Droplet Retraction Research Articles

Retraction of Rod-like and Spheroidal Droplets and Stress Relaxation after Step Shear Strain in Polymer Blends

After application of a large step shear strain, a polymer droplet in an immiscible polymer matrix takes rod-like and spheroidal shapes before returning to the spherical shape. Change in semi axes of those droplets is calculated based on the Cohen-Carriere theory and the extension of the theory by Okamoto et al. From comparison with experimental data, it has been found that retraction of semi axes is well described by the theory using a hydrodynamic factor for the droplet associated with the viscous resistance of the matrix. The excess shear stress for rod-like and spheroidal droplets is predicted based on the Doi-Ohta theory by evaluating the interface tensor from the semi axes calculated. The predicted excess shear stress for the deformed droplet is close to experimental data of a polymer blend with narrow distribution of droplet size after normalization per one droplet with the volume-averaged radius. The effects of polydispersity and interaction with adjacent droplets in the blend are suggested for the remaining difference between the prediction and the data.

The influence of electric field-induced orientation on the retraction of a liquid crystal droplet immersed in a flexible polymer matrix

We measured the apparent interfacial tension between a liquid crystal and a flexible polymer by deformed droplet retraction method. An external electric field is applied to change the director orientation in liquid crystal droplet. The deformation and recovery of a single liquid crystal droplet dispersed in a polydimethylsiloxane (PDMS) matrix were realized by a transient shear flow and observed by polarized optical microscope. In order to control the director orientation in LC droplet, the electric field is applied perpendicular and parallel to the flow field, respectively. The different orientation induced by electric field in liquid crystal droplet has different behavior during droplet retraction and affect the apparent interfacial tension between liquid crystal and flexible polymer.

A study on interfacial tension between flexible polymer and liquid crystal

The interfacial property in polymer–liquid crystal systems is quite different from flexible polymer–polymer mixtures due to the anisotropic properties of liquid crystals. The apparent interfacial tension between a liquid crystal and a flexible polymer was measured by deformed droplet retraction method. The deformation and recovery of a single liquid crystal droplet dispersed in a poly(dimethylsiloxane) matrix were realized by a transient shear flow and observed by polarized optical microscope. The apparent interfacial tension of polymer–liquid crystal system was found to be greatly dependent on the temperature, initial droplet deformation and liquid crystal droplet size.

Retraction dynamics of aqueous drops upon impact on non-wetting surfaces

We study the impact and subsequent retraction of liquid droplets upon high-speed impact on hydrophobic surfaces. Extensive experiments show that the drop retraction rate is a material constant and does not depend on the impact velocity. We show that on increasing the Ohnesorge number, $\Oh\,{=}\,\eta/\sqrt{\rho R_{\rm I} \gamma}$, the retraction, i.e. dewetting, dynamics crosses from a capillary-inertial regime to a capillary-viscous regime. We rationalize the experimental observations by a simple but robust semi-quantitative model for the solid-liquid contact line dynamics inspired by the standard theories for thin-film dewetting.

Interfacial Tension of a Liquid Crystalline Polymer in an Isotropic Polymer Matrix

We investigated the interfacial tension of a thermotropic liquid crystalline polymer (LCP) embedded in a flexible isotropic matrix, poly(dimethylsiloxane) (PDMS), using a modified deformed droplet retraction method (MDDR). The thermotropic polymer employed, PSHQ-6,12, was nematic and featured a well-defined nematic−isotropic clearing transition temperature so that MDDR experiments could be conducted over a temperature range spanning nematic, isotropic, or biphasic regions for the droplet phase. Our results showed that the interfacial tension for temperatures in the nematic range of the droplet is ∼5 mN/m and increases slightly with temperature. Within the isotropic phase, the interfacial tension is significantly higher, starting at a value greater than 20 mN/m and decreasing with temperature with a slope of −0.3 mN/(m K). On crossing the transition from a nematic to isotropic phase for the LCP, the interfacial tension increases in a nearly stepwise manner. Imaging of both retardance and orientation with compensated polarizing optical microscopy clearly revealed homeotropic orientation of the LCP near the LC/isotropic interface, especially below the bulk isotropization temperature, but also for temperatures near, but above, this temperature. We conclude that the interfacial tension for this system is sensitive to the level of nematic ordering at the interface, with homeotropic anchoring yielding significantly lower values than an interface with no preferential anchoring.

Experimental determination of interfacial tension by different dynamical methods under simple shear flow conditions with a novel computer-controlled parallel band apparatus

We present experimental investigations on droplet deformation under simple shear flow conditions, using a computer-controlled parallel band apparatus and an optical device which allows us to record the time dependence of the droplet shape. Several methods are applied to determine the interfacial tension from the observed shape and relaxation mechanism. Specific software developed in our laboratory allows the droplet to be fixed in a certain position for extended times, in fact, indefinite. This is an advantage over most other work done in this area, where only limited time is available. In our experiments, the transient deformation of sheared droplets can be observed to reach the steady state. The measured systems were Newtonian, both droplet and fluid phase. Droplet deformation, orientation angle and retraction were studied and compared to several models. The interfacial tension of the different systems was calculated using the theories of Taylor, Rallison, and Hinch and Acrivos. The results obtained from the analysis of the droplet deformation were in very good agreement with drop detachment experiments of Feigl and co-workers. The study of orientation angle shows qualitative agreement to the theory of Hinch and Acrivos but reveals larger quantitative discrepancies for several empirical fitting parameters of the used model. Analysis of the relaxation of sheared drops provided estimates of the interfacial tension that were in very good agreement with the steady-state measurements.

