# A Review of Mixture Theory for Deformable Porous Media and Applications
## 4 Further Applications of Mixture Theory  
It is well known that organs, tissues and cells can be considered as mixture-composites, as they consist of multiple solid and fluid constituents. Therefore authors employed the idea of continuum mixture theory to describe the behaviors of soft biological tissues. Moreover, Growth and remodeling of porous biological tissues are studied by incorporating the effect of chemical reactions among mixture constituents. [PERSON] [32] provided a comprehensive review of continuum biomechanics of soft biological tissues mentioning the work of [PERSON] and [PERSON] [11] and [PERSON] et al. [12; 13] for the development of biphasic mixture theory for biological tissues. The so-called linear biphasic theory considered cartilage as a solid which exhibited a linearly elastic isotropic response and the viscous  
Figure 8: The dynamics of capillary rise for both zero and non–zero gravity cases. fluid. Extending the idea of biphasic to triphasic mixture theory, [PERSON] et al. [33] developed mathematical models for soft tissues including the ion concentration as a third phase in addition to solid and fluid phase. Large numbers of papers [34; 35; 36; 37] have been reported considering triphasic approach. Treating the ions in a mixture as a combination of cations and anions, a quadiphasic mixture theory for soft biological tissue was developed by [PERSON] et al. [38]. [PERSON] [39; 40] has also contributed in mixture modeling of soft tissues particularly articular cartilage. Another important application of mixture theory in biomechanics is the resorption phenomena in bones reconstructed with bio-resorbable materials. [PERSON] and [PERSON] et al. [41] presented a continuum poro-elastic mixture model where two apparent mass densities were introduced to describe the situations in which bone tissues and bio-resorbable materials coexist and interact. They focused on the final healing stage process until the bone is remodeled and eventually replaced by newly synthesised living tissue. A similar study was undertaken by [PERSON] et al. [42] where a finite element analysis was carried out to investigate the phenomena of resorption and growth of bone tissue. The mixture theory approach is also followed by authors to include, for example, arterial tissue [21; 43; 44], cornea [45], skin [46] and lung [47]. Mathematical models based on mixture theory for the growth of tumors and the growth and remodeling of soft tissues were developed by many researchers, for example, [PERSON] and [PERSON] [48], [PERSON] and [PERSON] [49], [PERSON] and [PERSON] [50] and [PERSON] et al. [51]. In the model of tumor growth, they considered avascular tumor as a mixture comprising of solid, cellular and liquid phase. Their novel feature includes the dependence of cell proliferation rate on the cellular stress and the incorporation of mass exchange between the two phases. In case of growth and remodeling of tissues, the emergence of residual stress is considered in the framework of mixture theory. [PERSON] et al. [52] studied the case of one-dimensional sedimentation using continuum mixture theory approach and developed the constitutive equations by using the method of Lagrangian multipliers. The governing diffusion equation for quasi-steady sedimentation is derived and analyzed to understand some physical aspect of the problem. [PERSON] [53] discussed the heat conduction in laminated composites using mixture theory. Governing equations for the actual composite are obtained and the cases of both harmonic and transient temperature pulses were considered in his work. [PERSON] et al. [54] considered an interesting application of the mixture theory by proposing a mathematical model involving a deformable porous media saturated by compressible nematic liquid crystal under slowly varying electric fields and assumed that the system follows a Biot-type model. A two-phase mixture theory approach for the deflagration-to-detonation transition (DDT) in reactive granular materials was under taken by [PERSON] and [PERSON] [55] in 1986.