Diffusion in glycerol–water mixtures

Stokes–Einstein diffusion of a spherical particle, with solvent viscosity predicted from glycerol concentration (fit to Takamura et al., 2012). Set the glycerol content, a viscosity, or a target diffusion coefficient — the other two follow. Imaging parameters translate D into displacements on your camera.

Physical parameters

Hydrodynamic diameter

Temperature

°C

These three are linked. Edit any one; the field you edited last stays fixed when you change size or temperature.

Glycerol fixed

% w/w

Dynamic viscosity fixed

mPa·s (cP)

Diffusion coefficient fixed

µm²/s

Make a solution

g total

Imaging parameters

Frame interval

Exposure time

Pixel size (sample plane)

µm/px

Tracking dimensionality

Diffusion coefficient

–µm²/s

RMS step per frame
RMS step per axis √(2DΔt)
Motion blur during exposure
Time to diffuse 1 pixel (RMS)
Longest frame interval for RMS step ≤ px

Viscosity of aqueous glycerol

Model, data & assumptions

Stokes–Einstein: D = k_BT / (3πηd), with d the hydrodynamic diameter. Mean-squared displacement in n dimensions: ⟨r²⟩ = 2nDΔt.

Viscosity at 20 °C (fit to Takamura et al. 2012, Table 10, zero salinity), with x the glycerol mass fraction:
η₂₀(x) = η_w · exp[(Ax + Bx²) / (1 + Cx)], η_w = 1.002 mPa·s, A = 2.5139, B = 0.0712, C = −0.6208.

Temperature: the Takamura data are at 20 °C only. For other temperatures the 20 °C fit is scaled by the ratio η(T, x)/η(20 °C, x) from the Cheng (2008) correlation (Ind. Eng. Chem. Res. 47, 3285). At 20 °C the factor is exactly 1.

Range: data span 0–91 % w/w. Above that the fit is an extrapolation and underestimates viscosity (it gives ~916 mPa·s for pure glycerol; the measured value is ~1410 mPa·s at 20 °C).

Glycerol (% w/w)	Measured η (mPa·s)	Fit η (mPa·s)

Glycerol volume in the recipe uses ρ = 1.261 g/mL and water ρ = 0.998 g/mL (20 °C). Weigh glycerol when you can: it is too viscous to pipette accurately.