Surfactant-induced instability of a sheared liquid layer

Pozrikidis, C.; Hill, Antonio

doi:10.1093/imamat/hxq067

Cited by 7 publications

(15 citation statements)

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“…We observe a nonuniform distribution of the surface tension for the BLV, ∂σ * /∂s = 0. This is in line with the surfactant multilamellar droplet [18] and the instability of thin liquid films on a solid substrate [19].…”

Section: Observations and Discussionsupporting

confidence: 78%

Complex dynamics of a bilamellar vesicle as a simple model for leukocytes

Kaoui

Harting

2013

Soft Matter

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The influence of the internal structure of a biological cell (e.g., a leukocyte) on its dynamics and rheology is not yet fully understood. By using 2D numerical simulations of a bilamellar vesicle (BLV) consisting of two vesicles as a cell model, we find that increasing the size of the inner vesicle (mimicking the nucleus) triggers a tank-treading-to-tumbling transition. A new dynamical state is observed, the undulating motion: the BLV inclination with respect to the imposed flow oscillates while the outer vesicle develops rotating lobes. The BLV exhibits a non-Newtonian behavior with a time-dependant apparent viscosity during its unsteady motion. Depending on its inclination and on its inner vesicle dynamical state, the BLV behaves like a solid or a liquid.

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Section: Observations and Discussionsupporting

confidence: 78%

Complex dynamics of a bilamellar vesicle as a simple model for leukocytes

Kaoui

Harting

2013

Soft Matter

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“…The two boundary conditions ensure that there is no flux of surfactant through the wall and that the flux of surfactant onto the interface matches the adsorption/desorption flux J b defined in (5).…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…Non-trivial solutions are obtained if det(M) = 0; owing to the presence of the Airy functions in Equation (14), this gives a transcendental equation for the complex wave speed c that in general yields an infinite number of normal modes and which must be solved numerically. In the insoluble limit attained either by taking B → 0 or R b → ∞, the equation det(M) = 0 reduces to a quadratic equation for c corresponding to just two normal modes [5].…”

Section: Normal Modesmentioning

confidence: 99%

“…It is well known that an insoluble surfactant can destabilise the interface between two fluids subjected to a shear flow, even if the fluids are stably stratified and have no inertia (which is essential for the development of interfacial instabilities in shear flows devoid of surfactant [1] [2-4]). The onset of this surfactant-induced instability depends crucially on the presence of a wall bounding one of the fluids [5]: with no wall and two semi-infinite fluids, the flow is stable. However, if a second wall is also present, as is the case for channel flow, then instability is not always possible.…”

Section: Introductionmentioning

confidence: 99%

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Instabilities at a sheared interface over a liquid laden with soluble surfactant

Kalogirou

Blyth

2021

J Eng Math

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The linear stability of a semi-infinite fluid undergoing a shearing motion over a fluid layer that is laden with soluble surfactant and that is bounded below by a plane wall is investigated under conditions of Stokes flow. While it is known that this configuration is unstable in the presence of an insoluble surfactant, it is shown via a linear stability analysis that surfactant solubility has a stabilising effect on the flow. As the solubility increases, large-wavelength perturbations are stabilised first, leaving open the possibility of mid-wave instability for moderate surfactant solubilities, and the flow is fully stabilised when the solubility exceeds a threshold value. The predictions of the linear stability analysis are supported by an energy budget analysis which is also used to determine the key physical effects responsible for the (de)stabilisation. Asymptotic expansions performed for long-wavelength perturbations turn out to be non-uniform in the insoluble surfactant limit. In keeping with the findings for insoluble surfactant obtained by Pozrikidis & Hill (IMA J Appl Math 76:859–875, 2011), the presence of the wall is found to be a crucial factor in the instability.

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“…Viscosity stratification is not required (in contrast to the instability found by Yih (1967)) and the instability is switched off in the absence of shear or interfacial surfactant. Interestingly, the presence of a wall appears to be a necessary but not sufficient condition for the Marangoni instability -see the analysis discussion by Pozrikidis & Hill (2011). A recent review of Marangoni instabilities in thin films can be found in Craster & Matar (2009).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of surfactant-laden two-fluid Couette flows in the presence of inertia

Kalogirou

Papageorgiou

2016

J. Fluid Mech.

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The nonlinear stability of immiscible two-fluid Couette flows in the presence of inertia is considered. The interface between the two viscous fluids can support insoluble surfactants and the interplay between the underlying hydrodynamic instabilities and Marangoni effects is explored analytically and computationally in both two and three dimensions. Asymptotic analysis when one of the layers is thin relative to the other yields a coupled system of nonlinear equations describing the spatiotemporal evolution of the interface and its local surfactant concentration. The system is nonlocal and arises by appropriately matching solutions of the linearised Navier-Stokes equations in the thicker layer to the solution in the thin layer. The scaled models are used to study different physical mechanisms by varying the Reynolds number, the viscosity ratio between the two layers, the total amount of surfactant present initially and a scaled Péclet number measuring diffusion of surfactant along the interface. The linear stability of the underlying flow to two-and three-dimensional disturbances is investigated and a Squire's type theorem is found to hold when inertia is absent. When inertia is present, three-dimensional disturbances can be more unstable than two-dimensional ones and so Squire's theorem does not hold. The linear instabilities are followed into the nonlinear regime by solving the evolution equations numerically; this is achieved by implementing highly accurate linearly implicit schemes in time with spectral discretisations in space. Numerical experiments for finite Reynolds numbers indicate that for two-dimensional flows the solutions are mostly nonlinear travelling waves of permanent form, even though these can lose stability via Hopf bifurcations to time-periodic travelling waves. As the length of the system (that is the wavelength of periodic waves) increases, the dynamics become more complex and include time-periodic, quasi-periodic as well as chaotic fluctuations. It is also found that one-dimensional interfacial travelling waves of permanent form can become unstable to spanwise perturbations for a wide range of parameters, producing three-dimensional flows with interfacial profiles that are two-dimensional and travel in the direction of the underlying shear. Nonlinear flows are also computed for parameters which predict linear instability to three-dimensional disturbances but not two-dimensional ones. These are found to have a one-dimensional interface in a rotated frame with respect to the direction of the underlying shear and travel obliquely without changing form.

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Surfactant-induced instability of a sheared liquid layer

Cited by 7 publications

References 0 publications

Complex dynamics of a bilamellar vesicle as a simple model for leukocytes

Complex dynamics of a bilamellar vesicle as a simple model for leukocytes

Instabilities at a sheared interface over a liquid laden with soluble surfactant

Nonlinear dynamics of surfactant-laden two-fluid Couette flows in the presence of inertia

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