As a logical extension of previous work conducted into viscoelastic atomization, initially motivated by the need to improve spray coating transfer efficiencies, an experimental investigation into the spray-surface interaction for a number of Newtonian and non-Newtonian substitute test liquids is presented. Three model elastic liquids of varying polymer molecular weight and three inelastic liquids of varying shear viscosity were sprayed upon a moving surface to isolate the effect of elasticity and shear viscosity, respectively, on spray impaction behavior. In addition, two liquids exhibiting shear thinning behavior and an industrial top of rail liquid friction modifier, KELTRACK, for use in the railroad industry, were included in the spray tests. High-speed photography was used to examine the impingement of these liquids on the surface. Ligaments, formed as a consequence of a liquid’s viscoelasticity, were observed impacting the surface for 300K PEO, 1000K PEO, and KELTRACK. These ligaments were broadly classified into four groups, based on their structure. Splashing of elastic liquid ligaments and droplets led to filamentary structures being expelled from the droplet periphery, which were then carried away by the atomizing air jet, leading to reductions in transfer efficiency. The effect of increasing elasticity amongst the three varying molecular weight elastic solutions was shown to increase the splash threshold; a similar effect was noted with increasing shear viscosity. Attempts were made at quantifying a critical splash-deposition limit for all test liquids however due to imaging system limitations, no quantitative conclusions could be made. For KELTRACK, both droplets and ligaments spread and deposited on the rail surface upon impact, with no observed splash or rebound. Splash was only noted when droplets impinged directly on a previously deposited liquid film and even then, splashing was well contained. Thus, KELTRACK’s current rheological formulation proved to be very effective in ensuring high coating transfer efficiencies.

As a logical extension of previous work conducted into viscoelastic atomization, initially motivated by the need to improve spray coating transfer efficiencies, an experimental investigation into the spray-surface interaction for a number of Newtonian and non-Newtonian substitute test liquids is presented. Three model elastic liquids of varying polymer molecular weight and three inelastic liquids of varying shear viscosity were sprayed upon a moving surface to isolate the effect of elasticity and shear viscosity, respectively, on spray impaction behavior. In addition, two liquids exhibiting shear thinning behavior and an industrial top of rail liquid friction modifier, KELTRACK, for use in the railroad industry, were included in the spray tests. High-speed photography was used to examine the impingement of these liquids on the surface. Ligaments, formed as a consequence of a liquids viscoelasticity, were observed impacting the surface for 300K PEO, 1000K PEO, and KELTRACK. These ligaments were broadly classified into four groups, based on their structure. Splashing of elastic liquid ligaments and droplets led to filamentary structures being expelled from the droplet periphery, which were then carried away by the atomizing air jet, leading to reductions in transfer efficiency. The effect of increasing elasticity amongst the three varying molecular weight elastic solutions was shown to increase the splash threshold; a similar effect was noted with increasing shear viscosity. Attempts were made at quantifying a critical splash-deposition limit for all test liquids however due to imaging system limitations, no quantitative conclusions could be made. For KELTRACK, both droplets and ligaments spread and deposited on the rail surface upon impact, with no observed splash or rebound. Splash was only noted when droplets impinged directly on a previously deposited liquid film and even then, splashing was well contained. Thus, KELTRACKs current rheological formulation proved to be very effective in ensuring high coating transfer efficiencies.

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This work uses high-speed video imaging to study the formation of filaments, during impact and rebounding of drops with polymer additives. We use PEO of different concentrations from 10 to 1000 ppm and study how drops rebound from various different surfaces: superhydrophilic, hydrophilic, hydrophobic, and superhydrophobic. Bouncing occurs for all surfaces at low impact velocities. We specifically focus on the phenomenon of the generation of polymer filaments, which are pulled out of the free surface of the drop during its rebounding from micro-pillared or rough substrates. We map the parameter regime, in terms of polymer concentration and impact Weber number, where the filaments are generated in the most repeatable manner. This occurs for regularly pillared surfaces and drops of 100 ppm PEO concentrations, where numerous separated filaments are observed. In contrast, for superhydrophobic coatings with random roughness the filaments tend to merge forming a branching structure. Impacts on inclined surfaces are used to deposit the filaments on top of the pillars for detailed study.

