# Formula: boundary-layer diffusion flux (film model)

Parent: Fick's first law · class: transport, diffusion and dissolution · names as written: boundary-layer diffusion flux (Fick's first law form); boundary-layer diffusion flux (film model); diffusion-controlled flux across a boundary layer (film model); steady-state diffusion across the UWL

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.

## 2021 Hate · E6 · steady-state diffusion across the UWL · Bioperformance / Bioperformance

[2021-hate-drug-mass-transport-supersaturated-pampa-membranes](../../../cards/2021-hate-drug-mass-transport-supersaturated-pampa-membranes/paper.html) · Bioperformance / Bioperformance

- expression: Cb − Cm1 = (J × dUWL)/D
- symbols and units: Cb bulk donor concentration; Cm1 aqueous concentration at the UWL-membrane interface, donor side; J overall mass flow rate; dUWL UWL thickness; D solute diffusion coefficient
- assumptions stated: steady state: mass flow across UWL equals mass flow across membrane (ref 61)
- used for: R19
- status: printed, checked against page image · recomputed: inputs not printed (dUWL and D not given)
- locator: p.112

## 2023 Bapat · E2 · diffusion-controlled flux across a boundary layer (film model) · Dissolution / A. Release mechanism and LoC

[2023-bapat-hpmcas-asd-media-choice-buffer-capacity-release](../../../cards/2023-bapat-hpmcas-asd-media-choice-buffer-capacity-release/paper.html) · Dissolution / A. Release mechanism and LoC

- expression: J_p = (D_p/δ) C_p
- symbols and units: J_p polymer flux; D_p polymer diffusion coefficient; C_p polymer solubility at the polymer-solution interface; δ boundary-layer thickness
- assumptions stated: diffusion-controlled regime; rotating disc under laminar flow (refs 51, 66)
- used for: R5, R16, R18
- status: printed, checked against page image · recomputed: inputs not printed (D_p, C_p)
- locator: p.5723

## 2024 Bapat · E3 · boundary-layer diffusion flux (Fick's first law form) · Dissolution / A. Release mechanism and LoC

[2024-bapat-hpmcas-drug-polymer-complexation-release-performance](../../../cards/2024-bapat-hpmcas-drug-polymer-complexation-release-performance/paper.html) · Dissolution / A. Release mechanism and LoC

- expression: J_p = (D_p/δ) C_p
- symbols and units: J_p polymer flux; D_p polymer diffusion coefficient; C_p polymer solubility at the polymer-solution interface; δ boundary layer thickness
- assumptions stated: rate-limiting step of HPMCAS dissolution is polymer solubility at the gel-solution interface (postulated, ref 46)
- used for: R14 (through C32)
- status: printed, checked against page image · recomputed: inputs not printed
- locator: p.1474

## 2025 Kaur · E1 · boundary-layer diffusion flux (film model) · Dissolution / A. Release mechanism and LoC

[2025-kaur-bdq-hpmcas-complexation-media-asd-release](../../../cards/2025-kaur-bdq-hpmcas-complexation-media-asd-release/paper.html) · Dissolution / A. Release mechanism and LoC

- expression: J_p = (D_p/δ) C_p
- symbols and units: J_p polymer flux across the aqueous boundary layer; D_p polymer diffusion coefficient; C_p polymer solubility at the polymer-solution interface; δ boundary layer thickness; units not printed
- assumptions stated: release is polymer-controlled; polymer dissolution rate equals this flux
- used for: C41, C42, C44 (no record computed with it)
- status: printed, checked against page image · recomputed: inputs not printed
- locator: Eq. 1, p.10