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Chaos in Space
Published in Pier Luigi Gentili, Untangling Complex Systems, 2018
The aqueous solution displaces the viscous fluid generating beautiful structures characterized by fingers of different shapes and sizes. The phenomenon of viscous fingering has been studied for a long time because it is relevant in engineering. For instance, the petroleum industry has been trying consistently to find ways of inhibiting viscous fingering because it limits oil recovery in a porous media. Viscous fingering is also important for the study of pattern formation in non-equilibrium conditions when the interplay between microscopic interfacial dynamics and external macroscopic forces plays a crucial role (Ben-Jacob and Garik 1990). Figure 11.16 shows just a few examples of the uncountable morphologies that can be obtained in the Hele-Shaw cell.
Polymer Dynamics and Rheology
Published in Richard A. Pethrick, Gennadi E. Zaikov, Teiji Tsuruta, Naoyuki Koide, Polymer Yearbook 13, 2019
When fluid with low viscosity is injected onto viscous liquid, viscous fingering occurs at the interface. K. Makino, M. Kawaguchi (3684, E1291) used aqueous poly electrolyte solution and compressed air to observe the pattern formation. Fingers grew while making side branching. Change in surface tension by addition of isopropyl alcohol surpressed side branching. The shape of the pattern is quite different from that observed in glycerin, indicating the important role of the elasticity of the system.
Experimental and numerical study of the impact of viscosity ratio and velocity on the multiphase flow in micromodels
Published in Journal of Dispersion Science and Technology, 2020
Qumars Azizi, Seyed Hassan Hashemabadi, Soheil Akbari
Aker[5] showed that at low capillary numbers, when capillary force becomes more important compared with viscous force, the observed structures include a rough and wide front, with open structures on many length scales bounded by surrounded defending fluid clusters ranging from the size of the pore to the length of the system. The width of the finger is similar to the pore size, and the general form of the pattern intensely depends on the capillary number, structure of pore and geometry. In capillary fingering, the fluid can advance from a pore through the largest pore throat in any direction. Therefore, it may advance normally to the flow direction or even in the backward direction into new pores. Viscous fingering arising from adverse mobility contrasts, when a less viscous fluid displaces a more viscous fluid (m < 1), the fluids interface may become unstable. The interface stability of two-fluids of different viscosity has been studied extensively.[6–13] The fingering pattern is considered by several loosely connected or disconnected flow paths that advance toward the outlet. The morphology of the growing phase is complicated and describable in terms of fractal geometry. Fractal is a mathematical set that exhibits a repeating pattern that displays at every scale and replication is exactly the same at every scale, and also includes the idea of a detailed pattern that repeats itself. Fractal geometry is a rough or fragmented geometric shape that can be divided into segments, in which each segment is a small scale of the whole (named self-similarity).[14–16] The region where the kind of unstable fingers changes (capillary to viscous) or unstable regime to stable one is normally represented as the crossover zone.[17–20] The transition from these forms happens at a capillary number that depends on the system (heterogeneity,[21] contact angle and size of the system[22]).