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T7 · Transport / BarrierMedical Plastics & BiocompatibilityGATE 2027 Syllabus (XE5)
Higuchi Model for Fickian Drug Release from Polymeric Matrices
Classical square-root-of-time kinetic relation describing diffusion-controlled drug release from planar non-degradable polymeric matrices (EVA, PDMS, PMMA).
Mathematical Canonical Relation
Plain Formula: Mt = A * sqrt(D * (2*C0 - Cs) * Cs * t)
Live Engineering Parameter Solver
Input your production or test values below for instant, verified output.
Verified Engine
C0_val
Range: 10 – 150 mg/cm³
Cs_val
Range: 0.2 – 10 mg/cm³
A_val
Range: 0.5 – 10 cm²
t_hours
Range: 1 – 168 hours
Calculated Engineering Result:
0.823 mg total released
Engineering Verification:Release flux is 0.412 mg/cm².
When & Where to Apply
Use when modeling transdermal patches, contraceptive implants, or biomedical stent coatings where drug release is governed by Fickian matrix diffusion.
Common Engineering Pitfalls
- Applying the Higuchi model to biodegradable polymers undergoing surface erosion
- Forgetting that release fraction plotted against sqrt(t) must yield a straight line passing through the origin
Physical Assumptions & Validity Limits
- Initial drug loading C0 is much greater than drug solubility Cs in matrix (C0 >> Cs)
- Pseudo-steady state diffusion with planar one-dimensional release geometry
- Constant diffusion coefficient D without polymer matrix swelling or dissolution
Variable Symbols, SI Units & Dimensional Specifications
| Symbol | Variable Meaning | SI Unit | Typical Industrial Range |
|---|---|---|---|
| M_t / A | Cumulative drug released per unit surface area | mg/cm² | — |
| C_0 | Initial drug concentration in polymer matrix | mg/cm³ | 50.0 |
| C_s | Drug saturation solubility in polymer matrix | mg/cm³ | 2.5 |
| D | Drug diffusion coefficient in polymer matrix | cm²/s | 1.2e-8 |
| t | Release time duration | hours | 24 |
Worked Industrial Numerical Example: Silicone PDMS Subdermal Implant Drug Release
Problem Statement:
A planar silicone implant with area A = 2.0 cm² contains initial drug load C0 = 50 mg/cm³ and solubility Cs = 2.0 mg/cm³. Diffusion coefficient D = 1.0 × 10^-8 cm²/s. Calculate cumulative drug released after 24 hours (86,400 s).
Step-by-Step Numerical Solution:
- Calculate term (2*C0 - Cs) * Cs: (100 - 2) * 2 = 98 * 2 = 196 mg²/cm^6
- Multiply by D * t: 1.0e-8 * 86,400 * 196 = 8.64e-4 * 196 = 0.1693 mg²/cm^4
- Take square root: sqrt(0.1693) = 0.4115 mg/cm²
- Multiply by area A = 2.0 cm²: Mt = 2.0 * 0.4115 = 0.823 mg
Final Answer: Mt = 0.823 mg released in 24 hours
💡 Engineering Interpretation: The square-root-of-time dependence delivers 0.82 mg in the first 24 hours. Release rate gradually decreases as the depletion boundary recedes into the polymeric matrix.
Authoritative Technical Reference & Source Provenance
Mechanism of Sustained-Action Medication: Theoretical Analysis of Rate of Release of Solid Drugs Dispersed in Solid Matrices by Takeru Higuchi (J. Pharm. Sci., 1963), Vol 52, Page 1145-1149.
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