Confectionery Rheology & Food Physics, IOCCC / ICA Casson Chocolate Flow Model
Casson Chocolate Yield Stress & Plastic Viscosity Formula
Calculate IOCCC Casson High-Shear Stress tau (Pa), Apparent Pumping Viscosity (Pa·s), Low-Shear 2 s⁻¹ Gravity-Drain Stress (Pa), and Low-Shear Coating Viscosity (Pa·s).
Adding 0.4% soy lecithin slashes chocolate yield stress by 66% without expensive cocoa butter—thinning biscuit enrobing shells on command!
Molten tempered chocolate (`40 °C` viscometry per **IOCCC / ICA Method 46**) is a concentrated suspension of hydrophilic sugar + cocoa solids in hydrophobic cocoa butter—exhibiting strong non-Newtonian shear-thinning governed by **N. Casson’s Square-Root Rheology Law**: **`SQRT(tau) = SQRT(tau_{CA}) + SQRT(eta_{CA} * gamma_dot)`**, or **`tau = (SQRT(tau_{CA}) + SQRT(eta_{CA} * gamma_dot))^2`** (`Pa`)! Confectionery engineers tune TWO independent knobs: **Casson Yield Stress `tau_{CA}`** (`Pa`—controls low-shear `~2 s⁻¹` gravity drainage, vertical enrobing curtain wall thickness, and air-bubble release in molded bars; dramatically lowered by `0.3%–0.5%` soy lecithin or `PGPR`!) vs **Casson Plastic Viscosity `eta_{CA}`** (`Pa·s`—controls high-shear `40 s⁻¹` pipe pumping pressure drop and spraying, lowered primarily by adding costly cocoa butter)!
Verify on a `55%` Dark Enrobing Couverture—Casson_Yield_Stress `tau_{CA}` = 12.50 Pa (B2), Casson_Plastic_Viscosity `eta_{CA}` = 1.85 Pa·s (B3), and ICA_Reference_Shear_Rate `gamma_dot` = 40.0 s⁻¹ (B4): High-Shear Stress hits `147.33` Pa (E2), `40 s⁻¹` Apparent Viscosity equals `3.683` Pa·s (E3), while `2.0 s⁻¹` Gravity-Curtain Stress equals `29.80` Pa (E4 = `14.90` Pa·s low-shear viscosity in E5)! Note for R&D teams collaborating on cloud recipe workbooks: while external OAuth review via the Arte Sheets ChatGPT plugin `0.1.0` (currently `In review` / `Not published`) uses atomic `apply_changes` (`<= 100` cells, `0` Arte AI credits consumed by MCP calls) with `pendingReview` protection on concurrent edits, in-app Pro Assistant hints draw from metered monthly Arte AI credits—and ChatGPT subscription credits never transfer between the two.
| ICA Casson Chocolate Rheology KPI (gamma=40 s⁻¹: Un-Lecithinated 12.5 Pa vs +0.4% Lecithin 4.2 Pa) | Formula | Verified Output |
|---|---|---|
| High-Shear Stress tau (Pa) | (SQRT(tau_CA) + SQRT(eta_CA * gamma)) ^ 2 | 147.33 Pa (103.50 Pa @ +0.4% lecithin) |
| Apparent Viscosity @ gamma (Pa·s) | High_Shear_Stress_Pa / Shear_Rate_inv_s | 3.683 Pa·s (2.587 Pa·s @ +0.4% lecithin) |
| Gravity-Drain Stress @ 2 s⁻¹ (Pa) | (SQRT(tau_CA) + SQRT(eta_CA * 2)) ^ 2 | 29.80 Pa (14.95 Pa = -50% thinner coat!) |
| Low-Shear Viscosity @ 2 s⁻¹ (Pa·s) | Gravity_Drain_Stress_2s_Pa / 2 | 14.90 Pa·s (7.47 Pa·s crisp biscuit shell!) |
IOCCC / ICA Casson Square-Root Constitutive Viscometry Formula
Validate `Casson_Yield tau_{CA}` in `[0.1, 80.0]` Pa, `Casson_Plastic_Viscosity eta_{CA}` in `[0.2, 15.0]` Pa·s, and `Shear_Rate gamma_dot` in `[1.0, 200.0]` s⁻¹!
=LET(tc_p, B2, ec_p, B3, gd_s, B4, tl_p, (SQRT(tc_p) + SQRT(ec_p * 2)) ^ 2, IF(OR(tc_p < 0.1, tc_p > 80, ec_p < 0.2, ec_p > 15, gd_s < 1, gd_s > 200), "Invalid Casson Input", ROUND(tl_p / 2, 2)))0.4% Soy Lecithin Addition (tau_CA = 4.2 Pa, eta_CA = 1.65 Pa·s) Thin-Shell Enrobing Check
Dose `0.4%` soy lecithin at the end of conching (`tau_{CA}` B2 = 4.2 Pa, `eta_{CA}` B3 = 1.65 Pa·s): `40 s⁻¹` Pumping Viscosity E3 drops `-30%` to `2.587` Pa·s, while `2 s⁻¹` Gravity-Drain Viscosity E5 **halves from `14.90` down to `7.47` Pa·s**—draining excess couverture off wafer bars without adding a single gram of cocoa butter!
=IF(ISTEXT(E5), E5, LET(th_p, (SQRT(B2) + SQRT(B3 * B4)) ^ 2, ROUND(th_p / B4, 3)))Try the example
Use the original values or change them to test your understanding.