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Pearlstein, Arne J Caraway IV, Willie D 2021-03-05T21:42:54Z 2021-03-05T21:42:54Z 2023-03-05T21:43:00Z 2020-12-11 2020-12 Pressure-driven diffusion, in which a flux of species in a binary or multi-component fluid is driven by a pressure gradient, is known to be an important mechanism for effecting separations in a variety of chemical systems, including the separation of 238UF6 from 235UF6 in gas centrifuges, and in analytical-scale separation of proteins and other macromolecules in their aqueous solutions. In both of those cases, the pressure-gradient is either steady or varies on a time scale which is large compared to other relevant time scales. Here, we investigate the effect of a standing or traveling pressure wave on the composition distribution in a binary liquid. The governing equations involve conservation of mass, momentum, energy, and species, which we simplify to a model involving only a diffusion-like equation for conservation of species, based on neglecting the effects of mass transfer on conservation of momentum and energy and thermoacoustic effects, which allows us to set the mass-averaged velocity to zero and to neglect the Dufour contribution to the energy flux. We focus on understanding the behavior of the resulting nonlinear, time-dependent, and time-periodically forced partial differential equation, of a type that has received relatively little attention. To better understand the importance of nonlinearity to the underlying physics of pressure-driven diffusion in the context of ultrasonically-driven separation, we first linearize our governing equation, and compare the solutions of the original nonlinear equation with the solutions of the linear analogue. A spectral-element technique is employed to obtain long-time solutions of the linear and nonlinear equations as the coefficients are varied. This study analyzes these long-time solutions to better understand the behavior of the solutions and to determine whether ultrasound can affect the separation of a binary liquid mixture by means of pressure-driven diffusion. Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2022-12-01 The student, Willie Caraway IV, accepted the attached license on 2020-12-10 at 20:56. The student, Willie Caraway IV, submitted this Thesis for approval on 2020-12-10 at 21:13. This Thesis was approved for publication on 2020-12-11 at 11:38. DSpace SAF Submission Ingestion Package generated from Vireo submission #16119 on 2021-03-04 at 16:20:52 Made available in DSpace on 2021-03-05T21:42:54Z (GMT). No. of bitstreams: 11 CARAWAYIV-THESIS-2020.pdf: 2483762 bytes, checksum: 716af07ac08cc8ddcd826c770a15626f (MD5) CarawayThesis_Movie1.zip: 4173785 bytes, checksum: 6f98a8c627c4bfb76a6efc66bb0a6c4a (MD5) CarawayThesis_Movie2.zip: 4087726 bytes, checksum: adc733171b7c9b018adf635ca402d0a9 (MD5) CarawayThesis_Movie3.zip: 3807530 bytes, checksum: 0d1180a74bab21d5019342b9ac707870 (MD5) CarawayThesis_Movie4.zip: 4268296 bytes, checksum: afa7417f635ffbbc9a229d5b1caece58 (MD5) CarawayThesis_Movie5.zip: 3512391 bytes, checksum: 0cff77136bdf510e27158d0934568d99 (MD5) CarawayThesis_Movie6.zip: 3215352 bytes, checksum: 61046ec0025f3964a2aab07b903baa73 (MD5) CarawayThesis_Movie7.zip: 13080009 bytes, checksum: fbd3976798545fa96a210d9d93ce4b63 (MD5) CarawayThesis_Movie8.zip: 2609498 bytes, checksum: 14cf64cc3fa240ca001cf1089ae931ae (MD5) CarawayThesis_Movie9.zip: 3305582 bytes, checksum: 68ffb4e7eca0061eef327aabeedcbf17 (MD5) LICENSE.txt: 4209 bytes, checksum: f7c6c02ec0a33987537a0ca0bc91420a (MD5) Previous issue date: 2020-12-11 Embargo set by: Seth Robbins for item 117247 Lift date: 2023-03-05T21:43:00Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only application/pdf http://hdl.handle.net/2142/109542 en Copyright 2020 Willie D. Caraway IV pressure-driven diffusion periodic forcing acoustic ultrasound separation Analysis of a partial differential equation related to pressure-driven separations of binary liquids text Thesis Mechanical Sci & Engineering Mechanical Engineering University of Illinois at Urbana-Champaign Thesis M.S.