Capillary Breakup Research Articles

Micro-PIV of viscoelastic fluid flow in microporous media

The present experimental investigation combines the bulk flow properties of polymer solutions and measurable rheological parameters as they flow through a distinctive micro-porous structure, with micro-PIV (micro-particle image velocimetry) to measure the velocity distribution and velocity fluctuations within individual pores of a novel porous glass structure. To investigate the effects of fluid elasticity at pore scale, aqueous solutions of a polyacrylamide (PAA) & polyethylene oxide (PEO) in the concentration range of 50–200 ppm, which were characterized in both shear and extensional flows using shear and capillary break-up extensional rheometers (CaBER) respectively, were used as working fluids. The velocity field measurement includes the velocity magnitude and fluctuation intensity in several different pores within the porous material across a Weissenberg number Wi range of approximately 0.01 to 1 for each of the test fluids. The global averaged fluctuation intensity increases with Wi but the critical value, which indicates the onset of significant unsteadiness (i.e. well above noise floor/Newtonian baseline) within the flow at pore scale gives an approximately constant value of Wi≈0.4, which is almost 40 times higher than the value that is observed in the pressure-drop measurements for the data to rise above the Newtonian base line. We therefore postulate that the enhanced pressure-drop behaviour of the bulk flow may not be due to local velocity fluctuations within the pores but due to mean flow effects, at least over a significant portion of the data (up to Wi≈0.4).

The fluid dynamics of a viscoelastic fluid dripping onto a substrate.

Extensional flows of complex fluids play an important role in many industrial applications, such as spraying and atomisation, as well as microfluidic-based drop deposition. The dripping-on-substrate (DoS) technique is a conceptually-simple, but dynamically-complex, probe of the extensional rheology of low-viscosity, non-Newtonian fluids. It incorporates the capillary-driven thinning of a liquid bridge, produced by a single drop as it is slowly dispensed from a syringe pump onto a solid partially-wetting substrate. By following the filament thinning and pinch-off process the extensional viscosity and relaxation time of the sample can be determined. Importantly, DoS allows experimentalists to measure the extensional properties of lower viscosity solutions than is possible with commercially available capillary break-up extensional rheometers. Understanding the fluid mechanics behind the operation of DoS will enable users to optimise and extend the performance of this protocol. To achieve this understanding, we employ a computational rheology approach, using adaptively-refined time-dependent axisymmetric numerical simulations with the open-source Eulerian code, Basilisk. The volume-of-fluid technique is used to capture the moving interface, and the log-conformation transformation enables a stable and accurate solution of the viscoelastic constitutive equation. Here, we focus on understanding the roles of surface tension, elasticity and finite chain extensibility in controlling the elasto-capillary (EC) regime, as well as the perturbative effects that gravity and substrate wettability play in setting the evolution of the self-similar thinning and pinch-off dynamics. To illustrate the interplay of these different forces, we construct a simple one-dimensional model that captures the initial rate of thinning when the dynamics are dominated by a balance between inertia and capillarity. This model also captures the structure of the transition region to the nonlinear EC regime in which the rapidly growing elastic stresses in the thread balance the capillary pressure as the filament thins towards breakup. Finally, we propose a fitting methodology based on the analytical solution for FENE-P fluids to improve the accuracy in determining the effective relaxation time of an unknown fluid.

Free surface tension modelling using particle-grid hybrid method without considering gas particles

