Viscosity of cooking oil: From kitchen to classroom

Technical Summary: Viscosity of Cooking Oil: From Kitchen to Classroom

Problem Statement
Fluid mechanics is a fundamental discipline often taught using abstract concepts or specialized laboratory equipment, which can create barriers for students lacking formal training in physics or mathematics. While "kitchen flows" offer a relatable context for understanding fluid dynamics, many existing kitchen-based experiments (e.g., analyzing pancake batter spreading or ketchup flow) rely on complex theoretical models and sophisticated data fitting techniques suitable primarily for university-level engineering students. There is a need for an accessible, tangible experiment that utilizes household tools to teach core physical principles—specifically friction, Newton's laws, and Archimedes' buoyancy—without requiring advanced mathematical backgrounds.

Methodology
The paper proposes a 90-minute classroom experiment designed for a general physics audience ("Physics for the public") at the University of Oslo. The experiment adapts the established "falling sphere viscometry" method, traditionally performed with steel balls and calibrated oils, to a kitchen setting using dried peas and rapeseed oil.

The experimental protocol involves the following steps:

1. Force Balance Theory: The experiment is grounded in the force balance equation for a sphere falling at terminal velocity ($a=0$). The forces considered are weight ($W$), buoyancy ($F_b$), and viscous drag ($F_d$). At terminal velocity, $W - F_b - F_d = 0$.
2. Stokes' Law Application: The drag force is modeled using Stokes' law ($F_d = 3\pi\mu U d$), allowing for the derivation of the oil's dynamic viscosity ($\mu$) based on measurable quantities:
   $$\mu_{oil} = \frac{(m_{pea} - \rho_{oil}V_{pea})g}{3\pi d_{pea}U_{pea}}$$
3. Data Collection: Students use household tools (kitchen scales, rulers, measuring cylinders, and smartphones for video recording) to measure:
   • Mass ($m_{pea}$) and volume ($V_{pea}$) of dried peas.
   • Density ($\rho_{oil}$) of the oil.
   • Diameter ($d_{pea}$) of the peas.
   • Sedimentation speed ($U_{pea}$) by timing the fall through a known distance.
4. Variable Geometry: To investigate fluid friction and wall effects, different student groups utilized measuring cylinders with varying diameters ($D_{cylinder}$ ranging from 11 mm to 27 mm).

Key Contributions

• Accessibility: The paper demonstrates that viscosity measurement can be performed using only common household ingredients (rapeseed oil, frozen peas) and tools, removing the need for specialized laboratory equipment like rheometers or calipers.
• Pedagogical Approach: The experiment fosters critical thinking by requiring students to determine sample sizes (how many peas to measure) and repeat measurements to reduce error, rather than simply following a rigid procedure.
• Conceptual Bridge: It effectively bridges the gap between abstract high school physics concepts (Newton's Second Law, Archimedes' Principle) and tangible observation.
• Analysis of Wall Effects: The study explicitly incorporates the analysis of "wall effects," where the proximity of cylinder walls increases drag on the falling object. The paper applies a correction factor ($K_p$) based on the fill ratio ($d_{pea}/D_{cylinder}$) to refine the viscosity calculation.

Results
The experiment was conducted with five student groups using cylinders of different diameters.

• Raw Data: The measured sedimentation speeds ($U_{pea}$) varied significantly across groups (1.90 to 7.91 cm/s), resulting in uncorrected viscosity values ($\mu_{oil}$) ranging from 102 to 865 mPa·s.
• Wall Effect Correction: The variation was primarily attributed to the cylinder diameter. Groups using narrower cylinders (e.g., 11 mm) observed significantly slower sedimentation due to increased drag. After applying the wall correction factor ($K_p$), the corrected viscosity values ($\mu'_{oil}$) ranged from 35 to 127 mPa·s.
• Comparison with Literature: The literature value for rapeseed oil viscosity at 20°C is approximately 73 mPa·s. The corrected experimental values (35–127 mPa·s) bracket this value, with Group 4 (20 mm cylinder) yielding 75 mPa·s, which is nearly identical to the literature value.
• Sources of Error: The paper identifies several sources of deviation, including:
  • Non-straight falling paths of the peas.
  • Air bubbles trapped on dry peas (increasing buoyancy).
  • Inertia effects: The Reynolds numbers ($Re$) for the experiment ranged from 0.8 to 11.7. Since Stokes' law strictly applies only when $Re < 1$, the paper notes that Oseen's correction for inertial effects would further improve accuracy for groups with higher $Re$.
  • Sample size: Statistical analysis suggests that measuring only 3–18 peas (as done by the groups) introduces significant sample mean error compared to the 100+ repeats recommended for stable averages.

Significance
The paper claims that the primary significance of this work is educational rather than metrological. It successfully creates a "fun and relatable" learning environment where students develop intuition for fluid mechanics without requiring formal training in advanced mathematics or physics. By engaging in the experimental design, data collection, and error analysis, students gain ownership of their learning and a deeper understanding of the physical forces governing fluid motion. The paper concludes that while the experimental setup is imperfect and prone to error compared to professional rheometry, it serves as an effective vehicle for teaching fundamental principles and fostering critical thinking in a general audience.