An indirect boundary-element method for slow viscous flow in a bounded region containing air bubbles
This paper presents a novel formulation of the completed indirect boundary-element method to study the shrinkage of air bubbles on a slow viscous flow in a bounded region subject to surface tension. The formulation has application to viscous sintering, a process for manufacturing high-quality glass...
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| Published in | Journal of engineering mathematics Vol. 37; no. 4; pp. 305 - 326 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer
01.05.2000
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-0833 1573-2703 |
| DOI | 10.1023/A:1004631329906 |
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| Abstract | This paper presents a novel formulation of the completed indirect boundary-element method to study the shrinkage of air bubbles on a slow viscous flow in a bounded region subject to surface tension. The formulation has application to viscous sintering, a process for manufacturing high-quality glass by means of sol-gel processing. The theoretical background is explained in detail, including mathematical proofs of existence and uniqueness of solutions. Numerical results are included and compared to analytical and previous numerical solutions. |
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| AbstractList | This paper presents a novel formulation of the completed indirect boundary-element method to study the shrinkage of air bubbles on a slow viscous flow in a bounded region subject to surface tension. The formulation has application to viscous sintering, a process for manufacturing high-quality glass by means of sol-gel processing. The theoretical background is explained in detail, including mathematical proofs of existence and uniqueness of solutions. Numerical results are included and compared to analytical and previous numerical solutions. |
| Author | Power, H. Wrobel, L.C. Primo, A.R.M. |
| Author_xml | – sequence: 1 givenname: A.R.M. surname: Primo fullname: Primo, A.R.M. – sequence: 2 givenname: L.C. surname: Wrobel fullname: Wrobel, L.C. – sequence: 3 givenname: H. surname: Power fullname: Power, H. |
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| Cites_doi | 10.1080/00986448908940638 10.1017/CBO9780511624124 10.1137/0147047 10.1017/S0022112090001203 10.1007/978-3-642-48873-3 10.1016/0022-247X(89)90269-2 10.1017/S0022112090000234 10.1007/978-3-642-48860-3 10.1016/0021-9991(92)90309-M 10.1122/1.550040 10.1016/S0955-7997(97)00021-0 10.1007/BF00250771 10.1007/BF02238931 10.1093/imamat/51.2.123 10.1017/S002211209300326X |
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| Issue | 4 |
| Keywords | Bubbles Sintering Digital simulation Surface tension Slow flow Liquid phase sintering Viscous fluids Boundary element method Stokes flow |
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| References | H. K. Kuiken (232028_CR1) 1990; 214 S. J. Karrila (232028_CR8) 1989; 33 S. J. Karrila (232028_CR10) 1989; 82 H. Power (232028_CR6) 1987; 47 H. Power (232028_CR17) 1995 J. E. Gómez (232028_CR24) 1997; 19 H. A. Lorentz (232028_CR5) 1896; 5 H. Power (232028_CR11) 1990; 9 C. A. Brebbia (232028_CR21) 1984 H. Power (232028_CR9) 1989; 137 R. Courant (232028_CR19) 1992 A. R. M. Primo (232028_CR23) 1998 C. Pozrikidis (232028_CR26) 1989; 210 E. Goursat (232028_CR27) 1964 F. Hartmann (232028_CR20) 1989 S. Kim (232028_CR15) 1991 S. G. Mikhlin (232028_CR14) 1957 I. D. Chang (232028_CR25) 1961; 7 G. A. L. van de Vorst (232028_CR4) 1992; 49 O. A. Ladyzhenskaya (232028_CR18) 1963 G. A. L. van de Vorst (232028_CR22) 1993; 257 H. K. Kuiken (232028_CR2) 1996 H. Power (232028_CR12) 1992; 16 G. A. L. van de Vorst (232028_CR3) 1992; 100 H. Power (232028_CR7) 1987 H. Power (232028_CR13) 1993; 51 C. Pozrikidis (232028_CR16) 1992 |
