TY - JOUR
T1 - A case study of chaotic mixing in deterministic flows
T2 - The partitioned-pipe mixer
AU - Khakhar, D. V.
AU - Franjione, J. G.
AU - Ottino, J. M.
N1 - Funding Information:
Acknowledgements-The authors would like to thank Professor H. Aref, Institute of Geophysics and Planetary Physics, University of California, San Diego, for timely comments regarding an earlier version of this paper, Dr. J. M. Greene, GA Technologies, San Diego, for suggesting the use of symmetries described in Section 6, and to the National Science Foundation for support in the form of grant CBT-8513686.
PY - 1987
Y1 - 1987
N2 - We exploit the connection between the kinematics of mixing and the theory of dynamical systems. The presentation takes the form of a case study of a novel continuous flow mixer-the partitioned-pipe mixer-to exemplify the application of theoretical concepts relating fluid mixing in deterministic chaotic systems. Two general points are stressed: firstly, the complexities that are invariably encountered during the course of analysis limit the detail to which it may be carried out, and secondly, naive analysis based on direct use of the theory may result in misleading conclusions. Starting with an approximate Stokes flow velocity field in the partitioned-pipe mixer, we study the mixing in terms of the flow patterns in the cross-section (Poincaré sections) and their relation to the conventionally used continuous mixing diagnostic, the residence time distribution, as well as to the local specific rate of stretching of material lines and the mixing efficiency. Some of the limitations of each of these methods of characterizing the mixing are exposed; however, together they provide a broad description of the mixing in the partitioned-pipe mixer, and indicate the utility of the theory. The applications of the ideas, within and outside chemical engineering, are many. The most obvious are the mixing of viscous liquids (such as molten polymers), the design of mixing devices for shear sensitive molecules and cells under non-turbulent conditions, prototype models of porous media, enhanced mass transfer devices, etc. Other applications can be expected in geophysics, environmental fluid mechanics, and condensed matter and plasma physics.
AB - We exploit the connection between the kinematics of mixing and the theory of dynamical systems. The presentation takes the form of a case study of a novel continuous flow mixer-the partitioned-pipe mixer-to exemplify the application of theoretical concepts relating fluid mixing in deterministic chaotic systems. Two general points are stressed: firstly, the complexities that are invariably encountered during the course of analysis limit the detail to which it may be carried out, and secondly, naive analysis based on direct use of the theory may result in misleading conclusions. Starting with an approximate Stokes flow velocity field in the partitioned-pipe mixer, we study the mixing in terms of the flow patterns in the cross-section (Poincaré sections) and their relation to the conventionally used continuous mixing diagnostic, the residence time distribution, as well as to the local specific rate of stretching of material lines and the mixing efficiency. Some of the limitations of each of these methods of characterizing the mixing are exposed; however, together they provide a broad description of the mixing in the partitioned-pipe mixer, and indicate the utility of the theory. The applications of the ideas, within and outside chemical engineering, are many. The most obvious are the mixing of viscous liquids (such as molten polymers), the design of mixing devices for shear sensitive molecules and cells under non-turbulent conditions, prototype models of porous media, enhanced mass transfer devices, etc. Other applications can be expected in geophysics, environmental fluid mechanics, and condensed matter and plasma physics.
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U2 - 10.1016/0009-2509(87)87056-2
DO - 10.1016/0009-2509(87)87056-2
M3 - Article
AN - SCOPUS:0023099621
SN - 0009-2509
VL - 42
SP - 2909
EP - 2926
JO - Chemical Engineering Science
JF - Chemical Engineering Science
IS - 12
ER -