class: center, middle, inverse, title-slide .title[ # Lecture 13 ] .subtitle[ ## Fluids Around <br> An Introduction ] .author[ ### Dr. Christopher Kenaley ] .institute[ ### Boston College ] .date[ ### 2024/02/27 ] --- class: top # Fluids <!-- Add icon library --> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.14.0/css/all.min.css"> .pull-left[ Today we'll .... - Define fluids - Define the conditions under which we can predict flows - Viscosity in the real (biological) world ] .pull-right[  ] --- class: top # Where We've Been, Where We're Going Solid and structural mechanics: stress and strain distributions, movements of bodies, their parts in response to muscle forces and gravity. Now on to . . . Fluid dynamics and mechanics. These govern . . . - Internal flows (blood and respiratory flow) - External flows (swimming and flying) - Dispersal (particles, seeds, aerosols) - Transport of nutrients to and from biological surfaces (CO2, H2O, O2, etc). Lastly . . . - A check in . . . How are you doing? --- class: top # Fluid Properties The **continuum hypothesis** explains so much. Roughly put, fluids can be treated as continuous, even though, on a microscopic scale, they are composed of molecules. So at our scales: - density - temperature - momentum - energy all vary **continuously** and these state variations are responsible for flow. --- class: top # Defining a Fluid A fluid (gas or liquid) deforms continuously under an applied stress .center[ <img src="img/shear2.png" width="400" /> `\(F\sim \Delta L/\Delta t\)` `\(\sigma\sim d\varepsilon/dt\)` `\(\sigma \sim d\mu \varepsilon/dt\)` `\(\mu=\textrm{viscosity}\)` Newton's third law ] --- class: top # Defining How a Fluid Flows: Two Conditions .pull-left[ `$$\tau=\mu \frac{du}{dy}=v\frac{d(\rho u)}{dy}$$` <img src="img/shearvelocity.png" width="400" /> ] .pull-right[ No-slip condition (fluids adhere to surfaces) <img src="img/noslip.png" width="400" /> } ] --- class: top # What Determines Viscosity? .pull-left[ - Temperature - Concentration of dissolved (solutes) or suspended entities - **Shear rate** ] .pull-right[ <img src="https://www.cradle-cfd.com/dcms_media/image/en_columnsic02_a0317.png" width="300" /> ] .center[ <img src="https://www.pumpfundamentals.com/images/visc_vs_strain.jpg" width="650" /> ] --- class: top # non-Newtonian Fluids .pull-left[ <img src="https://www.researchgate.net/profile/Helmut-Baumert/publication/290789681/figure/fig1/AS:318865641885696@1453034901545/The-effective-kinematic-viscosity-in-shear-thickening-green-shear-thinning-red-and.png" width="400" /> .foonote[ `\(\mu=\frac{\tau}{\frac{du}{dy}}\)` or slope of `\(\tau\)` vs `\(\frac{du}{dy}\)` ] ] .pull-right[ <img src="https://www.researchgate.net/profile/Claude-Vigneron-2/publication/13358433/figure/fig2/AS:771539007971333@1560960642865/Plot-of-whole-blood-viscosity-mPa-s-vs-shear-rate-s-1-determined-in-rabbit-blood.pbm " width="400" /> .foonote[gradient of velocity change changes (shear rate) with shear stress `$$S=\frac{du}{dy}$$` Functional significance? ] ] --- class: top # What Determines Viscosity? - **Temperature** - Concentration of dissolved (solutes) or suspended entities - Shear rate .center[ <img src="https://www.heatxperts.com/img/cms/1-viscosity-and-temperature.jpg" width="400" /> ] --- class: top # What Determines Viscosity? - **Temperature** - Concentration of dissolved (solutes) or suspended entities - Shear rate .center[ <img src="https://www.engineeringtoolbox.com/docs/documents/596/Water_viscosity_C.jpg" width="400" /> ] --- class: top # What Determines Viscosity? - Temperature - **Concentration of dissolved (solutes) or suspended entities** - Shear rate .center[ <img src="img/sugarblood.png" width="700" /> ] --- class: top # A coevolutionary process: Why do plants produce dilute nectars? .center[ <img src="img/butterflycoev.png" width="700" /> .footnote[Tom Daniel, UW] ] --- class: top # A coevolutionary process: Why do plants produce dilute nectars? .center[ <img src="https://www.researchgate.net/profile/Harald-Krenn/publication/49642863/figure/fig2/AS:268826830962692@1441104719219/A-Head-of-Eurybia-lycisca-SEM-with-coiled-proboscis-B-Proboscis-tip-with-four.png" width="700" /> ] --- class: top # A coevolutionary process: Why do plants produce dilute nectars? .center[ <img src="img/butterflyenergy.png" width="700" /> ] --- class: center, middle # Thanks! Slides created via the R package [**xaringan**](https://github.com/yihui/xaringan).