### Abstract

The extracellular matrix of cartilage is a charged porous fibrous material. Transport phenomena in such a medium are very complex. In this study, solute diffusive flux and convective flux in porous fibrous media were investigated using a continuum mixture theory approach. The intrinsic diffusion coefficient of solute in the mixture was defined and its relation to drag coefficients was presented. The effect of mechanical loading on solute diffusion in cartilage under unconfined compression with a frictionless boundary condition was analyzed numerically using the model developed. Both strain-dependent hydraulic permeability and diffusivity were considered. Analyses and results show that (1) In porous media, the convective velocity for each solute phase is different. (2) The solute convection in tissue is governed by the relative convective velocity (i.e., relative to solid velocity). (3) Under the assumption that all the frictional interactions among solutes are negligible, the relative convective velocity for α-solute phase is equal to the relative solvent velocity multiplied by its convective coefficient (H ^{α}) which is also known as the hindrance factor in the literature. The relationship between the convective coefficient and the relative diffusivity of solute is presented. (4) Solute concentration profile within the cartilage sample depends on the phase of dynamic compression.

Original language | English |
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Pages (from-to) | 63-72 |

Number of pages | 10 |

Journal | Biomechanics and Modeling in Mechanobiology |

Volume | 6 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 1 2007 |

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### ASJC Scopus subject areas

- Biotechnology
- Biophysics
- Computer Science(all)
- Physics and Astronomy (miscellaneous)

### Cite this

**Convection and diffusion in charged hydrated soft tissues : A mixture theory approach.** / Yao, H.; Gu, Weiyong.

Research output: Contribution to journal › Article

*Biomechanics and Modeling in Mechanobiology*, vol. 6, no. 1-2, pp. 63-72. https://doi.org/10.1007/s10237-006-0040-3

}

TY - JOUR

T1 - Convection and diffusion in charged hydrated soft tissues

T2 - A mixture theory approach

AU - Yao, H.

AU - Gu, Weiyong

PY - 2007/1/1

Y1 - 2007/1/1

N2 - The extracellular matrix of cartilage is a charged porous fibrous material. Transport phenomena in such a medium are very complex. In this study, solute diffusive flux and convective flux in porous fibrous media were investigated using a continuum mixture theory approach. The intrinsic diffusion coefficient of solute in the mixture was defined and its relation to drag coefficients was presented. The effect of mechanical loading on solute diffusion in cartilage under unconfined compression with a frictionless boundary condition was analyzed numerically using the model developed. Both strain-dependent hydraulic permeability and diffusivity were considered. Analyses and results show that (1) In porous media, the convective velocity for each solute phase is different. (2) The solute convection in tissue is governed by the relative convective velocity (i.e., relative to solid velocity). (3) Under the assumption that all the frictional interactions among solutes are negligible, the relative convective velocity for α-solute phase is equal to the relative solvent velocity multiplied by its convective coefficient (H α) which is also known as the hindrance factor in the literature. The relationship between the convective coefficient and the relative diffusivity of solute is presented. (4) Solute concentration profile within the cartilage sample depends on the phase of dynamic compression.

AB - The extracellular matrix of cartilage is a charged porous fibrous material. Transport phenomena in such a medium are very complex. In this study, solute diffusive flux and convective flux in porous fibrous media were investigated using a continuum mixture theory approach. The intrinsic diffusion coefficient of solute in the mixture was defined and its relation to drag coefficients was presented. The effect of mechanical loading on solute diffusion in cartilage under unconfined compression with a frictionless boundary condition was analyzed numerically using the model developed. Both strain-dependent hydraulic permeability and diffusivity were considered. Analyses and results show that (1) In porous media, the convective velocity for each solute phase is different. (2) The solute convection in tissue is governed by the relative convective velocity (i.e., relative to solid velocity). (3) Under the assumption that all the frictional interactions among solutes are negligible, the relative convective velocity for α-solute phase is equal to the relative solvent velocity multiplied by its convective coefficient (H α) which is also known as the hindrance factor in the literature. The relationship between the convective coefficient and the relative diffusivity of solute is presented. (4) Solute concentration profile within the cartilage sample depends on the phase of dynamic compression.

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U2 - 10.1007/s10237-006-0040-3

DO - 10.1007/s10237-006-0040-3

M3 - Article

C2 - 16767452

AN - SCOPUS:33845448544

VL - 6

SP - 63

EP - 72

JO - Biotechnology

JF - Biotechnology

SN - 1682-296X

IS - 1-2

ER -