Generalized behavior of the breakup of viscous drops in confinements

The breakup of confined drops in shear flow between parallel plates is investigated as a function of viscosity ratio and confinement ratio. Using a boundary-integral method for numerical simulations and a counter-rotating experimental device, critical capillary numbers in shear flow are obtained. It is observed that different viscosity ratios yield different trends with increasing confinement ratio: a low viscosity ratio drop shows an increase in critical capillary number, at a viscosity ratio of unity no major trend is seen, and the critical capillary number for a high viscosity ratio drop decreases significantly. A generalized explanation for all viscosity ratios is that confinement affects the orientation of the drop with respect to the direction of the local strain field. At moderate confinement ratios, the drop orients more towards the strain direction, where it experiences a stronger flow and hence, the critical capillary number is decreased. As the drop gets more confined, it aligns more in the flow direction. Hence, the drop experiences a weaker flow and thus, additionally stabilized by wall effects, it breaks at a higher critical capillary number. In principle, this behavior is the same for all viscosity ratios, but transitions occur at different confinement ratios. Most of the breakup is of a binary nature, but ternary breakup can occur if the drop length is larger than 6 undeformed drop radii, consistent with arguments based on the Rayleigh-Plateau instability

Deformation and relaxation of PMMA/PS and PMMA/PSOX blends

In this work we study the role of the interfaces in the rheological behavior of blends of PMMA with PS and PS functionalized with oxazoline (PSOX). The blends here studied are concentrated (20 w% of dispersed phase) and have viscosity ratios higher than 1. Linear and non-linear (both in shear and extension) experiments were performed. In terms of relaxation, the cessation of flow after steady shear experiments reveal the appearance of second very slow relaxation mechanism in the PMMA/PSOX blend as do those upon cessation of a step uniaxial extension. Small Angle Light Scattering (SALS), performed on 1 w% dispersed phase blends, was used during step shear to infer about the relaxation of the droplets and/or interface and the patterns show that this behavior is not due to a higher deformation of the PSOX droplets, but should be attributed to a relaxation of the interfaces. The reason for the very high elasticity of the interface is not a priori obvious, but is probably related with the existence of extra physical entanglements at the interface in the PMMA/PSOX blends since the chemical analysis does not indicate any type of chemical interaction between the oxazoline groups and the PMMA.The authors would like to thank the Foundation for Science and Technology-FCT for awarding one of them (Jorge Silva) aPhD Fellowship (ref BD/12833/2003)

The influence of swelling on elastic properties of polyacrylamide hydrogels

Polyacrylamide (PAM) hydrogels are commonly used as substrates for cell mechanical and mechanobiological studies because of their tunable stiffness and ease of handling. The dependence of bulk rheological and local elastic properties (assessed by Atomic Force Microscopy, or AFM) of PAM hydrogels on its composition and polymerization temperature has been extensively studied. PAM hydrogels swell when immersed in media, but the influence of swelling on local elastic properties is poorly characterized. Direct measurements of the effect of swelling on PAM elastic properties are scarce. We report here, for the first time, the direct measurements of volumetric swelling and local elastic properties of PAM gels throughout the post-polymerization swelling process until equilibrium. First, local and global elastic properties (measured by rheology), were obtained during polymerization in the absence of swelling, and showed good agreement with each other. Four PAM hydrogel compositions were characterized thus, with corresponding storage shear moduli (as measured immediately after polymerization) of 4,530 Pa (termed stiffest), 2,900 Pa (stiff), 538 Pa (soft), and 260 Pa (softest). Next, all compositions were subjected to swelling in phosphate buffered saline. Swelling ratios and local elastic moduli were measured at 0, 3, 6, 9, 12, and 24 h post-polymerization for the soft and softest compositions, and once daily till 6 days post-polymerization for all four compositions. For the stiffest and stiff gels, swelling ratio, and local elastic modulus changed negligibly with time, while for the soft and softest gels, substantial changes between Day 0 and Day 1 were found for both swelling ratio (increased by 21.6 and 133%, respectively), and local elastic modulus decreased (by 33.7 and 33.3%, respectively), substantially. Experimental data were analyzed by a model that combined ideal elastomer mechanics and poroelastic swelling kinetics model. Model predictions confirmed the validity of present measurements with respect to past studies where swelling and elastic properties were not measured simultaneously. The present study underlines the important effect swelling can have on PAM elastic properties and provides detailed quantitative data to guide the duration taken to reach equilibrium—a useful information for cell mechanics experiments. In addition, the simultaneous measurements of swelling and local elastic moduli provide novel data for the validation of theoretical models

