diff --git a/docs/index.md b/docs/index.md index b487918..991bfcd 100644 --- a/docs/index.md +++ b/docs/index.md @@ -120,9 +120,11 @@ rheofit install-skill New here? Read the **[Carbopol case study](walkthrough)** — a complete, reproducible head-to-head of the TC model against Herschel–Bulkley on real data, run the way the skill -runs it. Then see the **[wormlike-micelle + polymer case study](walkthrough-carreau-carreau)**, -where the microstructure-informed `carreau_carreau` model resolves two relaxation times across -a temperature series. And don't miss the **[polymer solution case study](walkthrough-carreau)**, +runs it. Then see the **[Carbopol-in-glycerin walkthrough](walkthrough-carbopol-glycerin)**, +which shows how a viscous continuous phase changes the reading of HB and TC parameters. Then +see the **[wormlike-micelle + polymer case study](walkthrough-carreau-carreau)**, where the +microstructure-informed `carreau_carreau` model resolves two relaxation times across a +temperature series. And don't miss the **[polymer solution case study](walkthrough-carreau)**, where a Carreau fit meets the Cox–Merz and Delaware–Rutgers rules on amplitude, flow, and frequency sweeps. Then browse the **[API reference](api)**. @@ -147,6 +149,7 @@ bottom of the page. :caption: Case studies walkthrough +walkthrough-carbopol-glycerin walkthrough-carreau-carreau walkthrough-carreau ``` diff --git a/docs/walkthrough-carbopol-glycerin.md b/docs/walkthrough-carbopol-glycerin.md new file mode 100644 index 0000000..6244607 --- /dev/null +++ b/docs/walkthrough-carbopol-glycerin.md @@ -0,0 +1,154 @@ +# 🧪 Walkthrough: Herschel–Bulkley and TC fits for 2% Carbopol in glycerin + +*A viscous continuous phase changes what the flow curve means. This walkthrough uses a +single 20 °C flow sweep of **2% Carbopol in glycerin** to show, step by step, what you +learn from a classical Herschel–Bulkley fit and what you gain when you also fit the +physically split TC model.* + +## 🧾 The sample data + +The TRIOS JSON for this example is archived in the docs as +`walkthrough/cp02_gly_20c_fc.json` (added from [issue #27](https://github.com/rheopy/rheofit/issues/27)). +It contains one equilibrium flow sweep: + +| # | Step | Range | Points | Temperature | +|---|------|-------|--------|-------------| +| 0 | Flow sweep - 1 | 0.001 → 100 1/s | 51 | 20 °C | + +This is a useful teaching sample because Carbopol contributes a yield-stress microgel +network, while glycerin raises the continuous-phase viscosity enough that the high-shear +tail is no longer a small correction. + +## 1. Load and process the sample + +Start with step discovery, then load the single flow-curve step: + +```python +import rheofit + +rheofit.print_steps("walkthrough/cp02_gly_20c_fc.json") +df = rheofit.load_step("walkthrough/cp02_gly_20c_fc.json", 0) +``` + +`load_step()` standardizes the TRIOS column names to the ones used throughout `rheofit`: + +- `Shear rate / 1/s` +- `Stress / Pa` +- `Viscosity / Pa.s` + +For this file the detected `test_type` is `flow_curve`, all 51 rows are usable, and no +points are dropped during fitting. + +## 2. Fit Herschel–Bulkley (HB) + +The [Herschel–Bulkley model](models/herschel_bulkley) + +$$\sigma = \sigma_y + K \dot{\gamma}^n$$ + +is the standard engineering baseline for a structured material with yield stress and +power-law flow above yield. + +```python +hb = rheofit.fit(df, "herschel_bulkley", effort="thorough", seed=0) +``` + +| Parameter | Value | Rel. error | Reading | +|---|---:|---:|---| +| σ_y | 0.674 Pa | 2.0 % | small fitted yield offset | +| K | 13.65 Pa·sⁿ | 0.9 % | consistency of the post-yield curve | +| n | 0.713 | 0.5 % | comparatively shallow high-shear thinning | + +**RedChi² = 1.83×10⁻³**, with no fit warnings. + +### How to read the HB result + +- The fit is clean and numerically strong. +- The fitted yield stress is **small** compared with the total stress over most of the + measured window. +- The exponent **n ≈ 0.71** is doing a lot of work: it is not just describing Carbopol's + yielding, it is also compensating for the viscous glycerin-rich background. + +That is the HB trade-off on this sample: one exponent must absorb several physical effects. + +## 3. Fit TC + +The [TC model](models/tc) + +$$\sigma = \sigma_y + \sigma_y\sqrt{\dot{\gamma}/\dot{\gamma}_c} + \eta_{bg}\dot{\gamma}$$ + +separates the response into elastic, plastic, and viscous contributions. + +```python +tc = rheofit.fit(df, "tc", effort="thorough", seed=0) +``` + +| Parameter | Value | Rel. error | Reading | +|---|---:|---:|---| +| σ_y | 0.376 