UNIVERSITÀ DI PARMA
DIPARTIMENTO DI SCIENZE MATEMATICHE, FISICHE E INFORMATICHE

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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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