Fluid Dynamics and Interfacial Lab: Viscosity and Surface Tension
Investigate two core fluid properties: **Viscosity ($\eta$)**, the fluid's resistance to flow, and **Surface Tension ($\gamma$)**, the elastic tendency of a fluid surface. Study their critical dependence on **Temperature**.
Key Equations & Concepts
▼**Liquids:** Viscosity generally **decreases** as temperature increases (due to reduced intermolecular forces). **Gases:** Viscosity generally **increases** as temperature increases.
Surface Tension is the force per unit length ($\text{N/m}$) that acts on the surface of a liquid. It is caused by cohesive forces between liquid molecules. $$ \gamma = \frac{1}{2} r h \rho g $$ (Capillary Rise Formula - assuming contact angle $\theta \approx 0$).
Viscosity can be measured using Stokes' Law by observing a sphere falling through a fluid: $v_t = \frac{2 r^2 (\rho - \rho_0) g}{9 \eta}$.
Experiment 1: Viscosity and Temperature Simulation
Observe the fall time of a sphere and the corresponding viscosity as temperature changes.
Viscosity $\eta$ Decreases with Temperature (Liquids).
Experiment 2: Surface Tension ($\gamma$) Capillary Rise Challenge
Calculate Surface Tension ($\gamma$) using the Capillary Rise formula: $\gamma = \frac{1}{2} r h \rho g$.
The SI unit of viscosity is the **poiseuille** ($\text{Pa}\cdot\text{s}$). Often, the **centipoise** ($\text{cP}$) or **millipascal-second** ($\text{mPa}\cdot\text{s}$) is used for convenience (1 $\text{mPa}\cdot\text{s} = 1 \text{ cP}$).
Fluid Mechanics and Interfacial Phenomena
Adding soluble impurities (like common salt to water) generally **increases** surface tension, while adding insoluble impurities (like oil) or detergents generally **decreases** it.
In the viscosity experiment, the sphere reaches a constant maximum velocity called **terminal velocity** ($v_t$) when the viscous drag force balances the net gravitational force.
The **contact angle** is the angle between the tangent to the liquid surface and the surface of the solid inside the liquid. It determines whether a liquid will **wet** a surface (e.g., water on glass) or not (e.g., water on wax).