In particle method, the number of particles is an important factor affecting the computational efficiency. For the free-surface flow, gas particles are usually necessary for surface tension calculation, but they have little impact to the liquid flow with a large density. If the free surface tension can be modeled without considering gas particles, it is of great significance to improve the computational efficiency. The existing potential-based surface tension model and the stress-based surface tension model don't need gas particles, but they have the problems of instability or are difficult to implement. Therefore, in this study, another free surface tension calculation method by coupling particles and grids is proposed. In the method, background mesh is applied to the entire computational domain, where the boundary of grid is extended outward by 3.1 l0 on the basis of particle boundary for curvature calculation. The level-set function is adopted to mark different phases on background mesh, whose value is set according to the normal distance between the grid and the nearest free surface particle. After obtaining the curvature and the level-set function gradient on background mesh, these variables are interpolated to corresponding particles to calculate the surface tension. Through the comparative study of area-weighted and distance-weighted interpolation schemes, it is found that the accuracy of distance-weighted interpolation scheme is higher than that of area-weighted interpolation scheme. Finally, the performance of the particle-grid hybrid method is verified by simulating four benchmark cases, including droplet oscillations, droplet spreading, capillary jet breakup and droplet impinging onto plate.

Fiber spinning from polymer solutions

The thinning of a cylinder of a polymer solution in a volatile solvent is argued to be controlled by solvent diffusion through a dense polymer layer at the cylinder surface. This naturally leads to the exponential time dependence of cylinder radius that is observed in experiments using a fast camera, such as capillary breakup extensional rheometry (CaBER). The relaxation time is controlled by the thickness of the dense (and often glassy) polymer layer and the diffusion coefficient of solvent through that layer. If correct, this means that while CaBER is very useful for understanding fiber spinning, the relaxation time does not yield a measure of the extensional viscosity of polymer solutions in volatile solvents.

Surface wave and splashing of liquid film by oblique water jet impinging on a vertical plate

Liquid film cooling by jet impingement, known as a common thermal protection technique, is extensively applied in liquid rocket engines. The present work investigates the impact of a water jet onto a vertical plate by high-speed visualization system and laser particle analyzer, with a focus on the characteristics of surface waves and droplets splashing during the formation of liquid film. Depending on whether the jet is broken before impact, two regimes are identified, i.e., droplet or continuous jet impingement regime. The frequency and velocity of the surface wave and the splashing rate are jointly affected by the jet angle and the impingement distance. The splashing is mainly caused by the capillary breakup of the crown film that forms at the edge of the surface wave, and most of the splashing droplets are generated from the top of the crown film. The larger the jet angle, the smaller the wave frequency and velocity, but the higher the splashing rate. A large impingement distance causes a small wave frequency and velocity due to the shift of the impingement regime, further resulting in different tendencies in the splashing rate. A parameter expression for the size distributions of splashing droplets is established by the fitting result of the log-normal distribution and the Rosin-Rammler (R-R) distribution, where the parameters are associated with the jet Weber number.

Multimaterial fiber as a physical simulator of a capillary instability

Capillary breakup of cores is an exclusive approach to fabricating fiber-integrated optoelectronics and photonics. A physical understanding of this fluid-dynamic process is necessary for yielding the desired solid-state fiber-embedded multimaterial architectures by design rather than by exploratory search. We discover that the nonlinearly complex and, at times, even chaotic capillary breakup of multimaterial fiber cores becomes predictable when the fiber is exposed to the spatiotemporal temperature profile, imposing a viscosity modulation comparable to the breakup wavelength. The profile acts as a notch filter, allowing only a single wavelength out of the continuous spectrum to develop predictably, following Euler-Lagrange dynamics. We argue that this understanding not only enables designing the outcomes of the breakup necessary for turning it into a technology for materializing fiber-embedded functional systems but also positions a multimaterial fiber as a universal physical simulator of capillary instability in viscous threads.

Energy mechanism for the instability of liquid jets with thermocapillarity

Xu and Davis [J. Fluid Mech. 161, 1–25 (1985)] examined the stability of long axisymmetric liquid jet subjected to an axial temperature gradient, finding capillary, surface-wave, and hydrodynamic modes. They showed that capillary breakup can be retarded or even suppressed for a small Prandtl number (Pr < 1) and a large Biot number (Bi ≥ 1). In the present work, the energy mechanism is carried out for these three kinds of flow instabilities, and the mechanism of suppressing capillary breakup is clarified. When the Reynolds number (RB) is not large, the work done by the pressure on the free surface (PS) is the main energy source of the capillary instability. At small Pr and large Bi, the phase difference between the radial velocity and surface deformation increases with RB, leading to the decrease in PS, which prevents the occurrence of capillary breakup. Meanwhile, the work done by thermocapillary force becomes the main energy source, making hydrodynamic modes unstable. The perturbation flow fields are displayed, which shows that the temperature fluctuations of three modes differ from each other.

