caa a22 4500 46316251X CHVBK 20180406164751.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s11242-007-9122-7 doi (NATIONALLICENCE)springer-10.1007/s11242-007-9122-7 Stabilizing effect of diffusion in enhanced oil recovery and three-layer Hele-Shaw flows with viscosity gradient [Elektronische Daten] [Prabir Daripa, G. Paşa] In the presence of diffusion, stability of three-layer Hele-Shaw flows which models enhanced oil recovery processes by polymer flooding is studied for the case of variable viscosity in the middle layer. This leads to the coupling of the momentum equation and the species advection-diffusion equation the hydrodynamic stability study of which is presented in this paper. Linear stability analysis of a potentially unstable three-layer rectilinear Hele-Shaw flow is used to examine the effects of species diffusion on the stability of the flow. Using a weak formulation of the disturbance equations, upper bounds on the growth rate of individual disturbances and on the maximal growth rate over all possible disturbances are found. Analytically, it is shown that a short-wave disturbance if unstable can be stabilized by mild diffusion of species, where as an unstable long-wave disturbance can always be stabilized by strong diffusion of species. Thus, an otherwise unstable three-layer Hele-Shaw flow can be completely stabilized by a large enough diffusion, i.e., by increasing enough the magnitude of the species diffusion coefficient. The magnitude of this diffusion coefficient required to completely stabilize the flow will depend on the magnitude of interfacial viscosity jumps and the viscosity gradient of the basic viscous profile of the middle layer. Springer Science+Business Media, Inc., 2007 Three-layer Hele-Shaw flows nationallicence Improved oil recovery nationallicence Stability of flows nationallicence Sturm-Liouville problem nationallicence Upper bound nationallicence Daripa Prabir Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA aut Paşa G. Institute of Mathematics "Simion Stoillow” of Romanian Academy, 70700, Bucharest, Romania aut Transport in Porous Media Springer Netherlands 70/1(2007-10-01), 11-23 0169-3913 70:1<11 2007 70 11242 https://doi.org/10.1007/s11242-007-9122-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-007-9122-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Daripa Prabir Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA aut NATIONALLICENCE 700 1- Paşa G. Institute of Mathematics "Simion Stoillow” of Romanian Academy, 70700, Bucharest, Romania aut NATIONALLICENCE 773 0- Transport in Porous Media Springer Netherlands 70/1(2007-10-01), 11-23 0169-3913 70:1<11 2007 70 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer