Simple linear viscoelastic models of dilute solutions of polymer molecules and emulsion droplets

Mellema, J.; Blom, C.; Beekwilder, J.P.

doi:10.1007/bf01333842

Cited by 15 publications

(7 citation statements)

References 17 publications

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“…Replacing this result into eq and expanding it in power series of qR , we get a perturbation solution which, in the limit of small elasticity (λ 1 ≪ 1, λ 2 ≈ 0), yields an overdamped behavior: where: and Re(α n ) and Im(α n ) meaning the real and imaginary parts of α n . For large elasticity values (λ 1 ≫ 1,λ 2 ≈ 0), we find Qualitatively similar expressions relating the decay rate α n to the fluid viscosity η have been reported in the literature for bubbles (see, e.g., refs , ) or drops in a vacuum , or in a viscoelastic medium. − …”

Section: A Phenomenological Modelsupporting

confidence: 87%

Anomalous Behavior of Ultra-Low-Amplitude Capillary Waves. A Glimpse of the Viscoelastic Properties of Interfacial Water?

2017

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We investigate, both theoretically and by a differential interferometric technique, the behavior of large-wavelength capillary waves (of the order of 10 m) selectively excited at the surface of drops and bubbles with typical eigenfrequencies of the order of 10 Hz. The resonance peaks of gas bubbles or hydrocarbon drops in water (radius less than 1 mm) highlight anomalously small dissipation in the region of ultralow (sub-nanometric) oscillation amplitudes, reaching a plateau at higher amplitudes. This is in sharp contrast to the usual oscillating systems, where an anomalous behavior holds at large amplitudes alone. Dissipation is strongly dependent on the excited vibrational modes and, in spite of remarkable numerical differences, water-vapor and water-hydrocarbon interfaces exhibit the same overall trend. A phenomenological model was developed, based on the assumption that water possesses a threshold viscoelasticity, above which it behaves like a regular viscous fluid. The well-known Deborah number was then estimated within the anomalous region and found to lie in the range of viscoelastic fluids. In agreement with previous studies of nanohydrodynamics (e.g., atomic force microscopy measurements with sub-nanometric tip motions), the present one lends support to the idea that every self-aggregating fluid exhibits yield stress behavior, including classical Newtonian fluids like water. The essential requirement is that the applied perturbation lie below a critical threshold, above which viscous behavior is recovered. Our differential interferometric technique seems particularly suitable for this type of studies, as it allows measurement of long-wavelength capillary waves with sub-nanometric resolution on the oscillation amplitudes.

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Section: A Phenomenological Modelsupporting

confidence: 87%

Anomalous Behavior of Ultra-Low-Amplitude Capillary Waves. A Glimpse of the Viscoelastic Properties of Interfacial Water?

2017

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“…The deformation is determined using the approach as used by, e.g., Mellema et al 21 A weakly deformed sphere with an initial radius R0 can be described in spherical coordinates by 22 The function s(θ, φ) can be expanded in spherical harmonics. Here, we approximate s(θ, φ) by the second-order Legendre polynomial s ) ( 1 /2)s2(3 cos 2 θ -1), where s2 is the amplitude of the deformation, equal to ( 2 /3)(ab).…”

Section: Methodsmentioning

confidence: 99%

Effect of Interfacial Permeability on Droplet Relaxation in Biopolymer-Based Water-in-Water Emulsions

et al. 2005

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In this paper, we show that for aqueous phase-separated biopolymer mixtures (water-in-water emulsions) both interfacial tension and permeability of the interface are important for the relaxation process of deformed droplets. We give an expression for the characteristic relaxation time that contains both contributions. With this description, the interfacial tension and the permeability can be deduced from cessation-of-flow experiments. The results show that for samples that are very close to the critical point the interfacial tension, calculated without taking into account the permeability, are overestimated significantly. For samples close to the critical point, the permeability has to be taken into account in the description for the relaxation time to get a reliable estimation of the interfacial tension. Our experiments show that for these systems the effective permeability is inversely proportional to the interfacial tension, lambda(eff) proportional, variant1/gamma, and proportional to the square of the interfacial thickness, lambda(eff) proportional, variant xi(2). We find that the permeability is related to an effective diffusion coefficient as D(eff) proportional, variant lambdagamma(eff). From this relation, we find that the diffusion coefficient is equal to 0.9.10(-9) m(2)/s, which is close to the self-diffusion coefficient of water; = 2.3.10(-9) m(2)/s. This indicates that only water diffuses through the interface, and the diffusion coefficient is independent of the composition of the system for the concentration regime that is used.

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“…The techniques commonly used for these systems often involve the deformation of droplets, either in a flow field or in a rotational field. The interfacial tension can be determined from the degree of deformation or the relaxation time after the cessation of the flow field. − Both the spinning drop and the droplet relaxation methods are techniques widely accepted as reliable methods for the measurement of interfacial tension. However, these techniques are valid only in the case where the interfaces are not permeable to any of the components in the system and in the case where effects of the bending rigidity are negligible.…”

Section: Effect Of Permeability On Interfacial Tension Measurementsmentioning

confidence: 99%

Effect of Bending Rigidity and Interfacial Permeability on the Dynamical Behavior of Water-in-Water Emulsions

2006

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Phase separation in aqueous biopolymer mixtures results in the formation of an interface, separating two aqueous bulk phases. The properties of that interface are key parameters to understand and predict phenomena, such as the phase-separation process and deformation of droplets in a flow field. In these processes, the structures and sizes of the morphologies depend on the balance between viscous and interfacial forces. Normally, one assumes that the interfacial tension is the only important parameter regarding the interfacial forces. However, we will show that in these water-in-water emulsions, bending rigidity and interfacial permeability also play an important role. Spinning drop experiments show that at long time scales the interface is permeable to both dissolved biopolymers and water. From droplet relaxation experiments, we could conclude that, for shorter time scales, water is the only ingredient that can diffuse through the interface. Due to this permeability, these methods cannot be used to calculate the interfacial tension accurately, without taking into account the permeability of the interface. Including the permeability, we give a full description for the relaxation time of deformed droplets. From this description, the interfacial tension and the permeability of the interface can be deduced simultaneously. We also incorporate the permeability and the bending rigidity into the description of the kinetics of phase separation. From this theoretical description, we predict four different regimes to occur in the phase-separation process depending on the size of the domains. For the scaling of the domain size with time, we find an exponent of (1)/(4) for bending- and permeability-dominated coarsening, an exponent of (1)/(3) for bending-dominated coarsening, an exponent of (1)/(2) for interfacial tension- and permeability-dominated coarsening, and an exponent of 1 for interfacial tension-dominated coarsening. The crossover between the different regimes depends on two different critical radii, R(c), equal to (2k/gamma)(1/2) and R(lambda), equal to etalambda(eff). Taking values for the interfacial properties, we find these critical radii to be larger than a micrometer, indicating that both bending rigidity and permeability are of importance during phase separation.

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Simple linear viscoelastic models of dilute solutions of polymer molecules and emulsion droplets

Cited by 15 publications

References 17 publications

Anomalous Behavior of Ultra-Low-Amplitude Capillary Waves. A Glimpse of the Viscoelastic Properties of Interfacial Water?

Anomalous Behavior of Ultra-Low-Amplitude Capillary Waves. A Glimpse of the Viscoelastic Properties of Interfacial Water?

Effect of Interfacial Permeability on Droplet Relaxation in Biopolymer-Based Water-in-Water Emulsions

Effect of Bending Rigidity and Interfacial Permeability on the Dynamical Behavior of Water-in-Water Emulsions

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