Droplet relaxation in blends with one viscoelastic component : bulk and confined conditions

Using a counter rotating parallel plate shear flow cell, the shape relaxation of deformed droplets in a quiescent matrix is studied microscopically. Both the effects of geometrical confinement and component viscoelasticity are systematically explored at viscosity ratios of 0.45 and 1.5. The flow conditions are varied from a rather low to a nearly critical Ca number. Under all conditions investigated, viscoelasticity of the droplet phase has no influence on shape relaxation, whereas matrix viscoelasticity and geometrical confinement result in a slower droplet retraction. Up to high confinement ratios, the relaxation curves for ellipsoidal droplets can be superposed onto a master curve. Confined droplets with a sigmoidal shape relax in two stages: the first consists of a shape change to an ellipsoid with a limited amount of retraction, and the second is the retraction of this ellipsoid. The latter stage can be described by means of one single relaxation time that can be obtained from the relaxation of initially ellipsoidal droplets. The experimental results are compared to the predictions of a recently published phenomenological model for droplet dynamics in confined systems with viscoelastic components (Minale et al., Langmuir 26:126–132, 2010). However, whereas the model predicts additive effects of geometrical confinement and component viscoelasticity, the experimental data reveal more complex interactions

Relaxation of fibrils in blends with one viscoelastic component: Bulk and confined conditions

Using a counter rotating parallel plate shear flow cell, shape relaxation of fibrils in a quiescent matrix is studied microscopically. Both the effects of geometrical confinement and component viscoelasticity are systematically explored. By applying a supercritical shear flow for varying amounts of time, droplets with a wide range of initial elongation ratios have been generated. The shape relaxation of these elongated droplets occurs in two stages; the first one consists of shape changes and retraction from a fibril to an ellipsoid, the second one is the retraction of this ellipsoid to a sphere. During both stages of the relaxation process, droplet viscoelasticity has no influence on the relaxation, whereas matrix viscoelasticity and geometrical confinement result in a slower retraction. However, the effect of confinement on the shape relaxation during the first stage of the relaxation process is less pronounced than its influence on the retraction of ellipsoidal droplets. The relaxation time of the second stage of the relaxation corresponds to the relaxation time of initially ellipsoidal droplets. Finally, for confinement ratios up to 0.75 and Deborah numbers around 1, no effect of confinement and component viscoelasticity on the critical initial elongation ratio for breakup during relaxation has been foun

Critical conditions and breakup of non-squashed microconfined droplets: Effects of fluid viscoelasticity

Droplet breakup in systems with either a viscoelastic matrix or a viscoelastic droplet is studied microscopically in bulk and confined shear flow, using a parallel plate counter rotating shear flow cell. The ratio of droplet diameter to gap spacing is systematically varied between 0.1 and 0.85. In bulk shear flow, the effects of matrix and droplet viscoelasticity on the critical capillary number for breakup are very moderate under the studied conditions. However, in confined conditions a profoundly different behaviour is observed: the critical capillary numbers of a viscoelastic droplet are similar to those of a Newtonian droplet, whereas matrix viscoelasticity causes breakup at a much lower capillary number. The critical capillary numbers are compared with the predictions of a phenomenological model by Minale et al. (Langmuir 26:126–132, 2010); the model results are in qualitative disagreement with the experimental data. It is also found that the critical dimensionless droplet length, the critical capillary number, and the dimensionless droplet length at breakup show a similar dependency on confinement ratio. As a result, confined droplets in a viscoelastic matrix have a smaller dimensionless length at breakup than droplets in a Newtonian matrix, which affects the breakup mode. Whereas confined droplets in a Newtonian matrix can break up into multiple parts, only two daughter droplets are obtained after breakup in a viscoelastic matrix, up to very large confinement ratios