Entanglements via Slip Springs with Soft, Coarse-Grained Models for Systems Having Explicit Liquid-Vapor Interfaces.

Recent advances in nano-rheology require that new techniques and models be developed to precisely describe the equilibrium and non-equilibrium characteristics of entangled polymeric materials and their interfaces at a molecular level. In this study, a slip-spring (SLSP) model is proposed to capture the dynamics of entangled polymers at interfaces, including those between liquids, liquids and vapors, and liquids and solids. The SLSP model employs a highly coarse-grained approach, which allows for comprehensive simulations of entire nano-rheological characterization systems using a particle-level description. The model relies on many-body dissipative particle dynamics (MDPD) non-bonded interactions, which permit explicit description of liquid-vapor interfaces; a compensating potential is introduced to ensure an unbiased representation of the shape of the liquid-vapor interface within the SLSP model. The usefulness of the proposed MDPD + SLSP approach is illustrated by simulating a capillary breakup rheometer (CaBR) experiment, in which a liquid droplet splits into two segments under the influence of capillary forces. We find that the predictions of the MDPD + SLSP model are consistent with experimental measurements and theoretical predictions. The proposed model is also verified by comparison to the results of explicit molecular dynamics simulations of an entangled polymer melt using a Kremer-Grest chain representation, both at equilibrium and far from equilibrium. Taken together, the model and methods presented in this study provide a reliable framework for molecular-level interpretation of high-polymer dynamics in the presence of interfaces.

Extensional rheology of hydrophobically associating polyacrylamide solution used in chemical flooding: Effects of temperature, NaCl and surfactant

The study provides an insight into the oil washing mechanism of hydrophobically associating polyacrylamide (HAHPAM) in chemical flooding from the perspective of extensional rheology. The extensional rheology of HAHPAM solution was systematically investigated under different influencing factors (concentration, temperature, NaCl and surfactant) using capillary breakup extensional rheometry (CaBER). Compared with partially hydrolyzed polyacrylamide (HPAM), the HAHPAM solution shows better extensibility due to the additional hydrophobic interaction between molecular chains, particularly at high temperature and high salinity. By increasing the concentration and decreasing the temperature, the filament breakup time and extensional viscosity of the HAHPAM solution increase. NaCl delays the attenuation of the HAHPAM filament by increasing the solution extensional viscosity and surface tension. In the presence of sodium dodecyl sulfate (SDS), the reduced surface tension dominates the stability of the filament and weakens the extensibility of the HAHPAM/SDS composite solution.

液体中での音波照射による閉端孔内に存在する複数気柱の排出

In the cleaning and coating processes of product manufacturing, some cases require filling liquid into closed-end holes. We have developed a liquid infiltration method, i.e., gas removal, into closed-end holes by irradiating acoustic waves. The method uses gas oscillation inside the holes; however, the final removal process of break-up gas columns is still unclear. This study observed the multiple gas column oscillation inside a closed-end hole during acoustic wave irradiation and its removal process. We also visualized the liquid flow between columns using the PIV technique. As a result, we found that the gas removal occurrence depends on the size, distance, and the number of gas columns. The removal process shows that the gas columns were approached and coalesced. They were then ejected through capillary wave propagation, necking, break-up, and re-coalescence. The oscillation of the gas column near the hole exit induced the flow between columns and approaching the other gas column. The PIV analysis shows that the long-distance gas column cases induced smaller flow velocities and could not achieve gas removal due to liquid inertia.

Fluid Flow Templating of Polymeric Soft Matter with Diverse Morphologies.

