Electroviscoelasticity of liquid/liquid interfaces: Fractional order van der Pol model -nonlinear and linearized case
Апстракт
A number of theories that describe the behavior of liquid-liquid interfaces have been developed and applied to various dispersed systems e.g., Stokes, Reiner-Rivelin, Ericksen, Einstein, Smoluchowski, Kinch. A new, recently developed, theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids. Up to day, there are three possible mathematical formalisms discussed related to the theory of electroviscoelasticity. The first is tension tensor model where the normal and tangential forces are considered, only in mathematical formalism, regardless of their origin (mechanical and/or electrical). The second is van der Pol derivative model presented by the linear and non-linear differential equations. Finally, the third model presents an effort to generalize the previous van der Pol equation, i.e. the ordinary time derivatives and integrals are now replaced with corresponding fracti...onal-order time derivatives and integrals of order p lt 1. Central parts of this paper are: proposed algorithm, using suitable numerical method, to obtain a homogeneous solution of a previous nonlinear equation of van der Pol type, and numerical solution of linearized fractional equation of the van der Pol type, using Grunwald definition of fractional differ-integral forms.
Кључне речи:
Fractional-order model / Finely dispersed systems / Emulsions / Electroviscoelasticity / Deformable interfacesИзвор:
CHISA 2006 - 17th International Congress of Chemical and Process Engineering, 2006Scopus: 2-s2.0-34748860412
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Lazarević, Mihailo AU - Spasić, Aleksandar M. AU - Krstić, Dimitrije N. PY - 2006 UR - https://machinery.mas.bg.ac.rs/handle/123456789/558 AB - A number of theories that describe the behavior of liquid-liquid interfaces have been developed and applied to various dispersed systems e.g., Stokes, Reiner-Rivelin, Ericksen, Einstein, Smoluchowski, Kinch. A new, recently developed, theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids. Up to day, there are three possible mathematical formalisms discussed related to the theory of electroviscoelasticity. The first is tension tensor model where the normal and tangential forces are considered, only in mathematical formalism, regardless of their origin (mechanical and/or electrical). The second is van der Pol derivative model presented by the linear and non-linear differential equations. Finally, the third model presents an effort to generalize the previous van der Pol equation, i.e. the ordinary time derivatives and integrals are now replaced with corresponding fractional-order time derivatives and integrals of order p lt 1. Central parts of this paper are: proposed algorithm, using suitable numerical method, to obtain a homogeneous solution of a previous nonlinear equation of van der Pol type, and numerical solution of linearized fractional equation of the van der Pol type, using Grunwald definition of fractional differ-integral forms. C3 - CHISA 2006 - 17th International Congress of Chemical and Process Engineering T1 - Electroviscoelasticity of liquid/liquid interfaces: Fractional order van der Pol model -nonlinear and linearized case UR - https://hdl.handle.net/21.15107/rcub_machinery_558 ER -
@conference{ author = "Lazarević, Mihailo and Spasić, Aleksandar M. and Krstić, Dimitrije N.", year = "2006", abstract = "A number of theories that describe the behavior of liquid-liquid interfaces have been developed and applied to various dispersed systems e.g., Stokes, Reiner-Rivelin, Ericksen, Einstein, Smoluchowski, Kinch. A new, recently developed, theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids. Up to day, there are three possible mathematical formalisms discussed related to the theory of electroviscoelasticity. The first is tension tensor model where the normal and tangential forces are considered, only in mathematical formalism, regardless of their origin (mechanical and/or electrical). The second is van der Pol derivative model presented by the linear and non-linear differential equations. Finally, the third model presents an effort to generalize the previous van der Pol equation, i.e. the ordinary time derivatives and integrals are now replaced with corresponding fractional-order time derivatives and integrals of order p lt 1. Central parts of this paper are: proposed algorithm, using suitable numerical method, to obtain a homogeneous solution of a previous nonlinear equation of van der Pol type, and numerical solution of linearized fractional equation of the van der Pol type, using Grunwald definition of fractional differ-integral forms.", journal = "CHISA 2006 - 17th International Congress of Chemical and Process Engineering", title = "Electroviscoelasticity of liquid/liquid interfaces: Fractional order van der Pol model -nonlinear and linearized case", url = "https://hdl.handle.net/21.15107/rcub_machinery_558" }
Lazarević, M., Spasić, A. M.,& Krstić, D. N.. (2006). Electroviscoelasticity of liquid/liquid interfaces: Fractional order van der Pol model -nonlinear and linearized case. in CHISA 2006 - 17th International Congress of Chemical and Process Engineering. https://hdl.handle.net/21.15107/rcub_machinery_558
Lazarević M, Spasić AM, Krstić DN. Electroviscoelasticity of liquid/liquid interfaces: Fractional order van der Pol model -nonlinear and linearized case. in CHISA 2006 - 17th International Congress of Chemical and Process Engineering. 2006;. https://hdl.handle.net/21.15107/rcub_machinery_558 .
Lazarević, Mihailo, Spasić, Aleksandar M., Krstić, Dimitrije N., "Electroviscoelasticity of liquid/liquid interfaces: Fractional order van der Pol model -nonlinear and linearized case" in CHISA 2006 - 17th International Congress of Chemical and Process Engineering (2006), https://hdl.handle.net/21.15107/rcub_machinery_558 .