Comprehensive constitutive model for immiscible blends of Newtonian polymers

We present a comprehensive constitutive equation to describe the convection, retraction, breakup, and coalescence of single droplets and blends of immiscible Newtonian polymeric components. The model is tested by comparing its predictions to literature data that was collected under a variety of conditions. When the strain rate is below the critical value for breakup, the model shows good agreement with literature data for single-droplet deformation for a range of flow types from simple shear to planar extension. Droplet breakup is accounted for by a term chosen to match the time evolution of anisotropy predicted by the Tomotika theory for the capillary breakup of an elongated cylinder. In start-up of fast shearing flow, the comprehensive constitutive model predicts the transient shear and first normal stress difference qualitatively, but not quantitatively, possibly because of the ad hoc way in which the model combines droplet retraction with droplet breakup. More importantly, we find that the information provided in the anisotropy tensor is alone insufficient to describe the complex behaviors of retraction and breakup concurrently. Despite this deficiency, the comprehensive model predicts a steady-state droplet size for isolated droplets that is in agreement with theoretical predictions of the Taylor theory for the critical capillary number for breakup, and correctly predicts deviations from Doi–Ohta scaling of steady-state stresses with shear rate, due to the influence of the critical film thickness at which droplet coalescence occurs.

Interfacial tension measurement between immiscible polymers: improved deformed drop retraction method

This paper describes an improvement of the technique to measure interfacial tension in immiscible polymer blends. Our method is based on the droplet retraction method, in which one relates the kinetics of relaxation of a deformed droplet to the interfacial tension between the matrix and droplet. Previously, the problem with this technique has been the difficulty in preparing axisymmetric ellipsoidal droplets. In our work, we demonstrate that perfect axisymmetric ellipsoidal droplets are produced at a later stage of relaxation of short imbedded fibers. With this technique, we utilize the strengths of both the deformed droplet method and the imbedded fiber retraction method while overcoming their shortcomings. The interfacial tension value thus obtained was compared to that by conventional methods. Additionally, the effect of confinement by external walls on the interfacial tension measurement was studied. Confinement affects interfacial tension measurement when the gap between the walls is less than two times the equilibrium drop size.

The deformation and retraction of thermotropic LCP droplets in a flexible polymer matrix

We have studied the initial deformation and shape recovery of droplets of a flexible polymer and a liquid crystalline polymer in a flexible thermoplastic matrix. The LCP droplets exhibit a size dependence that is not observed for the flexible polymer droplets, possibly because of the effect of orientational elasticity in the liquid crystalline polymer.

Modelling and scaling of dichroism during relaxation in emulsions and polymer blends

Relaxation after cessation of flow is studied in mixtures of immiscible polymer fluids by means of linear conservative dichroism. Depending on the previous shear history, relaxation is known to proceed by either droplet retraction or break-up. Here, scaling relations for the evolution of the dichroism for both mechanisms of relaxation are presented. In addition a direct analysis of the rheo-optical relaxation curves is given. Starting from a suitable model for droplet retraction and applying Rayleigh–Gans–Debye scattering theory, this particular type of dichroism relaxation can be described quite accurately. A similar approach has been applied to relaxation by droplet break-up as induced by interfacial instabilities (Rayleigh instabilities). Tomotika theory is used to model the evolution of the droplet shape. The theoretical result deviates systematically from the experiments which is attributed to end-pinching. Lacking a suitable model for the latter, it is taken into account by an empirical correction similar to that used to describe the normal stress relaxation. With the rheo-optical technique the evolution of the relaxation time as a function of the initial aspect ratio of the droplets can be studied. In addition the effect of concentration on the relaxation time is investigated.

Rheo-optical investigation of immiscible polymer blends

Linear conservative dichroism has been investigated as a potential tool for tracking ( in situ and in real time) the flow-induced microstructure of immiscible polymer blends. Dilute mixtures of poly(dimethylsiloxane) in poly(isobutene) and vice versa have been used as model systems. It is demonstrated that different mechanisms for structural changes can be identified with this technique: droplet deformation, droplet retraction, fibril break-up and coalescence. Time-resolved in-situ SALS measurements support the structural interpretation of the dichroism data. Breaking up of stretched filaments by Rayleigh instabilities can be deduced from dichroism measurements. The resulting strings of droplets can be detected with SALS. The time scales for the structural changes can be determined by dichroism, which makes it possible to study in situ the effect of the various process and material parameters. As an illustration, the effect of shear rate on fibril break-up and on droplet coalescence after sudden changes in shear rate has been considered. Break-up times decreased only slightly with increasing shear rate; coalescence times scaled with the square of shear rate rather than with strain under the conditions of the present experiments.

Influence of Dynamic Surface Tension on the Spreading of Surfactant Solution Droplets Impacting onto a Low-Surface-Energy Solid Substrate

We have investigated the impact of single droplets of various surfactant solutions on a low-surface-energy solid substrate using a high-frequency visualization technique (one picture every 100 μs). Whatever the surfactant, the drop spreads and retracts in about 1 s under the action of inertia and capillarity, respectively. During retraction, the capillary waves can be amplified and, in some cases, even yield droplet bouncing. Then, the droplet may slowly spread again due to gravity and the unbalanced capillary forces at the contact line between the droplet and the substrate. During the fast spreading process (2–3 ms), the droplet surface increases by almost one order of magnitude since its shape changes from a sphere to a flat pancake; this causes a strong deviation from thermodynamic equilibrium. The relevant surface property is therefore the dynamic surface tension which we have evaluated using a maximum bubble pressure apparatus. We have shown that droplet retraction is drastically influenced by the adsorption kinetics of the surfactant which limits the return to equilibrium surface tension.