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Lattice Boltzmann method simulations of swelling of cuboid-shaped IPN hydrogel tablets with experimental validation

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Abstract

The swelling behavior of IPN hydrogel tablets in the shape of cuboid or rectangular parallelepiped tablets in contact with buffer solutions at different pH and temperature conditions were estimated by a three-dimensional multiple-relaxation-time lattice Boltzmann (LB) model. Adsorption isotherms were obtained experimentally for tablets of IPN hydrogel formulation immersed in buffer solution at 298.15 and 310.15 K at pH equal to 4.48, 7.25, and 8.225, and those of copolymer hydrogel formulation at 298.15 K at pH equal to 4.48, 7.25, and 8.225. A computational method based on an LB model is used to simulate the hydrogels swelling, employing dimensionless units of length and mass. The discretization error estimation of the computational simulations was calculated by the grid convergence index method. Excellent correlations were achieved between the computational data and experimental values of mass swelling percentage, achieving coefficients of determination equal to or higher than 0.993 for the finest grids. The equilibrium diffusion coefficient at low pH values is higher than at large pH values. The simulations allowed us to estimate the equilibrium diffusion coefficient for each case; a qualitative property of the polymer, and to observe how the inner regions of a sample are hydrated in the time domain, both of which cannot be done experimentally.

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Abbreviations

C :

Mass concentration of the liquid substance in the hydrogel network, [-]

C eq :

Mass concentration of the liquid substance in thermodynamic equilibrium, [-]

D :

Effective diffusion coefficient for Fick’s equation, [m2 s–1]

D ( ) :

Diffusion coefficient in a specific direction, [m2 s–1]

D eq :

Equilibrium diffusion coefficient, [m2 s–1]

D eq * :

Extrapolated equilibrium diffusion coefficient, [m2 s–1]

E A :

Activation energy of diffusion, [kJ mol–1]

e a :

Approximate relative error, [-]

e ext :

Extrapolated relative error, [-]

e α :

The discrete velocity set in lattice Boltzmann equation, [m2 s–1]

GCI:

Grid convergence index, [-]

g α :

Distribution function, [-]

\({g}_{\alpha}^{eq}\) :

Equilibrium distribution function, [-]

H :

Height, [mm]

h :

The representative cell size

k :

Constant which incorporates characteristics of this network, [-]

L :

Length [mm]

M:

Transformation matrix in lattice Boltzmann equation, [-]

M :

Mass of the liquid substance in the hydrogel sample at time “t”, [g]

M dry :

Dry hydrogel sample mass or xerogel mass, [g]

M eq :

Total mass of swollen hydrogel sample in thermodynamic equilibrium, [g]

M total :

Total mass of swollen hydrogel sample at time “t”, [g]

N :

Number of lattice elements used for the computation, [-]

n :

Diffusion exponent, [-]

N x :

Number of lattice elements along the x axis, [-]

N y :

Number of lattice elements along the y axis, [-]

N z :

Number of lattice elements along the z axis, [-]

p :

Apparent order of the method, [-]

R :

Gas constant, [J⋅K−1⋅mol−1]

R 2 :

Coefficient of determination, [-]

RMSE :

Root mean square error, [-]

r :

Grid refinement factor, [-]

S:

The relaxation-time matrix, [-]

T :

Temperature, [K]

t :

Time, [s]

W :

Width, [mm]

w α :

Weight coefficient, [-]

β :

Dimensionless constants in Eq. (4), [-]

ε :

Sound speed factor linked to the lattice dimensions, [-]

ε 21, ε 32 :

Changes between medium-fine and coarse-medium input, [m2 s–1]

τ ij :

Relaxation coefficient, [-]

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Acknowledgements

The facilities and support of B5IDA Group (GID-60 B5IDA-USB) and Biomechanics Group (GID-50), all of them at Simon Bolivar University in Caracas, Venezuela, were very useful to complete this research.

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Department of Industrial Technology, Universidad Simón Bolívar, Naiguatá, Edo. La Guaira, Venezuela

    Pedro J. Boschetti

  2. Undergraduate Student in Chemical Engineering, B5IDA Group, Universidad Simón Bolívar, Caracas, Venezuela

    David J. Toro

  3. Undergraduate Student in Mechanical Engineering, B5IDA Group, Universidad Simón Bolívar, Caracas, Venezuela

    Alejandro Ontiveros

  4. Department of Science and Technology, Valencian International University, Valencia, Spain

    Orlando Pelliccioni

  5. Department of Chemistry, B5IDA Group, Universidad Simón Bolívar, Caracas, Venezuela

    Marcos A. Sabino

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Boschetti, P.J., Toro, D.J., Ontiveros, A. et al. Lattice Boltzmann method simulations of swelling of cuboid-shaped IPN hydrogel tablets with experimental validation. Heat Mass Transfer 58, 763–777 (2022). https://doi.org/10.1007/s00231-021-03132-8

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