Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels
Complex fluids are used in a range of industries including the consumer goods, automotive, and oil and gas production sectors. Characterizing the rheology, understanding the flow behavior, and modeling the constitutive response of these complex fluids is important for predicting time-varying materia...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Published: |
Massachusetts Institute of Technology
2024
|
| Online Access: | https://hdl.handle.net/1721.1/155614 |
| _version_ | 1826200608311345152 |
|---|---|
| author | John Rathinaraj, Joshua David |
| author2 | McKinley FRS, Gareth H. |
| author_facet | McKinley FRS, Gareth H. John Rathinaraj, Joshua David |
| author_sort | John Rathinaraj, Joshua David |
| collection | MIT |
| description | Complex fluids are used in a range of industries including the consumer goods, automotive, and oil and gas production sectors. Characterizing the rheology, understanding the flow behavior, and modeling the constitutive response of these complex fluids is important for predicting time-varying material performance under various processing conditions, thus helping prevent failures in large-scale industrial operations. However, modeling the rheological behavior of such complex fluids using canonical constitutive laws that relate the state of stress to the deformation history can be challenging due to their broad relaxation spectrum and time-varying (or “mutating”) material response. Part I of this thesis therefore deals with developing constitutive models relevant for polymeric solutions that exhibit broad viscoelastic relaxation spectra, and mutating material systems such as colloidal gels that may exhibit age-dependent viscoelastic properties. Similarly, characterizing the rheological properties over the full range of time or frequency scales relevant to their use can be challenging, especially if the material properties are ‘thixotropic’ and change with time. Thus, part II of this thesis focuses on developing novel rheometric techniques that can robustly characterize time-varying rheological properties of complex fluids and soft solids. In Part I of this thesis, we utilize fractional differential equations, formulated into fractional constitutive models, to describe the strain and rate-dependence of the stress response in complex fluids. This formulation is capable of quantitatively modeling the linear viscoelastic response of a wide range of polymeric solutions and colloidal gels. Subsequently, we incorporate material nonlinearities into the (inherently linear) fractional models using an integral Boltzmann-like framework which combines a frame-indifferent strain measure with a strain-dependent softening or damping function. This enables quantitative description of rheological nonlinearities such as shear thinning and normal stress differences. From here, we evaluate analytical expressions for the steady shear viscosity and viscoelastic moduli in terms of the linear relaxation kernel and the parameters of the damping function. Such analytical expressions provide physical and mathematical understanding for empirical relations such as the Cox-Merz rule and the Gleissle mirror relations that are widely used in industrial rheological characterization. In addition to broad viscoelastic response, many complex fluids “mutate”; i.e. they also show more complex time-dependent dynamics due to rheological aging, thixotropy, and continuous yielding behaviors which are not captured by the integral viscoelastic framework discussed above. To explore these complexities, we first study ‘rheological aging’ in a drilling mud formulated from a bentonite dispersion (a discotic colloidal gel). We present a framework for modeling the linear viscoelastic response in the presence of physical aging based on the transformation to a ‘material time’ domain. In this transformed reference domain, we can again quantitatively describe the constitutive relationship between stress and strain-rate measured in these time-dependent clay dispersions using fractional differential equations; however the spectrum of time constants continuously evolves with the material age. In the final section of Part I we turn to scientific machine learning techniques, informed by existing rheophysical laws, to formulate a universal differential equation to describe the thixotropic and yielding behavior response of time-evolving complex fluids. We demonstrate using experimental data from a model discotic colloidal dispersion that this framework, which incorporates a neural network into an existing physical model comprising of coupled fractional differential equations, can accurately learn the effective constitutive relationship governing the thixotropic and yielding behavior of the complex fluid directly from experimental data. The resulting framework can accurately model and predict the full thixo-elasto-visco-plastic (TEVP) response of an aging or mutating system. For an aging or gelling fluid, extracting dynamic rheological properties, such as the storage modulus and loss modulus obtained from small amplitude oscillatory deformation, can be challenging due to the fast mutation time of the material. Conventional oscillatory techniques employ discrete Fourier transforms, which inherently assume the time signal to be time-translation invariant. This assumption results in systematic errors for mutating materials and there is also a need to develop novel rheometric techniques that can rapidly and accurately extract the time-frequency information of mutating material systems. Therefore, in Part II of this thesis, we develop a discrete Gabor transform procedure (a special case of the short-time Fourier transform) that can be implemented in commercial rheometric hardware to robustly extract time-frequency information of aging and thixotropic material systems. It is often challenging to discern whether the resulting time-dependent material response should be attributed physically to thixotropic microstructural mechanisms or material viscoelasticity. To address this, we augment the Gabor transform with a parallel superposition flow protocol. The resulting deformation history superimposes a nonlinear external drive and probes the material response using superposed small oscillatory perturbation. The resulting ‘pump/probe” protocol allows us to distinguish between locally-reversible viscoelastic material responses and irreversible thixoplastic effects that can lead to large, time-dependent material deformations even in the absence of elasticity. These new advanced rheometric protocols make use of modern high-resolution electromechanical rheometer systems that are confined to laboratory settings and not suitable for monitoring the rheological properties of the fluid in industrial settings. Therefore, in a final contribution, we develop a novel compact mechanical tuning fork resonator that can be deployed in the field and can continuously measure both time-independent and time-varying rheological properties of a range of complex fluids. |
| first_indexed | 2024-09-23T11:39:05Z |
| format | Thesis |
| id | mit-1721.1/155614 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:39:05Z |