| References_xml | – volume-title: A Course in Mathematical Analysis year: 1964 ident: 232028_CR27 – volume: 9 start-page: 111 year: 1990 ident: 232028_CR11 publication-title: Math. Appl. Comp. – volume: 82 start-page: 123 year: 1989 ident: 232028_CR10 publication-title: Chem. Eng. Commun. doi: 10.1080/00986448908940638 – volume-title: Boundry Integral and Singularity Methods for Linearized Viscous Flow year: 1992 ident: 232028_CR16 doi: 10.1017/CBO9780511624124 – volume-title: Novel Boundary Integral Formulations for Slow Viscous Flow with Moving Boundaries year: 1998 ident: 232028_CR23 – volume: 47 start-page: 689 year: 1987 ident: 232028_CR6 publication-title: SIAM J. Appl. Math. doi: 10.1137/0147047 – volume: 16 start-page: 61 year: 1992 ident: 232028_CR12 publication-title: Eng. Anal. with Boundary Elements – volume: 210 start-page: 1 year: 1989 ident: 232028_CR26 publication-title: J. Fluid Mech. doi: 10.1017/S0022112090001203 – volume-title: Introduction to Boundary Elements year: 1989 ident: 232028_CR20 doi: 10.1007/978-3-642-48873-3 – volume-title: Microhydrodynamics: Principles and Selected Applications year: 1991 ident: 232028_CR15 – start-page: 477 volume-title: Boundary Elements IX, Vol. 3 year: 1987 ident: 232028_CR7 – volume: 5 start-page: 168 year: 1896 ident: 232028_CR5 publication-title: Versl. Acad. Wetensch – volume: 137 start-page: 1 year: 1989 ident: 232028_CR9 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(89)90269-2 – volume-title: Integral Equations and their Application to Certain Problems in Mechanics, Mathematical Physics and Technology year: 1957 ident: 232028_CR14 – volume: 214 start-page: 503 year: 1990 ident: 232028_CR1 publication-title: J. Fluid Mech. doi: 10.1017/S0022112090000234 – volume-title: Boundary Element Techniques year: 1984 ident: 232028_CR21 doi: 10.1007/978-3-642-48860-3 – start-page: 75 volume-title: The Mathematics of Deforming Surfaces year: 1996 ident: 232028_CR2 – volume: 100 start-page: 50 year: 1992 ident: 232028_CR3 publication-title: J. Comp. Phys. doi: 10.1016/0021-9991(92)90309-M – volume: 33 start-page: 913 year: 1989 ident: 232028_CR8 publication-title: J. Rheology doi: 10.1122/1.550040 – volume: 19 start-page: 17 year: 1997 ident: 232028_CR24 publication-title: Eng. Anal. with Boundary Elements doi: 10.1016/S0955-7997(97)00021-0 – volume: 7 start-page: 388 year: 1961 ident: 232028_CR25 publication-title: Arch. Rational Mech. Anal. doi: 10.1007/BF00250771 – volume-title: Boundary Integral Methods in Fluid Mechanics year: 1995 ident: 232028_CR17 – volume-title: The Mathematical Theory of Viscous Incompressible Flow year: 1963 ident: 232028_CR18 – volume-title: Methods of Mathematical Physics year: 1992 ident: 232028_CR19 – volume: 49 start-page: 239 year: 1992 ident: 232028_CR4 publication-title: Computing doi: 10.1007/BF02238931 – volume: 51 start-page: 123 year: 1993 ident: 232028_CR13 publication-title: IMA J. Appl. Math. doi: 10.1093/imamat/51.2.123 – volume: 257 start-page: 667 year: 1993 ident: 232028_CR22 publication-title: J. Fluid Mech. doi: 10.1017/S002211209300326X |
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| SubjectTerms | Computational methods in fluid dynamics Cross-disciplinary physics: materials science; rheology Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Laminar flows Low-reynolds-number (creeping) flows Materials science Materials synthesis; materials processing Physics Powder processing: powder metallurgy, compaction, sintering, mechanical alloying, and granulation |
| Title | An indirect boundary-element method for slow viscous flow in a bounded region containing air bubbles |
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