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Abstract
An experimental and theoretical methodology is proposed to calculate the permeability of microcapsules that contain a core of oil-based active ingredient. Theoretical analysis is performed considering the polydispersity of the measurable capsule size, which allows the estimation of the permeability polydispersity via three different methods. The models proposed were applied in order to determine the permeability of melamine-formaldehyde microcapsules with hexyl salicylate as core oil. Release experiments were performed with four different co-solvents (ethanol, propan-1-ol, propan-2-ol and 1,3-butanediol) of different concentration. Permeability values were found to be constant, despite a two order magnitude of difference in the solubility concentrations.
Nomenclature
| Acaps: | = | surface area of the capsule(s) (m2) |
| cin: | = | oil concentration in the solvent inside the capsule(s) (g mL−1) |
| cin(s): | = | oil concentration in the inner side of the shell(s) (g mL−1) |
| cout: | = | oil concentration in the solvent outside the capsule(s) (g mL−1) |
| cout(s): | = | oil concentration in the outer side of the shell(s) (g mL−1) |
| cmax(k): | = | maximum cout for a microcapsule size d(k) (g mL−1) |
| cs: | = | solubility concentration (g mL−1) |
| CDF: | = | cumulative distribution function of the diameter |
| = | capsule diameter (m) | |
| = | arithmetic mean diameter of the size interval d(k) to d(k + 1) | |
| = | antilogarithm of | |
| = | lognormal mean of the size distribution (log(µm)) | |
| D: | = | diffusivity of the oil in the shell (m2 s−1) |
| Dwater: | = | diffusivity of the oil in water (m2 s−1) |
| D4,3: | = | volume moment mean capsule diameter (m) |
| h: | = | shell thickness (m) |
| J: | = | Mass flux through the capsule(s) shell, g m mL−1 s−1 (≡106 g m−2 s−1) |
| k: | = | grid point of microcapsule diameter |
| K: | = | partition coefficient |
| Ncaps: | = | number of capsules in a release experiment |
| Nint: | = | number of size intervals |
| P: | = | permeability (m2 s−1) |
| P/h: | = | permeability to thickness ratio (m s−1) |
| (P/h)max and (P/h)min: | = | maximum and minimum P/h calculated at R < 0.6 (m s−1) |
| = | mean permeability thickness ratio (m s−1) | |
| = | two | |
| = | mean permeability to thickness ratio using two P/h populations (m s−1) | |
| PDF: | = | probability density function of the diameter (m−1) |
| R: | = | relative release |
| dR/dt: | = | slope of the linear increase of R with time (s−1) |
| (dR/dt)max and (dR/dt)min: | = | initial and final R slope within the linear regime (R < 0.6) (s−1) |
| RLin-Exp: | = | value of R at the limit of the linear regime |
| t: | = | release time (s) |
| tend: | = | time of complete release (s) |
| Vsolvent: | = | volume of solvent used in a release experiment (m3) |
| Greek letters | ||
| βP/h: | = | relative interval parameter for a random P/h distribution |
| µ: | = | solvent viscosity (cP) |
| ρoil: | = | oil density (g mL−1) |
| σP/h: | = | relative standard deviation of P/h |
| σLN: | = | lognormal standard deviation of the capsule sizes |
| τ: | = | exponent for the effect of the viscosity on the diffusivity |
| υ1 and υ2: | = | relative volume of the two populations with |