Título:	Comportamento não-linear de suspensões elásticas sujeitas a diferentes campos de escoamento : modelagem matemática e simulação
Autor(es):	Moreira Neto, Álvaro
Orientador(es):	Cunha, Francisco Ricardo da
Coorientador(es):	Sobral, Yuri Dumaresq
Assunto:	Viscoelasticidade Mecânica dos fluidos Líquidos elásticos Reologia
Data de publicação:	29-Jan-2019
Data de defesa:	27-Jul-2018
Referência:	MOREIRA NETO, Álvaro. Comportamento não-linear de suspensões elásticas sujeitas a diferentes campos de escoamento: modelagem matemática e simulação. 2018. xxxiii, 277 f., il. Tese (Doutorado em Ciências Mecânicas)—Universidade de Brasília, Brasília, 2018.
Abstract:	In the present thesis a theoretical study of mathematical formulation, modeling, asymptotic and numerical solutions, aiming the rheological characterization of elastic liquids or dilute polymeric suspensions in permanent and transient flows. The constitutive description of the fluid is based on a Dumbbell-FENE microhydrodynamic model of two coupled equations describing the time evolution of deformation of the macromolecule (i.e. conformation tensor) and stress tensors. One of the relevant contributions of the present work is to enable an evaluation of the non-linear behavior of a non-Newtonian elastic fluid subjected to different flow regimes. These are: simple shear, oscillatory shear, permanent and transient extensional flow, step-strain and unidirectional flow in capillary tube in the presence of a pressure gradient, in which the applied shear is non-linear. In order to identify the non-dimensional physical parameters of the present study, the pair of governing equations is made non-dimensional according to a new proposal referring to previous investigations. The main relaxation time of the polymer suspension is used as the characteristic time scale for defining the Deborah number. This being the most relevant non-dimensional physical parameter of the examined flows, since it measures the relative importance between the elastic relaxation time of the fluid and a characteristic time scale of the imposed flow. Asymptotic solutions for the different examined flows at the limit of small values limit of Deborah numbers, wich corresponds to the condition of equilibrium in the vicinity of the macromolecules, are developed for validation (``\emph{benchmarks}'') of the numerical simulations performed in arbitrary Deborah numbers. By comparing the asymptotic solutions with the numerical results of the simulations, it is possible to verify an excellent agreement between the theoretical and numerical results in the assumed asymptotic limit. A new approach is presented regarding the way of obtaining the time evolution equation of the conformation tensor in which the modal transformation process is used to uncouple the system from nonlinear differential equations resulting from the analysis of the rheological behavior of the fluid subjected to oscillatory simple shear. Nonlinear elastic schemes involving larger Deborah numbers are examined only by numerical simulation. The theoretical results of the model are also compared with experimental data concerning rheological quantities in low Deborah number. A good quantitative agreement can be observed, using only a calibration constant in the elastic term of the physical model. Although the polymer suspension is dilute, to investigate nonlinear regimes for different configurations of rheological flows in high Deborah numbers is a complex experimental task. The present proposal also contributes in an innovative way to partially overcome this difficulty by providing relevant information on rheological quantities that characterize the behavior of viscoelastic fluids in nonlinear regime. In addition, we present results from stress relaxation function, time relaxation spectrum and Fourier analysis of the fluid response in nonlinear regimes. The systems of nonlinear coupled differential equations are numerically integrated by using a numerical code developed in Fortran based on the fourth-order Runge-Kutta algorithm adapted for the solution of the initial value problem of the explored flows. The numerical time step is considered in a way compatible with the physical parameters involved in the flows, such as the Deborah number and the excitation frequency, in the case of transient flows and the flow generated by a step strain. A proposal of an algorithm based on continued fractions is also developed in order to fit both experimental data and numerical simulations data of the viscoelastic modules. The results showing the efficiency and accuracy of this proposal are demonstrated with experimental data. In the final part of the thesis is presented a theoretical-numerical study of the polymer suspension flow in the presence of a pressure gradient driving flow. We investigate the deviation of the standard parabolic profile of unidirectional flows in tubes as a consequence of the elastic effects in different Deborah numbers. In terms of rheological quantities, the non-dimensional wall viscosity is determined as a function of the Deborah number based on the shear rate on the wall as well as the relative intrinsic viscosity calculated in terms of Poiseuille's law. A shearthinning behavior for the for the both viscosities at low and high Deborah numbers is also captured by the numerical simulations.
Unidade Acadêmica:	Faculdade de Tecnologia (FT) Departamento de Engenharia Mecânica (FT ENM)
Informações adicionais:	Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2018.
Programa de pós-graduação:	Programa de Pós-Graduação em Ciências Mecânicas
Licença:	A concessão da licença deste item refere-se ao termo de autorização impresso assinado pelo autor com as seguintes condições: Na qualidade de titular dos direitos de autor da publicação, autorizo a Universidade de Brasília e o IBICT a disponibilizar por meio dos sites www.bce.unb.br, www.ibict.br, http://hercules.vtls.com/cgi-bin/ndltd/chameleon?lng=pt&skin=ndltd sem ressarcimento dos direitos autorais, de acordo com a Lei nº 9610/98, o texto integral da obra disponibilizada, conforme permissões assinaladas, para fins de leitura, impressão e/ou download, a título de divulgação da produção científica brasileira, a partir desta data.
Agência financiadora:	Fundação de Amparo à Pesquisa do Estado de Mato Grosso (FAPEMAT).
Aparece nas coleções:	Teses, dissertações e produtos pós-doutorado

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