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Permeability of porous gelcast scaffolds for bone tissue engineering

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Abstract

The permeability of metallic and ceramic open-cell foams prepared by the gelcasting technique was assessed by fitting of Forchheimer’s equation to experimental pressure drop curves. The ceramic composition was based on pure hydroxyapatite, while the metallic composition was based on titanium metal. Experimental Darcian (k 1) and non-Darcian (k 2) permeability constants displayed values in the range 0.40–3.24 × 10−9 m2 and 3.11–175.8 × 10−6 m respectively. Tortuosity was evaluated by gas diffusion experiments and ranged from 1.67 to 3.60, with porosity between 72 and 81% and average hydraulic pore size between 325 and 473 μm. Such features were compared to data reported in the literature for cancellous bones and synthetic scaffolds for bone graft. A detailed discussion concerning the limitations of Darcy’s law for fitting laboratory data and for predicting fluid flow through scaffolds in real biomedical applications is also performed. Pore size was obtained by image analysis and was also derived from permeation-absorption-diffusion experiments. In both cases, values were within the range expected for porous scaffolds applications.

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Abbreviations

A flow :

Face area of the sample exposed to flow (m2)

c :

Molar concentration of the gas mixture (mol/m3)

D AB :

Gas diffusivity in air (m2/s)

D eff :

Effective gas diffusivity through the scaffold (m2/s)

d :

Distance between the gas–liquid interface and the bottom face of the sample (m)

d h :

Hydraulic pore diameter (m)

d sphere :

Three-dimensional cell diameter (m)

d transp :

Pore diameter based on transport properties (m)

Fo :

Forchheimer number (−)

k 1 :

Darcian permeability constant (m2)

k 2 :

Non-Darcian permeability constant (m)

L :

Sample thickness along the macroscopic flow direction (m)

MM A :

Molar mass of diffusion gas (mol/kg)

N AZ :

Molar flux of diffusion gas along z-direction (mol/m2.s)

P :

Absolute fluid pressure at which v s, μ and ρ are measured or calculated (Pa)

P atm :

Atmospheric pressure at laboratory location (Pa)

P i :

Absolute fluid pressure at the sample entrance (Pa)

P o :

Absolute fluid pressure at the sample exit (Pa)

P VA :

Absolute vapor pressure of diffusion gas (Pa)

Q :

Volumetric flow rate (m3/s)

R :

Ideal gas constant (Pa m3/mol K)

Re pore :

Reynolds number at the pore level (−)

S :

Cross-sectional sample surface exposed to vapor diffusion (m2)

T :

Temperature of the fluid (K)

v i :

Interstitial fluid velocity (m/s)

v s :

Face or superficial fluid velocity (m/s)

z :

Distance in diffusion direction (m)

y :

Molar fraction of gas mixture (−)

Δm :

Mass variation measured during the diffusion experiment (kg)

ΔP :

Pressure drop through the medium (Pa)

ΔP viscous :

Pressure drop due to viscous effects (Pa)

ΔP inertial :

Pressure drop due to inertial effects (Pa)

Δt :

Duration of the diffusion experiment (s)

ε :

Porosity of the medium (−)

μ :

Absolute fluid viscosity (Pa s)

ρ :

Fluid density (kg/m3)

ρ b :

Bulk density of the scaffold (kg/m3)

ρ s :

Density of the solid fraction (kg/m3)

τ :

Tortuosity of the scaffold (−)

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Acknowledgments

The authors would like to thank VITO for supplying samples and MCT/CNPq, Process 471814/2088 3, for the financial support to this work.

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Authors and Affiliations

  1. Course of Chemical Engineering, University of Ribeirão Preto, UNAERP, Ribeirão Preto, SP, 14096-900, Brazil

    M. D. M. Innocentini, R. K. Faleiros & R. Pisani Jr.

  2. Materials Technology, VITO, Boeretang 200, 2400, Mol, Belgium

    I. Thijs, J. Luyten & S. Mullens

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  1. M. D. M. Innocentini
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  2. R. K. Faleiros
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Correspondence to M. D. M. Innocentini.

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Innocentini, M.D.M., Faleiros, R.K., Pisani, R. et al. Permeability of porous gelcast scaffolds for bone tissue engineering. J Porous Mater 17, 615–627 (2010). https://doi.org/10.1007/s10934-009-9331-2

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