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, 9 (1), 9402

Modulation of Viscoelastic Fluid Response to External Body Force

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Modulation of Viscoelastic Fluid Response to External Body Force

Meng Zhang et al. Sci Rep.

Abstract

Transient flow responses of viscoelastic fluids to different external body forces are studied. As a non-Newtonian fluid, the viscoelastic fluid exhibits significant elastic response which does not raise in Newtonian fluid. Here, we investigate the transient response of a viscoelastic Poiseuille flow in a two-dimensional channel driven by external body forces in different forms. The velocity response is derived using the Oldroyd-B constitutive model in OpenFOAM. Responses in various forms like damped harmonic oscillation and periodic oscillation are induced and modulated depending on the fluid intrinsic properties like the viscosity and the elasticity. The external body forces like constant force, step force and square wave force are applied at the inlet of the channel. Through both time domain and frequency domain analysis on the fluid velocity response, it is revealed that the oscillation damping originates from the fluid viscosity while the oscillation frequency is dependent on the fluid elasticity. The velocity response of the applied square waves with different periods shows more flexible modulation signal types than constant force and step force. An innovative way is also developed to characterize the relaxation time of the viscoelastic fluid by modulating the frequency of the square wave force.

Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Schematic of two-dimensional Poiseuille flow.
Figure 2
Figure 2
Process flow of the numerical simulation.
Figure 3
Figure 3
Velocity responses to constant force F0 = 2 on the Newtonian fluid flow with EN = 0 and viscoelastic fluid flow with EV = 1. β = 0.01. Insert figure: fast Fourier transform of the velocity of viscoelastic fluid flow.
Figure 4
Figure 4
(a) Centerline velocity of viscoelastic fluid flow and (b) the amplitude of velocity under different constant forces. The circles in (a) represent the numerically simulated results, and the solid line is the fitted value A in Eq. (12).
Figure 5
Figure 5
(a) Elasticity number dependent velocity of viscoelastic fluid flow with viscosity β = 0.01 response to a constant force F0 = 2; (b) frequency domain of the temporal response; (c) amplitude of the first velocity peak; (d) drop of domain frequency as elasticity number increases.
Figure 6
Figure 6
(a) Centerline velocity for viscoelastic fluid flow with E = 10, F0 = 2 and different β; (b) the corresponding Fourier transform of transient velocity.
Figure 7
Figure 7
(a) Velocity response of viscoelastic fluid flow to the rectangular force with different amplitudes applied with the same unloaded time Tr = 1; (b) the Fourier transform of the response in (a).
Figure 8
Figure 8
(a) Velocity response of viscoelastic fluid flow to the rectangular force with the same amplitude F0 = 2 applied with different unloaded time Tr; (b) the Fourier transform of the response in (a).
Figure 9
Figure 9
Velocity responses of viscoelastic fluid flow to the applied square wave force with periods of 1, 4, 8 and 16 s, respectively.
Figure 10
Figure 10
Frequency responses of viscoelastic fluid flow to the applied square wave force with periods of 1, 4, 8 and 16 s, respectively.

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