Drop Rise and Interfacial Coalescence Initiation in Complex Materials

Abstract

Drop rise and coalescence phenomena in complex materials hold significant relevance for various environmental and industrial processes. The intricate dynamics of the sequential steps of drop rise, collision, and film drainage are influenced by non-Newtonian behaviors such as plasticity and elasticity exhibited by the surrounding material. A comprehensive understanding of these processes is crucial for the efficient design and operation of industrial mixing and separating units. However, despite their importance, the underlying mechanisms governing these phenomena are not entirely comprehended. The primary objective of this thesis is to investigate the rise and interfacial coalescence initiation of a Newtonian drop in complex materials using time-dependent direct numerical simulations. The surrounding material is progressively modeled with formulations of increasing complexity, namely, Newtonian, inelastic viscoplastic, viscoelastic, and elasto-viscoplastic. To conduct the study, the elasto-viscoplastic Saramito model is implemented and validated. The investigation focuses on elucidating the influence of plastic, elastic, inertial, viscous, and surface tension effects, as well as their interaction on the dynamics of drop rise and coalescence initiation. Initially, the entrapment condition of spherical and non-spherical drops in inelastic viscoplastic materials is assessed in terms of the ratio of the force exerted by the yield stress and the buoyancy force. It is found that when determining the force exerted by the yield stress based on the radius of the maximum cross-sectional area of the drop (normal to buoyancy), this ratio remains constant for drops with low viscosity. However, for highly viscous drops, the ratio decreases asymptotically until it reaches the limit for solid spheres. For non-spherical drops, surface tension may yield the surrounding material to minimize the surface energy of the drop, making the drop to be permanently or only temporally mobile. For elasto-viscoplastic materials, elasticity increases the level of plasticity required for entrapment. Drop rise plays an important role in the initiation of the coalescence process. Inertial effects tend to increase the drop velocity and width, while an increase in the drop’s viscosity increases viscous dissipation and slows down the drop. The influence of surface tension on the droplet velocity and width depends on the dominant forces in the flow, which can cause both an increase or decrease in these quantities. Plastic effects result in a reduction of droplet velocity and width. Drop rise in viscoelastic materials is a dynamic process, influenced by the ratio of the relaxation time of the material to the characteristic rise time of the drop. Elastic effects also contribute to a reduction in drop width, facilitating its rise. In the case of elasto-viscoplastic materials, the interplay between elastic and plastic effects gives rise to intriguing behaviors. Plastic effects enhance the elastic behavior of the material, resulting in the appearance of the negative wake and teardrop shape (both characteristic of elastic behavior) for lower values of the elastic modulus when increasing the level of plasticity. Conversely, elastic effects suppress the plastic response of the material, leading to an expanded yielded region and reduced restriction on drop mobility by plasticity with increasing levels of elasticity. Regarding the coalescence phenomenon, plasticity manifests two main effects on the film drainage process. Firstly, it induces the formation of shorter and more spherical films, and secondly, it increases the resistance of the film to flow. The effect on the film shape facilitates the film drainage process, while the effect on the resistance of the film to flow hinders it. In regimes characterized by low surface tension, the influence of plasticity on the film geometry becomes more prominent than the resistance effect, resulting in a reduction in the drainage time. Conversely, in regimes characterized by high surface tension, where the interfaces between the fluids are less deformable, the resistance effect becomes more dominant compared to the effect of film shape, leading to an increase in the drainage time with the level of plasticity. Elastic effects also contribute to the formation of shorter films, thereby facilitating the drainage process. The partial or over activation of the viscosity of the elastic material further affects the rate of film drainage. Specifically, the partial activation of viscosity increases the drainage rate, while over-activation decreases it. In the case of elasto-viscoplastic materials, plastic effects enhance the partial activation of the material’s viscosity, facilitating the initial stage of the drainage process. Additionally, elastic deformation makes it more difficult for the drainage film to freeze due to yield stress.