Abstract
Beads are one of the particulate delivery systems used to achieve protection and/or controlled delivery of different active ingredients or microorganisms. Polyvinyl alcohol is a non-toxic and biodegradable polymer and possesses extensive applications as a biomaterial. In the present work, two different strategies were applied for the prediction of shape and size of polyvinyl alcohol beads. These beads were obtained by extrusion dripping of a boric acid–polyvinyl alcohol aqueous solution into a basic aqueous gelling bath. The shapes and sizes of immature, mature and dry beads were determined using optical microscopy. Two different strategies included statistical and fluid dynamical (mechanistic) models to fit the experimental data. The shape of immature and mature beads was found to be dependent on the viscosity of the dripping solution for the former and the maturation time for the latter. The shape of dry beads was found to be mainly dependent on the particle contraction in the drying process. The size of mature and dried beads was correctly predicted from the operating conditions by means of a statistically developed model and from the dripping solution properties by means of a fluid dynamical approach. The optimal conditions for minimal dried bead size were calculated. The obtained mathematical models allow reduction in the amount of resources and time taken in the initial stages of the development of a novel encapsulated formulation. The mechanistic model may be applied to other polymeric systems once the corresponding parameters have been determined during proof-of-concept experiments.
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Abbreviations
- [H3BO3/PVA]:
-
Boric acid to polyvinyl alcohol ratio, g H3BO3/100 g PVA
- [PVA]:
-
Polyvinyl alcohol concentration, %
- A b :
-
Area of the bead, mm2
- d b :
-
Equivalent diameter, mm
- d b,d :
-
Dried bead diameter, mm
- d b,i :
-
Immature bead diameter, mm
- d b,m :
-
Mature bead diameter, mm
- d b,t :
-
Bead diameter as obtained from Tate’s Law, mm
- d max :
-
Length of perpendicular major axis, mm
- d min :
-
Length of perpendicular minor axis, mm
- d o :
-
Outer needle diameter, mm
- F HB :
-
Harkins–Brown factor
- \( F_{\text{HB}}^{{{\text{H}}_{2} {\text{O}}}} \) :
-
Harkins–Brown factor for distilled water
- F snHB :
-
Harkins–Brown factor for polymeric solution
- g :
-
Gravity constant
- h :
-
Distance of flight, cm
- K D :
-
Drying factor
- K LF :
-
Liquid lost factor
- K SF :
-
Shrinkage factor
- \( m_{{{\text{H}}_{ 2} {\text{O}}}} \) :
-
Weight of a certain number of distilled water drops, g
- m sn :
-
Weight of a certain number of polymer solution drops, g
- Oh :
-
Ohnesorge number
- SF:
-
Sphericity factor
- SFb,d :
-
Dried bead sphericity factor
- SFb,i :
-
Immature bead sphericity factor
- SFb,m :
-
Mature bead sphericity factor
- V ideal :
-
Ideal volume of a drop detaching from the tip of a needle, mm3
- V real :
-
Real volume of a drop detaching from the tip of a needle, mm3
- μ sn :
-
Viscosity of the polymeric solution, cP
- ρ sn :
-
Density of the polymeric solution, kg/m3
- \( \sigma_{{{\text{H}}_{ 2} {\text{O}}}} \) :
-
Surface tension of bidistilled water, mN/m
- σ sn :
-
Surface tension of the polymeric solution, mN/m
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Acknowledgements
The authors thank the Consejo Nacional de Investigaciones Científicas y Técnicas and the Instituto de Promoción de la Carne Vacuna Argentina for their financial support.
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Weibel, M.I., Mengatto, L.N., Luna, J.A. et al. Accurate prediction of shape and size of polyvinyl alcohol beads produced by extrusion dripping. Iran Polym J 27, 161–170 (2018). https://doi.org/10.1007/s13726-017-0597-y
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DOI: https://doi.org/10.1007/s13726-017-0597-y