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Temporal stability of a viscoelastic immersed thread in a confined region
Gunawan A.Y.a, Molenaar J.b, van de Ven A.A.F.b
a Departemen Matematika, Institut Teknologi Bandung, Indonesia
b Dept. of Mathematics/Computer Sci., Eindhoven University of Technology, Netherlands
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]In this paper, we consider an infinitely long viscoelastic thread in a tube filled with a Newtonian fluid. We apply Jeffreys model as the rheological relation for the thread. The fluid and thread move due to a constant pressure gradient, but this highly viscous flow is so slowly that the quasi-static creeping flow approximation is applicable (low-Reynolds number flow). We investigate the effect of the ratio of viscosities, fluid elasticity, confinement and prescribed flow on the stability of the immersed thread. The stability is characterized by the maximum growth rate of a random perturbation. The more viscous the thread is, the more time it takes to break up. A viscoelastic thread breaks up initially faster than a Newtonian one, and with smaller wave number. The thread breaks up slower when the degree of confinement is higher. A critical gap width beyond which the presence of the wall of the tube has no longer an effect on the stability of the thread is found. In case of a Newtonian thread the surrounding flow only causes the thread to be oscillatory unstable with the growth rate equal to the one within a fluid at rest. Moreover, in case of a viscoelastic thread the flow contributes to both the real and the imaginary parts of the growth rate. So, a viscoelastic thread will be oscillatory unstable. Furthermore, it breaks up faster than the one within a fluid at rest. © 2004 Elsevier B.V. All rights reserved.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Jeffreys model,Newtonian fluid,Temporal stability,Viscoelastic thread[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Confinement,Creeping flow,Jeffreys model,Poiseuille flow[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]This research is supported by QUE-Project (IBRD Loan No. 4193-IND) of Departemen Matematika, Institut Teknologi Bandung, Indonesia.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1016/j.jnnfm.2004.02.014[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]