Rheological behavior of a confined bead-spring cube consisting of equal Fraenkel springs

A.I.M. Denneman, A.I.M. Denneman, R.J.J. Jongschaap, J. Mellema

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

A general bead-spring model is used to predict linear viscoelastic properties of a non-Hookean bead-spring cube immersed in a Newtonian fluid. This K×K×K cube consist of K 3 beads with equal friction coefficients and 3K 2(K–1) equal Fraenkel springs with length q. The cube has a topology based upon a simple cubic lattice and it is confined to a container of volume V s=(Kq)3. The confined cube is subjected to a small-amplitude oscillatory shear flow with frequency w, where the directions of the flow velocity and its gradient coincide with two principal directions of the simple cubic bead-spring structure. For this flow field an explicit constitutive equation is obtained with analytical expressions for the relaxation times and their strengths. It is found that the resulting relaxation spectrum belonging to a K×K×K Fraenkel cube has the same shape as the one belonging to a `two-dimensional' K×K cubic network consisting of equal Hookean springs. On the other hand, the dynamic moduli G'(w) and G''(w) belonging to a K×KK Fraenkel cube appear to have the same frequency-dependency as the ones belonging to a `three-dimensional' K×KK cube consisting of equal Hookean springs.
Original languageUndefined
Pages (from-to)219-232
Number of pages14
JournalJournal of engineering mathematics
Volume38
Issue number38
DOIs
Publication statusPublished - 2000

Keywords

  • IR-73593
  • METIS-128968
  • Rheology - bead-spring cube - Fraenkel springs - relaxation spectra - dynamic moduli

Cite this

Denneman, A.I.M. ; Denneman, A.I.M. ; Jongschaap, R.J.J. ; Mellema, J. / Rheological behavior of a confined bead-spring cube consisting of equal Fraenkel springs. In: Journal of engineering mathematics. 2000 ; Vol. 38, No. 38. pp. 219-232.
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abstract = "A general bead-spring model is used to predict linear viscoelastic properties of a non-Hookean bead-spring cube immersed in a Newtonian fluid. This K×K×K cube consist of K 3 beads with equal friction coefficients and 3K 2(K–1) equal Fraenkel springs with length q. The cube has a topology based upon a simple cubic lattice and it is confined to a container of volume V s=(Kq)3. The confined cube is subjected to a small-amplitude oscillatory shear flow with frequency w, where the directions of the flow velocity and its gradient coincide with two principal directions of the simple cubic bead-spring structure. For this flow field an explicit constitutive equation is obtained with analytical expressions for the relaxation times and their strengths. It is found that the resulting relaxation spectrum belonging to a K×K×K Fraenkel cube has the same shape as the one belonging to a `two-dimensional' K×K cubic network consisting of equal Hookean springs. On the other hand, the dynamic moduli G'(w) and G''(w) belonging to a K×KK Fraenkel cube appear to have the same frequency-dependency as the ones belonging to a `three-dimensional' K×KK cube consisting of equal Hookean springs.",
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Rheological behavior of a confined bead-spring cube consisting of equal Fraenkel springs. / Denneman, A.I.M.; Denneman, A.I.M.; Jongschaap, R.J.J.; Mellema, J.

In: Journal of engineering mathematics, Vol. 38, No. 38, 2000, p. 219-232.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Rheological behavior of a confined bead-spring cube consisting of equal Fraenkel springs

AU - Denneman, A.I.M.

AU - Denneman, A.I.M.

AU - Jongschaap, R.J.J.

AU - Mellema, J.

PY - 2000

Y1 - 2000

N2 - A general bead-spring model is used to predict linear viscoelastic properties of a non-Hookean bead-spring cube immersed in a Newtonian fluid. This K×K×K cube consist of K 3 beads with equal friction coefficients and 3K 2(K–1) equal Fraenkel springs with length q. The cube has a topology based upon a simple cubic lattice and it is confined to a container of volume V s=(Kq)3. The confined cube is subjected to a small-amplitude oscillatory shear flow with frequency w, where the directions of the flow velocity and its gradient coincide with two principal directions of the simple cubic bead-spring structure. For this flow field an explicit constitutive equation is obtained with analytical expressions for the relaxation times and their strengths. It is found that the resulting relaxation spectrum belonging to a K×K×K Fraenkel cube has the same shape as the one belonging to a `two-dimensional' K×K cubic network consisting of equal Hookean springs. On the other hand, the dynamic moduli G'(w) and G''(w) belonging to a K×KK Fraenkel cube appear to have the same frequency-dependency as the ones belonging to a `three-dimensional' K×KK cube consisting of equal Hookean springs.

AB - A general bead-spring model is used to predict linear viscoelastic properties of a non-Hookean bead-spring cube immersed in a Newtonian fluid. This K×K×K cube consist of K 3 beads with equal friction coefficients and 3K 2(K–1) equal Fraenkel springs with length q. The cube has a topology based upon a simple cubic lattice and it is confined to a container of volume V s=(Kq)3. The confined cube is subjected to a small-amplitude oscillatory shear flow with frequency w, where the directions of the flow velocity and its gradient coincide with two principal directions of the simple cubic bead-spring structure. For this flow field an explicit constitutive equation is obtained with analytical expressions for the relaxation times and their strengths. It is found that the resulting relaxation spectrum belonging to a K×K×K Fraenkel cube has the same shape as the one belonging to a `two-dimensional' K×K cubic network consisting of equal Hookean springs. On the other hand, the dynamic moduli G'(w) and G''(w) belonging to a K×KK Fraenkel cube appear to have the same frequency-dependency as the ones belonging to a `three-dimensional' K×KK cube consisting of equal Hookean springs.

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KW - METIS-128968

KW - Rheology - bead-spring cube - Fraenkel springs - relaxation spectra - dynamic moduli

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