It is challengingto find a conventional nanofabrication technique that can consistently produce soft polymeric matter of high surface area and nanoscale morphology in a way that is scalable, versatile, and easily tunable. Here, the capabilities of a universal method for fabricating diverse nano- and micro-scale morphologies based on polymer precipitation templated by the fluid streamlines in multiphasic flow are explored. It is shown that while the procedure is operationally simple, various combinations of its intertwined mechanisms can controllably and reproducibly lead to the formation of an extraordinary wide range of colloidal morphologies. By systematically investigating the process conditions, 12distinct classes of polymer micro- and nano-structures including particles, rods, ribbons, nanosheets, and soft dendritic colloids (dendricolloids) are identified. The outcomes are interpreted by delineating the physical processes into three stages: hydrodynamic shear, capillary and mechanical breakup, and polymer precipitation rate. The insights into the underlying fundamental mechanisms provide guidance toward developing a versatile and scalable nanofabrication platform. It is verified that the liquid shear-based technique is versatile and works well with many chemically diverse polymers and biopolymers, showing potential as a universal tool for simple and scalable nanofabrication of many morphologically distinct soft matter classes.

A revisit of Rayleigh capillary jet breakup at low Ohnesorge number

The average Rayleigh capillary breakup length of a cylindrical Newtonian viscous liquid jet moving with homogeneous velocity must be determined by the selection of normal modes with time-independent amplitude and wavelength. Invariant modes (IMs) with both positive and negative group and phase velocities exist in ample ranges of the parameter domain (Weber and Ohnesorge), which explains (i) the self-sustained average breakup length (long-term resonance) and (ii) the governing role on breakup of both spatial growth rate and wave number of the dominant positive group velocity IM. Published experimental results at low Ohnesorge numbers confirm our proposal.

A technical note on large normal-stress differences observed in a novel self-assembling functionalized dipeptide surfactant solution

A number of functionalised dipeptides self-assemble in water under specific conditions to give micellar aggregates. The micellar aggregates formed depend on the exact molecular structure and are important to understand as they control the properties both of the micellar phase and also of the gel phase which can be formed from these precursor solutions. Here, we investigate the rheological properties of a functionalised dipeptide which behaves as a surfactant at high pH. This solution has been shown previously to exhibit very “stringy” behaviour, and this has previously been characterised using capillary breakup extensional rheometry (CaBER). In the current technical note, we extend the rheological characterisation of an exemplar precursor solution via small-amplitude oscillatory shear and steady shear. Using a cone-and-plate geometry and a dedicated protocol, we can measure the first normal-stress difference N1 and using a parallel-plate geometry to also measure (N1-N2), subsequently determining the second normal-stress difference N2. In so doing, we confirm that these systems are highly elastic, e.g. for shear rates greater than ~ 30 s−1, corresponding to a Weissenberg number based on the longest relaxation time ~ 330, N1 > 10τ where τ is the shear stress, and also, we find that N2 can be significant, is negative and approximately equal in magnitude to ~ 0.36 ± 0.05 N1. Significant uncertainties associated with the normal-stress difference data led to us using a range of different rheometers (and geometries) and highlight the issues with determining N2 using this two-measurement approach. Despite these uncertainties, the non-negligible value of the second-normal stress difference is demonstrated for these fluids.

Instrumental characterization of xanthan gum and scleroglucan solutions: Comparison of rotational rheometry, capillary breakup extensional rheometry and soft-contact tribology