Current problems on the interaction of complex liquids (i.e. droplets or foams) with complex surfaces (i.e. soft deformable or porous surfaces) are addressed in the following areas: (1) wetting of deformable substrates and surface forces, (2) kinetics of wetting and spreading of non-Newtonian liquids over porous substrates, (3) kinetics of spreading of non-Newtonian solutions over hair, (4) free drainage of foams produced from non-Newtonian solutions, and (5) foam drainage placed on porous substrates. Equilibrium of liquid droplets on deformable substrates was investigated and the effect of disjoining pressure action in the vicinity of the apparent three phase contact line was taken into account. It was proven that the deformation of soft solids is determined by the action of surface forces inside the transition zone. Spreading/imbibition of blood, which is a power law shear thinning non-Newtonian liquid, over a dry porous layer was investigated from both theoretical and experimental points of view. It was found that blood droplet spreading/imbibition over porous substrates shows two different behaviours: (i) partial wetting case with three subsequent stages: initial fast spreading, constant maximum droplet base and the shrinkage of the droplet base; (ii) complete wetting case with only two stages: initial fast spreading and the shrinkage of the droplet base. The wetting of hair tresses by aqueous solutions of two commercially available polymers, AculynTM 22 (A22) and AculynTM 33 (A33) was investigated experimentally. Both A22 and A33 solutions demonstrate well pronounced shear thinning behaviour. Initial contact angle of the A22 and A33 solutions on hair tresses was about 100o. The A22 droplets remained on the hair tress after spreading for at least half an hour. However, a fast penetration of the A33 droplets inside the hair tresses was observed when advancing contact angle in the course of spreading reached a critical value of about 60o. This could be explained by Cassie-Wenzel wetting transition which is caused by filling the pores inside the porous media by liquid. The influence of non-Newtonian rheology of A22 and A33 solutions on foam drainage was also investigated experimentally and a new theory of foam drainage was presented for the case of free drainage. For lowly viscous polymeric solutions and under the assumption of rigid surface of the Plateau border, the predicted values of the time evolution of the foam height and liquid content were in good agreement with the experimental data. However, in the case of highly viscous solutions an interfacial mobility at the surface of the Plateau border has to be taken into account. A completely new theory of foam drainage placed on porous substrate was developed. It was found that there are three different regimes of the process: (i) a rapid imbibition, the imbibition into the porous substrate dominates as compared with the foam drainage; (ii) an intermediate imbibition, that is, the imbibition into the porous substrate and the rate of drainage are comparable; (iii) a slow imbibition, the rate of drainage inside the foam is higher than the imbibition into the porous substrate for a period of time and a free liquid layer is formed over the porous substrate.

The flow properties of two types of operating and clean coolants (A and B) were measured, both used in metalworking. Four samples of both operating liquids were sampled from the process monthly (from the beginning to the end of its use). All liquids were measured at 25 °C with an oil emulsion content of 4%. In addition, flow curves of pure cooling emulsions with concentration of coolant 2, 4, 6 and 8% were measured at 30, 35, 40, 45 and 50 °C. Rheological measurement was performed at geometry of concentric cylinders. Microbial activity and content of additives (Thermogravimetry) was determined in operating liquid A. Both operating liquids exhibited non-Newtonian behavior. Viscosity increased with the shear rate (10–100 s-1) and impurity level. Although the amount of impurity was approximately the same in both liquids, viscosity varied. For pure liquids, the viscosity increased with increasing concentration and decreased with increasing temperature, except for liquid A with concentration of coolants 6 and 8%, which, depending on the temperature, exhibited both shear thinning, shear thickening and Newtonian behavior. The results shown that impurity level of operating liquids has only minor effect on viscosity and flow properties, but it had an effect on cooling effect. Impurities diluted operating liquids, partial decomposition of the oil component may occur, but in particular, microbial activity causes skin problems of staff. Recommended is to introduce a specific control test for the presence of bacteria.

