### Abstract

In this chapter, a general energetic variational framework for modeling the dynamics of complex fluids is introduced. The approach reveals and focuses on the couplings and competitions between different mechanisms involved for specific materials, including energetic contributions vs. kinematic transport relations, conservative parts vs. dissipative parts and kinetic parts vs. free energy parts of the systems, macroscopic deformation or flows vs. microscopic deformations, bulk effects vs. boundary conditions, etc. One has to notice that these variational approaches are motivated by the seminal works of Rayleigh (Proc Lond Math Soc 1(1):357-368, 1871) and Onsager (Phys Rev 37(4):405, 1931; Phys Rev 38(12):2265, 1931). In this chapter, the underlying physical principles and background, as well as the limitations of these approaches, are demonstrated. Besides the classical models for ideal fluids and elastic solids, these approaches are employed for models of viscoelastic fluids, diffusion, and mixtures.

Original language | English (US) |
---|---|

Title of host publication | Handbook of Mathematical Analysis in Mechanics of Viscous Fluids |

Publisher | Springer International Publishing |

Pages | 73-113 |

Number of pages | 41 |

ISBN (Electronic) | 9783319133447 |

ISBN (Print) | 9783319133430 |

DOIs | |

State | Published - Apr 19 2018 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)
- Engineering(all)

### Cite this

*Handbook of Mathematical Analysis in Mechanics of Viscous Fluids*(pp. 73-113). Springer International Publishing. https://doi.org/10.1007/978-3-319-13344-7_2

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*Handbook of Mathematical Analysis in Mechanics of Viscous Fluids.*Springer International Publishing, pp. 73-113. https://doi.org/10.1007/978-3-319-13344-7_2

**Variational modeling and complex fluids.** / Giga, Mi Ho; Kirshtein, Arkadz; Liu, Chun.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Variational modeling and complex fluids

AU - Giga, Mi Ho

AU - Kirshtein, Arkadz

AU - Liu, Chun

PY - 2018/4/19

Y1 - 2018/4/19

N2 - In this chapter, a general energetic variational framework for modeling the dynamics of complex fluids is introduced. The approach reveals and focuses on the couplings and competitions between different mechanisms involved for specific materials, including energetic contributions vs. kinematic transport relations, conservative parts vs. dissipative parts and kinetic parts vs. free energy parts of the systems, macroscopic deformation or flows vs. microscopic deformations, bulk effects vs. boundary conditions, etc. One has to notice that these variational approaches are motivated by the seminal works of Rayleigh (Proc Lond Math Soc 1(1):357-368, 1871) and Onsager (Phys Rev 37(4):405, 1931; Phys Rev 38(12):2265, 1931). In this chapter, the underlying physical principles and background, as well as the limitations of these approaches, are demonstrated. Besides the classical models for ideal fluids and elastic solids, these approaches are employed for models of viscoelastic fluids, diffusion, and mixtures.

AB - In this chapter, a general energetic variational framework for modeling the dynamics of complex fluids is introduced. The approach reveals and focuses on the couplings and competitions between different mechanisms involved for specific materials, including energetic contributions vs. kinematic transport relations, conservative parts vs. dissipative parts and kinetic parts vs. free energy parts of the systems, macroscopic deformation or flows vs. microscopic deformations, bulk effects vs. boundary conditions, etc. One has to notice that these variational approaches are motivated by the seminal works of Rayleigh (Proc Lond Math Soc 1(1):357-368, 1871) and Onsager (Phys Rev 37(4):405, 1931; Phys Rev 38(12):2265, 1931). In this chapter, the underlying physical principles and background, as well as the limitations of these approaches, are demonstrated. Besides the classical models for ideal fluids and elastic solids, these approaches are employed for models of viscoelastic fluids, diffusion, and mixtures.

UR - http://www.scopus.com/inward/record.url?scp=85054352354&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054352354&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-13344-7_2

DO - 10.1007/978-3-319-13344-7_2

M3 - Chapter

AN - SCOPUS:85054352354

SN - 9783319133430

SP - 73

EP - 113

BT - Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

PB - Springer International Publishing

ER -