related to its
+intrinsic design. A measurement performed on a film characterized by a
+low value of $G$ may be strongly affected by contributions from the drag
+of the water subphase. At the same time, the technique is not suited to
+measure the response of very rigid films: the high force required to
+move the needle may induce undesired non-linear effects in the
+measurements of $G$.
+The low limits of the dynamic range of the instrument is usually related
+to the so-called **Boussinesq number**, defined as the ratio between the
+drag due to the film at the interface, and the drag due to the subphase,
+that affect the movement of the needle at the interface. It is expressed
+as
+$$B = \frac{d_{film}}{d_ {subphase}} = \frac{\eta_s \: P \: L_b}{\eta_b \: A \: L_s}$$
+{{ lmn:isr:isr.png|ISR - Scheme}}
+where $\eta_s$ and $\eta_b$ are the viscosities of the film and of the
+subphase, $A$ and $P$ are the area and the perimeter of the contact
+region between the needle and the film, $L_s$ and $L_b$ are the lengths
+over which the velocity fields vary in the film and in the bulk.
+Depending on the value of $B$, three regimes can be roughly identified:
+  * if $B \gg 1$, the effect of the subphase on the measurement of $G$ are negligible;
+  * if $B \ll 1$, the needle is probing the flow properties of the subphase;
+  * an intermediate regime for $B \simeq 1$, where the interpretation of the measurement of the shear modulus $G$ has to account in some way the contributions due to the drag of the subphase.
+====== Resources ======
+  - [[lmn:isr:theory | Instrument design and calibration ]]
+  - To operate the instrument, please follow this {{lmn:isr_operation_list.pdf|operation list}}.
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