| publishDate | 2024 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1556142024-07-11T03:36:59Z Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels John Rathinaraj, Joshua David McKinley FRS, Gareth H. Massachusetts Institute of Technology. Department of Mechanical Engineering Complex fluids are used in a range of industries including the consumer goods, automotive, and oil and gas production sectors. Characterizing the rheology, understanding the flow behavior, and modeling the constitutive response of these complex fluids is important for predicting time-varying material performance under various processing conditions, thus helping prevent failures in large-scale industrial operations. However, modeling the rheological behavior of such complex fluids using canonical constitutive laws that relate the state of stress to the deformation history can be challenging due to their broad relaxation spectrum and time-varying (or “mutating”) material response. Part I of this thesis therefore deals with developing constitutive models relevant for polymeric solutions that exhibit broad viscoelastic relaxation spectra, and mutating material systems such as colloidal gels that may exhibit age-dependent viscoelastic properties. Similarly, characterizing the rheological properties over the full range of time or frequency scales relevant to their use can be challenging, especially if the material properties are ‘thixotropic’ and change with time. Thus, part II of this thesis focuses on developing novel rheometric techniques that can robustly characterize time-varying rheological properties of complex fluids and soft solids. In Part I of this thesis, we utilize fractional differential equations, formulated into fractional constitutive models, to describe the strain and rate-dependence of the stress response in complex fluids. This formulation is capable of quantitatively modeling the linear viscoelastic response of a wide range of polymeric solutions and colloidal gels. Subsequently, we incorporate material nonlinearities into the (inherently linear) fractional models using an integral Boltzmann-like framework which combines a frame-indifferent strain measure with a strain-dependent softening or damping function. This enables quantitative description of rheological nonlinearities such as shear thinning and normal stress differences. From here, we evaluate analytical expressions for the steady shear viscosity and viscoelastic moduli in terms of the linear relaxation kernel and the parameters of the damping function. Such analytical expressions provide physical and mathematical understanding for empirical relations such as the Cox-Merz rule and the Gleissle mirror relations that are widely used in industrial rheological characterization. In addition to broad viscoelastic response, many complex fluids “mutate”; i.e. they also show more complex time-dependent dynamics due to rheological aging, thixotropy, and continuous yielding behaviors which are not captured by the integral viscoelastic framework discussed above. To explore these complexities, we first study ‘rheological aging’ in a drilling mud formulated from a bentonite dispersion (a discotic colloidal gel). We present a framework for modeling the linear viscoelastic response in the presence of physical aging based on the transformation to a ‘material time’ domain. In this transformed reference domain, we can again quantitatively describe the constitutive relationship between stress and strain-rate measured in these time-dependent clay dispersions using fractional differential equations; however the spectrum of time constants continuously evolves with the material age. In the final section of Part I we turn to scientific machine learning techniques, informed by existing rheophysical laws, to formulate a universal differential equation to describe the thixotropic and yielding behavior response of time-evolving complex fluids. We demonstrate using experimental data from a model discotic colloidal dispersion that this framework, which incorporates a neural network into an existing physical model comprising of coupled fractional differential equations, can accurately learn the effective constitutive relationship governing the thixotropic and yielding behavior of the complex fluid directly from experimental data. The resulting framework can accurately model and predict the full thixo-elasto-visco-plastic (TEVP) response of an aging or mutating system. For an aging or gelling fluid, extracting dynamic rheological properties, such as the storage modulus and loss modulus obtained from small amplitude oscillatory deformation, can be challenging due to the fast mutation time of the material. Conventional oscillatory techniques employ discrete Fourier transforms, which inherently assume the time signal to be time-translation invariant. This assumption results in systematic errors for mutating materials and there is also a need to develop novel rheometric techniques that can rapidly and accurately extract the time-frequency information of mutating material systems. Therefore, in Part II of this thesis, we develop a discrete Gabor transform procedure (a special case of the short-time Fourier transform) that can be implemented in commercial rheometric hardware to robustly extract time-frequency information of aging and thixotropic material systems. It is often challenging to discern whether the resulting time-dependent material response should be attributed physically to thixotropic microstructural mechanisms or material viscoelasticity. To address this, we augment the Gabor transform with a parallel superposition flow protocol. The resulting deformation history superimposes a nonlinear external drive and probes the material response using superposed small oscillatory perturbation. The resulting ‘pump/probe” protocol allows us to distinguish between locally-reversible viscoelastic material responses and irreversible thixoplastic effects that can lead to large, time-dependent material deformations even in the absence of elasticity. These new advanced rheometric protocols make use of modern high-resolution electromechanical rheometer systems that are confined to laboratory settings and not suitable for monitoring the rheological properties of the fluid in industrial settings. Therefore, in a final contribution, we develop a novel compact mechanical tuning fork resonator that can be deployed in the field and can continuously measure both time-independent and time-varying rheological properties of a range of complex fluids. Ph.D. 2024-07-10T20:19:25Z 2024-07-10T20:19:25Z 2024-05 2024-06-13T16:43:44.823Z Thesis https://hdl.handle.net/1721.1/155614 Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Copyright retained by author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | John Rathinaraj, Joshua David Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels |
| title | Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels |
| title_full | Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels |
| title_fullStr | Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels |
| title_full_unstemmed | Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels |
| title_short | Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels |
| title_sort | novel rheometric techniques and constitutive models for linear and nonlinear rheology applications to polymeric solutions and colloidal gels |
| url | https://hdl.handle.net/1721.1/155614 |
| work_keys_str_mv | AT johnrathinarajjoshuadavid novelrheometrictechniquesandconstitutivemodelsforlinearandnonlinearrheologyapplicationstopolymericsolutionsandcolloidalgels |