# Formula: lever rule

Parent: — · class: mixing and phase equilibria · names as written: lever rule

4 instances in 4 papers (of 207 kept papers). Each section heading ends with the paper's category / subcategory. Generated by tools/build_evidence.py from registry/formulas.csv; do not edit.

## 2022 Yang · E1 · lever rule · Solid state stability / Physical stability

[2022-yang-surfactant-containing-rtv-pvpva-asd-phase-separation](../../../cards/2022-yang-surfactant-containing-rtv-pvpva-asd-phase-separation/paper.html) · Solid state stability / Physical stability

- expression: ratio of the amount of phase A to phase B equals the ratio of the length BX to AX
- symbols and units: X overall composition in the two-phase region; A, B coexisting phase compositions joined by a tie line; lengths on the ternary diagram
- assumptions stated: thermodynamic equilibrium; compositions connected by a tie line
- used for: C50 (schematic; no record)
- status: printed in words · recomputed: inputs not printed
- locator: §5.3, p.13; Fig. 11, p.14

## 2023 Deac · E5 · lever rule · Dissolution / A. Release mechanism and LoC

[2023-deac-asd-drug-load-molecular-interactions-loc](../../../cards/2023-deac-asd-drug-load-molecular-interactions-loc/paper.html) · Dissolution / A. Release mechanism and LoC

- expression: 
- symbols and units: phase amounts from the distances of the overall composition to the two binodes on a tie line
- assumptions stated: complete phase separation to the binodal compositions immediately on entering the unstable region (C35)
- used for: C34, C36 (argument only)
- status: named only · recomputed: named only
- locator: p.730, p.731, p.733

## 2023 Yang · E2 · lever rule · Dissolution / A. Release mechanism and LoC

[2023-yang-surfactant-containing-asd-release-enhancement](../../../cards/2023-yang-surfactant-containing-asd-release-enhancement/paper.html) · Dissolution / A. Release mechanism and LoC

- expression: (amount of drug-rich phase) / (amount of polymer/water-rich phase) = (length P1X1) / (length D1X1)
- symbols and units: X1 overall composition where AAPS starts; P1 polymer/water-rich and D1 drug-rich coexisting compositions on the binodal, joined by a tie line
- assumptions stated: two phases at thermodynamic equilibrium on the binodal; phase separation only below the vitrification line
- used for: none (schematic argument for C41–C43)
- status: printed in words · recomputed: inputs not printed (schematic diagram only)
- locator: Discussion, p.2839; Fig. 15, p.2841

## 2024 Deac · E12 · lever rule · Dissolution / A. Release mechanism and LoC

[2024-deac-asd-ternary-phase-diagrams-release](../../../cards/2024-deac-asd-ternary-phase-diagrams-release/paper.html) · Dissolution / A. Release mechanism and LoC

- expression: W^α = m^α/m^T = (W_i^T − W_i^β)/(W_i^α − W_i^β)
- symbols and units: m mass; W mass fraction; T total; α hydrophobic phase; β hydrophilic phase; i any component
- assumptions stated: onset of phase separation at the spinodal; phases in local equilibrium immediately; phase inversion at W^α = 0.5
- used for: R35
- status: printed, checked against page image · recomputed: inputs not printed (spinodal and binode compositions behind Fig. 16 not tabulated; Table S1 check in X3)
- locator: p.1914