Xanthan gum and scleroglucan, two rod-like polysaccharide hydrocolloids, are compared using a wide range of instrumental techniques and methods: steady shear flow, small amplitude oscillatory shear, first normal stress difference, capillary break-up and soft-contact tribology. The aqueous solutions of these two hydrocolloids with similar flow and viscoelastic profile show marked differences in capillary break-up time and apparent extensional viscosity. This result correlates with differences in first normal stress difference and, to a lesser extent, Stribeck curve behaviour. Formulating the hydrocolloids in concentrated sucrose solution (40 wt%) shifts relaxation profiles to longer times which greatly diminishes differences in rheological and lubrication behaviour. With exception of capillary break-up tests, no other methods showed statistically significant differences between the polysaccharides dissolved in the viscosified matrix. The toolbox of techniques is also applied to probe interactions of xanthan gum and scleroglucan with human whole saliva and bovine submaxillary mucin. We report no specific interactions between either hydrocolloid and salivary proteins and suggest that any cumulative effects must stem from specific sets of linear and non-linear rheological properties of saliva/hydrocolloid mixtures. • Rheology and tribology of xanthan gum and scleroglucan are compared. • Capillary break-up provides sensitive discrimination between hydrocolloids. • Xanthan gum and scleroglucan have similar hydrodynamic volume. • Relaxation spectrum of xanthan features faster modes compared to scleroglucan.

Characterization of Dysphagia Thickeners Using Texture Analysis-What Information Can Be Useful?

Besides shear viscosity, other texture parameters (adhesiveness or cohesiveness) might be relevant for safe swallowing in people suffering from oropharyngeal dysphagia. Shear viscosity is assessed through protocols developed using a viscometer or a rheometer. In contrast, protocols and instruments (capillary break-up rheometer) to assess adhesiveness and cohesiveness are less common and much less developed. Other equipment such as texture analyzers can provide useful information on food properties. Here, we aimed to explore different texture analyzer settings (type of test, probe, and protocol) to characterize four commercial dysphagia thickeners at the shear viscosity levels recommended by manufacturers. Among the tests used (extrusion or penetration) with the different probes (disc, cone and shape holder, sphere, or cylinder), cone extrusion provided information about adhesivity, disc extrusion about sample cohesiveness, and sphere about penetration and sample elasticity. The test speeds used influenced the results, but only one speed is needed as the different speeds provided the same fluid information; for easiness, it is proposed to use 1 mm/s. Comparing the texture analyzer results with viscosity values obtained at different shears, the texture analyzer parameters reflected information that differ from shear viscosity. This information could be relevant for the therapeutic effect of thickening products and food characterization.

An axisymmetric multiphase moving particle semi-implicit method for simulation of 3D axisymmetric flow

Axisymmetric flows are widespread problems in the engineering field, but doing complete 3D simulations for them is very time-consuming. This study aims to develop an axisymmetric multiphase MPS method based on the Cartesian coordinate to transform the 3D problems onto 2D planes without losing important flow characteristics. To meet the calculation requirements of the MPS discretization, the virtual rotating particles were imaged within the effective radius of the real particles on the 2D plane, and particle number densities of the real particles were calculated by considering the contributions of the virtual rotating particles. The pressure Poisson equation, gradient, divergence, and Laplace operators were modified correspondingly to consider the interactions of the real particles with the virtual rotating particles. The method was validated by simulating 3D axisymmetric problems, namely, the capillary jet breakup, rising gas bubble, and droplet formation. The accuracy and stability of the developed method were demonstrated by comparing the numerical results with the reference data.

Understanding the Dynamics of Cellulose Dissolved in an Ionic Liquid Solvent Under Shear and Extensional Flows.

