Flow induced instability of the interface between a fluid and a gel at low Reynolds number
Year: 1994
Type: article
Abstract: The stability of the interface between a gel of thickness HR and a Newtonian fluid of thickness R subjected to a linear shear flow is studied in the limit where inertial effects are negligible. The shear stress for the gel contains an elastic part that depends on the local displacement field and a viscous component that depends on the velocity field. The shear flow at the surface tends to destabilize the surface fluctuations, and the critical strain rate γc, which is the minimum strain rate required for unstable fluctuations, is determined as a function of the dimensionless quantities H, ηr = (ηg/ηf), and T = (Γ/ER). Here ηg and ηf are the gel and fluid viscosities, E is the gel elasticity, Γ is the surface tension of the gel — fluid interface and the strain rate γ is scaled by (E/ηf). In the limit H ↦∞, we find that γc decreases proportional to H-1 independent of ηr and T. But at finite H, γc is strongly dependent on ηr and T. For ηr ≥1, the interface is stable for all values of the strain rate for $H < \sqrt{\eta_{\rm r}}$, while there are unstable traveling waves for $H > \sqrt{\eta_{\rm r}}$. For ηr = 1 and H ↦1, we find that γc ∝(H - 1)1/2 for T=0 and γc ∝(H - 1)3/4T1/4 for T ≠0. For ηr > 1, the analysis indicates that $\gamma_{\rm c} \propto(H-\sqrt{\eta_{\rm r}})^{-1}$ independent of T for $H \to \sqrt{\eta_{\rm r}}$. For ηr < 1, the onset of instability depends strongly on the parameter T. For T = 0, the critical strain rate is finite in the limit H ↦0, while for T ≠0 the critical strain rate diverges at a finite value of H. This minimum H decreases proportional to ηr for large T. The instability is caused by the energy transfer from the mean flow to the fluctuations due to the work done by the mean flow at the interface.
Source: Journal de Physique II
DOI: 10.1051/jp2:1994173
Authors: V. Kumaran, G. H. Fredrickson, P. Pincus
Institution: University of California, Santa Barbara
Language: English
Subfield: Fluid Flow and Transfer Processes
Field: Chemical Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2020554690