Polymer additives, such as polyacrylamide, have unique characteristics in liquids, including highly non-linear, non-Newtonian behavior. To augment transport, the polymers are stretched in constriction by flow strain, which is induced by, for example, streamline curvature. The extensibility of the polymer and resulting polymer deformation, leads to a sharp growth in the local elastic stress, a sequence of events referred to as the Weissenberg instability, which occurs when the Weissenberg number is greater than approximately ½ or 0.5. Overall consequences include increased polymer viscosity, in some cases, by up to 3 orders of magnitude. Such changes also lead to increases in effective polymer thermal conductivity, and augmentation of thermal transport. However, such increases in thermal transport from elastic turbulence have never before been investigated, and thus, to develop innovative methods to enhance mixing and thermal transport in small-scale environments at low Reynolds numbers, experiments and simulations will be coordinated and conducted on thermal transport in elastic turbulence. One principal aim is to determine the efficacy of using elastic turbulence to augment thermal transport, by characterizing the phenomena both experimentally and numerically. Numerical modeling and prediction of the physical trends of both measured and non-measured quantities will be performed with three-dimensional Direct Numerical Simulations (DNS). As such, another overall intent is enhancement of fundamental understanding of the associated physical processes associated with elastic turbulence, as it is induced in liquids by polymers subject to stretching and constriction by flow strain. A resulting product will be new numerical and analytic models to describe and represent the related elastic turbulence physical phenomena, especially thermal transport. Generally, milliscale (or millimeter-scale) devices and flow environments will be employed to produce flows in the rotating-Couette and Dean flow geometries. These flows each provide shear and streamline curvature (centrifugal effects) and thus are ideally suited to producing elastic turbulence in dilute polymer solutions. As part of this research, a new Prandtl number model and a new effective conductivity model for elastic turbulence will also be developed. This will be facilitated by measurements of flow characteristics (time-varying and time-averaged) and heat transfer coefficients, and fully three-dimensional direct numerical simulations (DNS) with non-linear elastic models, such the FENE-P, to elucidate polymer solution characteristics. The present study follows several important recent, related fluid mechanics investigations, and as such, will address important gaps in knowledge regarding the effects and influences of polymer additives on thermal transport in milliscale and microscale liquid flows. As such, the present study is highly transformational and relevant because of the new physical understanding which will be provided, and because of the variety of applications.
In recent years, much attention has been devoted to technological advances related to miniaturization, with particular attention to technologies at the micro-scale and nano-scale, but also to milli-scale devices. For example, improvements in manufacturing technology and micro-fabrication have led to the miniaturization of a variety of different types of devices and sensors. The ability to predict the fluid motion in and around these devices is essential for their design and optimization. As the length scales of these devices decrease for liquid flows, effects become significant which are not present in larger-scale devices. Because of the small dimensions and very low speeds which are involved, the flows within these components are generally laminar, with relatively low magnitudes of mixing and thermal transport. Such laminar flows are thus a consequence of the limitations imposed by the small sizes of the miniature devices. Such flows, and the devices associated with them, are vital and important for a range of applications in areas such as pharmaceutics, medicine, heat transfer, biomedical engineering, and electronics cooling. In every case, the devices associated with these application areas would generally benefit by increased mixing and augmented transport from elastic turbulence. Such mixing is important for a variety of situations within the mentioned application areas, including the use of liquids to cool electronic components, mixing of different chemical components to manufacture pharmaceuticals, lab-on-a-chip devices which involve the interaction and mixing of different fluid streams, and miniature heat exchangers for use in devices ranging from automobiles, to appliances, to components within space systems, including satellites.