Ionic liquids (ILs) hold great potential as solvents to dissolve, recycle, and regenerate cellulosic fabrics, but the dissolved cellulose material system requires greater study in conditions relevant to fiber spinning processes, especially characterization of nonlinear shear and extensional flows. To address this gap, we aimed to disentangle the effects of the temperature, cellulose concentration, and degree of polymerization (DOP) on the shear and extensional flows of cellulose dissolved in an IL. We have studied the behavior of cellulose from two sources, fabric and filter paper, dissolved in 1-ethyl-3-methylimidazolium acetate ([C2C1Im][OAc]) over a range of temperatures (25 to 80 °C) and concentrations (up to 4%) that cover both semidilute and entangled regimes. The linear viscoelastic (LVE) response was measured using small-amplitude oscillatory shear techniques, and the results were unified by reducing the temperature, concentration, and DOP onto a single master curve using time superposition techniques. The shear rheological data were further fitted to a fractional Maxwell liquid (FML) model and were found to satisfy the Cox-Merz rule within the measurement range. Meanwhile, the material response in the non-LVE (NLVE) regime at large strains and strain rates has special relevance for spinning processes. We quantified the NLVE behavior using steady shear flow tests alongside uniaxial extension using a customized capillary breakup extensional rheometer. The results for both shear and extensional NLVE responses were described by the Rolie-Poly model to account for flow-dependent relaxation times and nonmonotonic viscosity evolution with strain rates in an extensional flow, which primarily arise from complex polymer interactions at high concentrations. The physically interpretable model fitting parameters were further compared to describe differences in material response to different flow types at varying temperatures, concentrations, and DOP. Finally, the fitting parameters from the FML and Rolie-Poly models were connected under the same superposition framework to provide a comprehensive description within the wide measured parameter window for the flow and handling of cellulose in [C2C1Im][OAc] in both linear and nonlinear regimes.

Improved capillary rheometry for viscous Newtonian filaments

The efficacy of the kinematic differential analysis of McCarroll et al. [“Differential analysis of capillary breakup rheometry for Newtonian liquids,” J. Fluid Mech. 804, 116 (2016)], expanding on McKinley and Tripathi [“How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer,” J. Rheol. 44, 653 (2000)], to evaluate the surface tension to viscosity ratio for Newtonian filaments is examined. The analysis is valid during and after stretch, while the latter is traditionally applied after cessation of stretch as the midfilament radius approaches zero. Through numerical simulations, the evaluation of viscosity is investigated for two common stretch histories: (a) the ramp function and (b) the modified step strain. The challenges with stretch are twofold: rapid stretch (large capillary number) results in a nearly cylindrical filament with a rapid change near the plate that challenges the one-dimensional (1D) approximation, while slow stretch results in a nearly static solution with limited viscous information. We examine the capillary number-aspect ratio parameter space and find the ramp function with small stretching speeds optimal. Hence, the most accurate measurements are taken while the filament is being stretched.

Timing jitter of monodisperse droplets generated by capillary jet breakup

Uniform droplets generated by Rayleigh breakup of liquid jet are widely applied in science and engineering. The droplets are produced by imposing a periodic velocity perturbation on a micro-sized liquid jet. In practical situations, the frequency of droplet generation is not perfectly steady like the preset perturbation frequency. This unwanted timing jitter poses kinds of problems. We studied the fluid mechanism of the jitter at short working distance and its dependence on various parameters. We found that at short distance, the jitter is mainly affected by the reduction rather than the dispersion in the droplet velocity. The magnitude of the jitter is related to the velocity reduction and the unsteadiness of the perturbation. The velocity difference between the droplet and the jet is analytically obtained based on one-dimensional linear analysis of drop formation in liquid jet, and numerical simulations validate the results. The influence of the unsteady perturbation is explained by the evolution of control volumes with different initial amplitudes. The degree of jitter is finally deduced, and its relationships with each variable are compared with experiments. Optimization methods are given to mitigate jitter by adjusting the perturbation parameters and jet properties.

Influence of volume and aspect ratio of liquid bridges on capillary breakup rheometry

Capillary thinning of liquid bridges is routinely used for extensional rheology of Newtonian and complex fluids. Although it is expected that the volume and aspect ratio of a liquid bridge significantly influence its dynamics, the role played by these parameters in rheological characterization has not been previously studied. We perform numerical simulations of Newtonian as well as viscoelastic liquid bridges with the one-dimensional slender-filament approximation of Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and Ardekani et al. [“Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets,” J. Fluid Mech. 665, 46–56 (2010)]. Sample volume and bridge aspect ratio control two phenomena that can adversely impact rheological characterization: the tendency to form satellite drops at the necking plane and the slowing down of capillary thinning due to the proximity (in parameter space) of the liquid-bridge stability boundary. The optimal range of these parameter values to avoid drop formation and slowdown is discussed.