Lecture 11

.title[
# Lecture 11
]
.subtitle[
## Adhesion
]
.author[
### Dr. Christopher Kenaley
]
.institute[
### Boston College
]
.date[
### 2024/02/20
]

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<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.14.0/css/all.min.css">

Today we'll consider ....

- Mechanical adhesion mechanisms

- Molecular adhesion mechanisms

- Multiple mechanisms in biological systems

]

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![](https://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2Fs00360-008-0310-8/MediaObjects/360_2008_310_Fig1_HTML.jpg)

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# Types of adhesion mechanisms

.pull-left[
- Claws and hooks
- Suction
- Stefan adhesion
- Capillary adhesion
- Molecular adhesion
- All of the above

<img src="img/treefrogtoes.jpg" width="300" />
]

]

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# Claws

- Hook acts as a cantilever beam

<img src="img/hopper.jpg" width="250" /><img src="https://www.civilclick.com/wp-content/uploads/2020/05/Cantilever-load-pic.jpg" width="250" />
]

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<img src="img/tarsus.jpg" width="300" /><img src="https://www.icaboston.org/sites/default/files/styles/original_crop_height/public/2015-08aug-ica-first-fridays-63.jpg?itok=TZUkTMDx" width="300" />
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# Suction

- `$\rightarrow \textrm{huge } \Delta \textrm{ pressure}$`

<img src="img/octopus.jpg" width="500" />
]

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`$$F_1=P_{out}A_{out}-P_{in}A_{in}$$`

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# Stefan adhesion

.pull-left[
- Fluid between two structures
- Stress of fluid shear resists expansion 
- Viscosity important

`$$F\sim\mu\frac{dx}{dt}$$`

<img src="img/stefan.png" width="500" />
]

.pull.right[

For two discs of radius *R*

`$$F=\mu\frac{3\pi R^4}{2h^3}\frac{dh}{dt}$$`

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# Capillary adhesion

for discs of radius r

`$$\Delta p=\gamma \Big(\frac{1}{r}-\frac{2}{x}\Big)$$`
`$\gamma  \textrm{ = surface tension (N/m)}$`

<img src="img/capillary.png" width="600" />
]

.pull.right[

<img src="img/toepad.jpg" width="300" /><table class="table" style="margin-left: auto; margin-right: auto;">
<caption>Surface tenion of various fluids</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> fluid </th>
   <th style="text-align:right;"> `$^o$`C </th>
   <th style="text-align:right;"> `$\gamma$` </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Blood </td>
   <td style="text-align:right;"> 22 </td>
   <td style="text-align:right;"> 55.89 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Water </td>
   <td style="text-align:right;"> 100 </td>
   <td style="text-align:right;"> 58.85 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Water </td>
   <td style="text-align:right;"> 50 </td>
   <td style="text-align:right;"> 67.91 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Water </td>
   <td style="text-align:right;"> 25 </td>
   <td style="text-align:right;"> 71.97 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Water </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 75.64 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Sucrose (55%) + water </td>
   <td style="text-align:right;"> 20 </td>
   <td style="text-align:right;"> 76.45 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mercury </td>
   <td style="text-align:right;"> 15 </td>
   <td style="text-align:right;"> 487.00 </td>
  </tr>
</tbody>
</table>

]

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# Molecular mechanisms

for spheres of radius r and distance d

`$$F_{vdW}=\frac{Hr}{6d^2}$$`

*H* is Hamaker constant
<img src="img/toepads.jpg" width="600" />
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# Multiple Mechanisms
.pull-left[
- Suction
- Cantiliver

]

.pull.right[

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# Thanks!

Slides created via the R package [**xaringan**](https://github.com/yihui/xaringan).