Pa | 5.6 % | elastic yield plateau | +| γ̇_c | 1.82×10⁻³ 1/s | 14.9 % | onset scale for the plastic √γ̇ term | +| η_bg | 3.71 Pa·s | 2.7 % | viscous background from the continuous phase | + +**RedChi² = 3.55×10⁻³**, with no fit warnings. + +### How to read the TC result + +- The fit is still good, though not quite as close as HB on this dataset. +- The key payoff is **η_bg = 3.71 Pa·s**: the model gives the viscous background its own + parameter instead of hiding it inside an empirical exponent. +- In this sample the viscous term is already comparable to the elastic term by + **γ̇ ≈ 0.10 1/s**, exceeds the plastic term by **γ̇ ≈ 5.7 1/s**, carries about + **57 %** of the stress at **10 1/s**, and about **81 %** at **100 1/s**. + +That is exactly the signature of a yield-stress fluid with a strongly viscous continuous phase. + +## 4. Compare the two fits + +| model | RedChi² | main message | +|---|---:|---| +| Herschel–Bulkley | **1.83×10⁻³** | best empirical description of the whole curve | +| TC | 3.55×10⁻³ | explicit elastic / plastic / viscous split | + +![HB and TC fits on the 2% Carbopol in glycerin flow curve, with relative residuals](walkthrough/fig11_cp02_gly_tc_vs_hb.png) + +HB wins slightly on relative error, but the residual comparison is only part of the story. +For formulation work, TC exposes the parameter that matters most here: the continuous-phase +viscosity contribution. + +## 5. Interpret the TC decomposition + +![TC decomposition of the 2% Carbopol in glycerin flow curve into elastic, plastic, and viscous terms](walkthrough/fig12_cp02_gly_tc_decomposition.png) + +The TC terms show how the balance changes across the sweep: + +- **Low shear**: the response is mostly elastic + plastic, so the sample still behaves like a + structured Carbopol gel. +- **Intermediate shear**: the plastic term dominates as the microgel network rearranges. +- **High shear**: the **η_bg γ̇** term takes over, which is the glycerin-rich continuous phase + making itself felt directly in the stress. + +This is the practical difference between the models: HB says *what the curve looks like*, +while TC says *which mechanism is carrying the stress*. + +## 6. Why the viscous continuous phase matters + +This sample is a good reminder that a yield-stress material is not defined by its low-shear +plateau alone. Once the continuous phase is viscous enough, the high-shear branch contains +important extra physics: + +- In **HB**, that physics is folded into **K** and especially **n**. +- In **TC**, it is assigned to **η_bg**, which is much easier to connect back to formulation. + +So if the question is *"Which model reproduces the curve best with three parameters?"*, +HB is slightly better here. But if the question is *"How much of the stress at useful +processing rates is coming from the background liquid?"*, TC is the more revealing model. + +## 🎯 Takeaways + +- `walkthrough/cp02_gly_20c_fc.json` is a compact reference example for a **yield-stress + fluid with a viscous continuous phase**. +- **HB** gives the tighter overall fit on this sweep, but its exponent is an empirical + compromise across yielding and viscous dissipation. +- **TC** gives a slightly looser fit, but it isolates the physically important background + viscosity: **η_bg ≈ 3.71 Pa·s**. +- For this sample, the viscous term becomes dominant within the measured window, so any + interpretation that ignores the continuous phase will miss part of the material story. diff --git a/docs/walkthrough/cp02_gly_20c_fc.json b/docs/walkthrough/cp02_gly_20c_fc.json new file mode 100644 index 0000000..634b0c7 --- /dev/null +++ b/docs/walkthrough/cp02_gly_20c_fc.json @@ -0,0 +1,2826 @@ +{ + "Schema": { + "Url": 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"Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0030002593994, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.000280185369774699 + }, + { + "Displacement_rad": 0.0113482996821404, + "Axial force_N": -0.0221467334777117, + "Gap_\u00b5m": 45.0236002507154, + "Torque_\u00b5N.m": 18.0502065632027, + "Step time_s": 1846.31384277344, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0041007995605, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.000222544171265326 + }, + { + "Displacement_rad": 0.00903258007019758, + "Axial force_N": -0.0225283000618219, + "Gap_\u00b5m": 45.0371007900685, + "Torque_\u00b5N.m": 16.8516962730791, + "Step time_s": 1897.38916015625, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0069007873535, + "Procedure Step 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