Evidence Observatory | Tribology
A formulation is more than its viscosity.
Explore the forces behind the comparison.
A development team can match two liquids at one rheometer setting and still need to understand how their interfaces behave during use.
The valuable question is experimental: which measurements would separate a rheological difference from a change in load, speed or contact? This explorer gives that question a concrete starting point, through an external finger-pad spreading dataset.
These are published observations and a reproducible local comparison. They do not demonstrate the performance of a VARUNÉ Bio ingredient. Our proposed use is to help define a formulation study before promising a sensory outcome.
Published observations | Local secondary analysis
Move between viscosity and Hersey. Each dot remains the same trial median; its horizontal position changes to include speed, force, rheology and contact geometry.
R² | descriptive in-sample fit
Original friction scale · 77 trial medians
Viscosity alone groups each liquid at one horizontal position. Between-person speed and load differences remain outside that comparison.
Showing 77 trial medians | 7 highest-viscosity liquids | 11 participants.
Horizontal: reference viscosity at 500 s⁻¹ (Pa s). Vertical: coefficient of friction μ (dimensionless). Both axes use logarithmic display.
Select a dot or focus it with the keyboard. See the coded participant, liquid and measured trial medians behind its position.
Both views use the same 77-observation fit population. The checkbox changes the visible dots, never the reference fit or its R². Both axes are logarithmic for display; the fit minimises unweighted squared residuals on the original μ scale. No confidence interval or predictive validation is supplied.
| Participant | Liquid | Speed m s⁻¹ | Force N | Viscosity Pa s | Hersey | Friction μ | Fit? |
|---|
Source: Fehlberg et al. (2025), A Touch of Stribeck. Original dataset, CC BY 4.0. Download all 165 processed trial medians (CSV). Secondary calculation checked 2026-10-14.
The physical question
In this source experiment, eleven participants spread fifteen liquids on a rough solid substrate. The analysis retains one median for each participant–liquid trial. The seven highest-viscosity liquids supply the fitted branch (Fehlberg et al., 2025).
The viscosity view supplies one controlled comparison: the horizontal position belongs to the liquid at a reference shear rate. In the Hersey view, the position also depends on how that trial was performed. Moving the dots exposes that change without inventing any measurements.
A clearer alignment changes the next research question. It does not establish a validated prediction. A formulation decision still needs controlled measurements under relevant application conditions, with the comparison and acceptance criterion set before results are examined.
Each trial contributes its measured median speed and normal force. The liquid contributes consistency and flow index; the model also requires estimated contact geometry.
Model conditions. R and Rₛ are common estimates, not participant-specific measurements in this calculation. The model incorporates shear thinning but does not explicitly include the skin modulus. It is a contact/lubrication comparison, not an absorption model.
Equation and estimated radii: Fehlberg et al. (2025), Eq. 2.
A relevant contact. A defined application window. Measurements that can change a formulation decision.
Rheology and units
Viscosity is expressed in Pa s at 500 s⁻¹. K carries Pa sⁿ; n is dimensionless. The friction export stores n−1; processing adds one before evaluating Hersey. The parameter-file unit header is inconsistent with the friction file and paper; the friction-file SI consistency values are retained unchanged.
A viscosity evaluated at one rate should not quietly become a constant for a shear-thinning liquid. Geometry matters too: ηv/Fₙ alone has inverse-length dimensions. With n=1, the authors’ expression becomes ηvR²/(FₙRₛ); both radii remain essential.
For an ingredient partner, the practical discussion concerns the shear-rate window and application conditions the material must serve. A development brief should specify that window, the comparator, substrate and required measurement repeatability.
The viscosity-only view evaluates every liquid at the same reference shear rate. For n=1 viscosity is constant in this power-law description; n<1 gives shear thinning.
Model conditions. 500 s⁻¹ is the source study’s reference estimate, not a directly measured shear rate for every trial. A power-law approximation is used within its experimental context.
Reproducible secondary analysis
The local fit yields R² 0.372 for viscosity and 0.889 for Hersey, against the original friction values. The publication reports approximately 37% and 89% variance explained. Its Hersey exponent is 0.55; the local nonlinear reproduction gives 0.563. That difference remains visible.
The line stays within the fitted subset’s observed horizontal range. Revealing all fifteen liquids exposes the wider comparison but does not extend the power law across the entire Stribeck curve. Highlighting one participant or liquid retains the reference context and does not fit a new line.
Repeated trials across the same participants and recipes create dependence. Seventy-seven observations are not seventy-seven independent people. This is a descriptive fit, not a population effect estimate, causal test, out-of-sample score or uncertainty interval.
The fitted set ℱ contains the same 77 trial medians in both comparisons. x is reference viscosity or Hersey. Residuals are measured on the original friction scale; logarithmic axes only change the display.
Model conditions. Unweighted nonlinear least squares. Amplitude is solved analytically at each exponent; b is searched within [−1, 2]. No clustering correction, confidence band or held-out predictive validation is calculated.
A proposed VARUNÉ Bio study
Select a substrate, contact geometry, preparation and conditioning protocol relevant to the intended material use. Record roughness, hydration and temperature where they could affect the comparison. Begin with inert test surfaces before proposing a human study.
Choose a speed–load matrix and rheological measurements before comparing candidates. Include the base formulation, a matched comparator and independently prepared replicates. Randomise measurement order and document sample history rather than treating every repeated trace as an independent specimen.
Predefine the friction summary, instrument checks, exclusions and uncertainty calculation. Evaluate any follow-on model on held-out preparations or relevant contact conditions; address participant clustering if people are later involved. This is a proposed validation design, not a result supplied here.
Agree which difference would justify changing material concentration, rheology or the application brief. Compare the value of that information with development time, sample supply and measurement cost. An exploratory study needs a separately scoped deliverable and acceptance criteria.
What the data cannot answer
This dataset does not measure skin penetration, absorption, drying, cream disappearance or shelf life. It establishes no sensory benefit for a Bio material. Those questions need their own outcomes, methods and controls.
This explorer does not reconstruct within-trial time series, participant-specific contact radii or uncertainty bars from trial medians. Geometry is a model assumption. A future sensitivity analysis could ask whether a conclusion survives plausible geometry changes, but must be calculated and reviewed before being shown as evidence.
The immediate value for a formulation team is a sharper conversation: where does its current specification stop, which additional measurement could change a decision, and what would count as a useful negative result?
Discuss a defined formulation questionAttribution and audit trail
Fehlberg, M., Schmidt, D.S., Saikumar, S., Cavdan, M., Drewing, K. and Bennewitz, R. (2025) ‘A Touch of Stribeck – Finger-Pad Friction in Viscous Liquid Spreading’, Tribology Letters, 73, 91. doi:10.1007/s11249-025-02024-w.
Fehlberg et al. (2025) Data set for manuscript “A Touch of Stribeck – Finger-Pad Friction in Viscous Liquid Spreading”. Zenodo. doi:10.5281/zenodo.15365365. Dataset: CC BY 4.0; accessed 14 October 2026.
Changes: source trial medians were structured as a table; apparent viscosity and Hersey were recomputed in SI units with the stated geometry; both fixed-subset power fits were calculated locally. Source repository checksums, CSV row count and derived fields were checked. This presentation is secondary analysis; no endorsement by the original authors is implied.
Download the processed CSV · Inspect the original exports · Return to the Evidence Observatory
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