<p dir="ltr">Machine learning and deep learning techniques now provide innovative tools for addressing problems in biological, engineering, and physical systems. Physics-informed neural networks (PINNs) are a type of neural network that incorporate physical laws described by partial differential equations (PDEs) into their supervised learning tasks. This dissertation aims to enhance PINNs with improved training techniques and loss functions to tackle the complex physics of viscoelastic flow and rheology more effectively. The focus areas of the dissertation are listed as follows: i) Assigning relative weights to loss terms in training physics-informed neural networks (PINNs) is complex. We propose a solution using numerical integration via backward Euler discretization to leverage statistical properties of data for determining loss weights. Our study focuses on two and three-dimensional Navier-Stokes equations, using spatio-temporal velocity and pressure data to ascertain kinematic viscosity. We examine two-dimensional flow past a cylinder and three-dimensional flow within an aneurysm. Our method, tested for sensitivity and robustness against various factors, converges faster and more accurately than traditional PINNs, especially for three-dimensional Navier-Stokes equations. We validated our approach with experimental data, using the velocity field from PIV channel flow measurements to generate a reference pressure field and determine water viscosity at room temperature. Results showed strong performance with experimental datasets. Our proposed method is a promising solution for ’stiff’ PDEs and scenarios requiring numerous constraints where traditional PINNs struggle. ii) Machine learning algorithms are valuable for fluid mechanics, but high data costs limit their practicality. To address this, we present viscoelasticNet, a Physics-Informed Neural Network (PINN) framework that selects the appropriate viscoelastic constitutive model and learns the stress field from a given velocity flow field. We incorporate three non-linear viscoelastic models: Oldroyd-B, Giesekus, and Linear PTT. Our framework uses neural networks to represent velocity, pressure, and stress fields and employs the backward Euler method to construct PINNs for the viscoelastic model. The approach is multistage: first, it solves for stress, then uses stress and velocity fields to solve for pressure. ViscoelasticNet effectively learned the parameters of the viscoelastic constitutive model on noisy and sparse datasets. Applied to a two-dimensional stenosis geometry and cross-slot flow, our framework accurately learned constitutive equation parameters, though it struggled with peak stress at cross-slot corners. We suggest addressing this by exploring smaller domains. ViscoelasticNet can extend to other rheological models like FENE-P and extended Pom-Pom and learn entire equations, not just parameters. Future research could explore more complex geometries and three-dimensional cases. Complementing Particle Image Velocimetry (PIV), our method can determine pressure and stress fields once the constitutive equation is learned, allowing the modeling of future fluid applications. iii) Physics-Informed Neural Networks (PINNs) are widely used for solving inverse and forward problems in various scientific and engineering fields. However, most PINNs frameworks operate within the Eulerian domain, where physical quantities are described at fixed points in space. We explore coupling Eulerian and Lagrangian domains using PINNs. By tracking particles in the Lagrangian domain, we aim to learn the velocity field in the Eulerian domain. We begin with a sensitivity analysis, focusing on the time-step size of particle data and the number of particles. Initial tests with external flow past a cylinder show that smaller time-step sizes yield better results, while the number of particles has little effect on accuracy. We then extend our analysis to a real-world scenario: the interior of an airplane cabin. Here, we successfully reconstruct the velocity field by tracking passive particles. Our findings suggest that this coupled Eulerian-Lagrangian PINNs framework is a promising tool for enhancing traditional experimental techniques like particle tracking. It can be extended to learn additional flow properties, such as the pressure field for three-dimensional internal flows, and infer viscosity from passive particle tracking, providing deeper insights into complex fluids and their constitutive models. iv) Time-fractional differential equations are widely used across various fields but often present computational and stability challenges, especially in inverse problems. Leveraging Physics-Informed Neural Networks (PINNs) offers a promising solution for these issues. PINNs efficiently compute fractional time derivatives using finite differences and handle other derivatives via automatic differentiation. This study addresses two inverse problems: (1) anomalous diffusion and (2) fractional viscoelasticity. Our approach defines residual loss scaled with the standard deviation of observed data, using numerically generated and experimental datasets to learn fractional coefficients and calibrate parameters for the fractional Maxwell model. Our framework demonstrated robust performance for anomalous diffusion, maintaining less than 10% relative error in predicting the generalized diffusion coefficient and the fractional derivative order, even with 25% Gaussian noise added to the dataset. This highlights the framework’s resilience and accuracy in noisy conditions. We also validated our approach by predicting relaxation moduli for pig tissue samples, achieving relative errors below 10% compared to literature values. This underscores the efficacy of our fractional model with fewer parameters. Our method can be extended to model non-linear fractional viscoelasticity, incorporate experimental data for anomalous diffusion, and apply it to three-dimensional scenarios, broadening its practical applications.</p>

<p dir="ltr">Non-Newtonian fluid models such as the Bingham and Herschel-Bulkley models are used to characterize the flow behavior of many complex fluids and soft solids. The three parameter Herschel-Bulkley model captures the yield stress behavior and the nonlinear power law behavior. In this thesis, the semi-analytical solution of Herschel-Bulkley fluids provided by Covey and Stanmore is used to experimentally characterize the squeeze flow behavior. A ‘Squeeze Flow and Thermal Resistance Tester’ was custom designed to perform velocity controlled squeeze flow experiments. The tester has an additional capability of performing thermal resistance characterization adhering to the ASTM-D5470 standard. A novel framework is described for characterizing the three Herschel-Bulkley parameters (τy, n and ηHB) using the developed tester. </p><p dir="ltr">Thermal Interface Materials (TIMs) are used to efficiently dissipate heat from a heat generating component to a heat sink in an electronic package. Thermal grease is a type of TIM comprising of a base material (e.g. polymer) loaded with highly conducting filler particles (e.g, boron nitride, alumina or sometimes conducting metals such as aluminum or silver). These greases are expected to exhibit Herschel-Bulkley flow behavior. Hence, thermal greases are used as candidate materials for squeeze flow characterization. In addition to the flow characterization, the thermal resistance across these thermal greases are also characterized using the custom designed tester. Characterization of mechanical and thermal behavior of TIMs is crucial to predicting their long-term reliability. </p><p dir="ltr">The effect of in-situ isothermal baking duration and test temperature on flow behavior is studied. The increase in duration of isothermal baking at test temperature of 55◦C showed that the material tends to stiffen with baking duration. The increase in test temperature from 5◦C to 100◦C resulted in a decrease in the power law index n and viscosity ηHB. </p><p dir="ltr">Finally, a numerical simulation strategy for performing squeeze flow simulations is described. The characterized flow parameters from the squeeze flow experiments were used as input material parameters for a dynamic mesh-based numerical simulation of squeeze flow between parallel surfaces. The results of the experimental force response and numerical simulation results were compared and found to be in close agreement. In order to simulate flow of thermal greases in a package undergoing deformation, a non-flat test setup was fabricated and squeeze experiments were performed. Numerical simulations were subsequently performed for the non-flat surface using material parameters extracted from previous experiments and the results were compared. The results from both experiments and numerical simulations showed that the force response of thermal greases under non-flat surfaces was significantly higher than the planar case.</p>