B0 Experimental Dataset: Rodenborn et al. (2013)#

Status: Confirmed as primary B0 dataset.

Citation#

[@Rodenborn2013] Rodenborn, B., Chen, C.-H., Swinney, H.L., Liu, B., & Zhang, H.P. (2013). Propulsion of microorganisms by a helical flagellum. PNAS, 110(5), E338–E347.

Why This Dataset#

Rodenborn et al. provides:

  1. Experimental measurements of thrust, torque, and drag for helical swimmers

  2. Published simulation codes (regularised Stokeslet method) for comparison

  3. Parameter documentation sufficient for simulation reproduction

  4. Definitive evidence that RFT is insufficient (helix radius ~ wavelength)

  5. Data across the parameter ranges relevant to microrobotics

Robot Parameters#

Parameter

Value

Units

Source

Helix wavelength (lambda)

2.08–6.25

mm

Table 1

Helix amplitude (A)

0.5–2.5

mm

Table 1

Filament radius (r_f)

0.4

mm

Methods

Number of wavelengths

1–4

-

Table 1

Rotation rate

0.01–1.0

rev/s

Methods

Note: These are macro-scale experiments (mm-scale) in high-viscosity silicone oil, designed to match the low-Re regime of microrobots. The Reynolds number is Re << 1, matching our target regime.

Fluid Properties#

Parameter

Value

Units

Fluid

Silicone oil

-

Viscosity

1.0

Pa.s

Density

971

kg/m^3

Validation Approach for B0#

  1. Configure RigidBodyNode with helical resistance tensor matching one of Rodenborn’s geometries

  2. Apply known rotation rate via ExternalMagneticFieldNode

  3. Compare simulated thrust and drag against Table 1 measurements

  4. Pass criterion: position RMSE < 15% of channel diameter, velocity RMSE < 20% of mean velocity

Simulation Codes#

The Rodenborn et al. regularised Stokeslet simulation codes are publicly available on MATLAB File Exchange (“Helical Swimming Simulator”). These serve as the high-fidelity reference for B1 (step-out frequency within ±5%).

Scaling to Microrobot Parameters#

The experimental data is in the low-Re regime and thus dynamically similar to a microrobot in CSF. To map to MIME’s default parameters:

  • Scale lengths by the ratio of characteristic sizes

  • Viscosity and density use CSF values (mu = 8.5e-4 Pa.s, rho = 1002 kg/m^3)

  • The Re matching ensures the same Oberbeck-Stechert coefficients apply