non-Newtonian Droplets Research Articles

Dynamics of non-Newtonian droplets eccentrically impacting hydrophobic spherical surfaces

In this study, the dynamic behaviors of non-Newtonian fluid droplets with shear-thinning properties eccentrically impacting hydrophobic particle surfaces are investigated through a combination of numerical simulations and experiments. The simulation integrates the dynamic contact angle and a non-Newtonian fluid power-law model within the volume of fluid model framework. The effects of apparent viscosity (η), impact velocity (v0), and dimensionless eccentricity parameter (B) on the dynamic behaviors of non-Newtonian droplets are analyzed. Furthermore, the study offers insight into the progression of pressure distribution, kinetic energy, and liquid viscosity across droplets during the entire impact process. An energy balance analysis, which includes kinetic energy, surface energy, potential energy, and viscous dissipation, is employed to elucidate the fundamental physical mechanisms that govern the dynamics of eccentric impacts of non-Newtonian droplets. Finally, a model (Recr D* = −95.7 + 11 450.6e−B/0.18) is proposed to predict the adhesion or detachment of shear-thinning droplets eccentrically impacting hydrophobic particle surfaces.

Dilute Polymer Droplets Show Generalized Wetting Dynamics via an Average Viscosity.

Despite the prevalence of non-Newtonian fluids in various practical applications, comprehensive dynamic wetting models are lacking. Existing models often oversimplify complex rheological behavior, limiting our ability to predict wetting dynamics. This work introduces and experimentally validates a generalized model for the dynamic wetting of non-Newtonian shear-thinning fluids (dilute polymer solutions) on solid substrates. We experimentally analyzed 12 different shear-thinning fluids using both a power-law model and Carreau-Yasuda model. The data clearly show that the dynamic contact angle can be generalized using an average viscosity to capture rheological changes during droplet spreading. The average viscosity was defined using the fluid's constitutive model over shear rates relevant to the spreading process. Using a small droplet approximation, we propose and validate a semianalytical spreading model to predict the basal radius of non-Newtonian droplets. The model agrees well with the experimental data. Additionally, the average viscosity was used to define a spreading time scale, which is capable of collapsing the spreading of different non-Newtonian fluids onto a master spreading curve. This work offers significant potential for predicting the dynamic shape and spreading of non-Newtonian fluids with complex rheologies in a range of applications and industrial processes.

Capillary wave-assisted collapse of non-Newtonian droplets

Understanding the peripheral capillary wave propagation during droplet impact is crucial for comprehending the physics of wetting onset and droplet fragmentation. Although Newtonian droplets have been extensively studied, we show how capillary waves deform non-Newtonian droplets in such a way that rheological features, such as the critical concentrations for the overlap (c*) and entangled polymer molecules (c**), may be directly obtained from the deformation history. Determining these critical concentrations is essential as they mark transitions in the rheological behavior of aqueous polymeric solutions, influencing viscosity, elasticity, and associated fluid dynamics. We have also compared capillary waves among Newtonian, shear-thinning, and Boger fluid droplets and found that although the fluid kinematics appear to be purely biaxial extensional flow, the infinite-shear properties of the droplets dominate the physics of capillary wave formation and propagation.

Dynamic behaviors of shear-thinning droplet impacting on a spherical particle surface

Non-Newtonian droplet impact is common in nature and industry. The viscosity of non-Newtonian liquids changes with shear stress, leading to different impact behaviors compared to Newtonian liquids. This study prepared shear-thinning solutions by adding HPMC polymer into deionized water and investigated its impact dynamics on hydrophobic spherical surface. The evolution patterns of droplet spreading factor, film thickness, and dynamic contact angle are investigated under different impact conditions. The results show that addition of polymers increases the energy dissipation during impact and suppresses droplet rebound from spherical surface compared to Newtonian droplet with similar viscosity. The droplet-impacting process is distinguished into three phases: (I) initial deformation, (II) inertia-dominated, and (III) viscosity-dominated phases. The temporal evolution of film thickness in Phases I and II is fitted by simple equations. In addition, an empirical formula that integrates Weber and Reynold numbers is proposed to predict the maximum spreading factor of HPMC droplets.

Numerical investigation of non-Newtonian droplet collisions: Comparison of volume of fluid and the local front reconstruction method with experimental data

Droplet-droplet collisions of non-Newtonian fluids are often encountered in industrial applications such as spray drying, fluid catalytic cracking, coating and granulation. However, there has been limited focus on a comprehensive analysis of the dynamics of these non-Newtonian binary droplet collisions. In this work, the non-Newtonian binary droplet collisions of 500 ppm xanthan gum solutions are simulated using the Volume of Fluid method and the Local Front Reconstruction Method to determine the applicability of these methods for the simulations of binary non-Newtonian droplet collisions. After verification, the simulations are compared to experimental data from literature. The outcomes for off-center collisions in the simulations resemble the experimental observations, including the oscillation of the ligament. For head-on collisions, the initial interactions and collision dynamics can be predicted with both methods at low Weber numbers, while LFRM shows improved performance at higher Weber numbers. Further, the use of an effective viscosity for the simplified representation of the droplet collision has been proven unsuccessful due to the absence of a universal effective viscosity for all situations.

Three-dimensional internal flow evolution of an evaporating droplet and its role in particle deposition pattern

The internal flow within an evaporating sessile droplet is one of the driving mechanisms that lead to various particle deposition patterns seen in applications such as inkjet printing, surface patterning, and blood stain analysis. Despite decades of research, the causal link between droplet internal flow and particle deposition patterns has not been fully established. In this study, we employ a three-dimensional (3D) imaging technique based on digital inline holography to quantitatively assess the evolution of internal flow fields and particle migration in three distinct types of wetting droplets, namely water droplets, sucrose aqueous solution droplets, and sodium dodecylsulfate aqueous solution droplets, throughout their entire evaporation process. Our imaging reveals the three-stage evolution of the 3D internal flow regimes driven by changes in the relative importance of capillary flow, Marangoni flow, and droplet boundary movement during evaporation. Moreover, the migration of individual particles from their initial locations to deposition can be divided into five categories, with some particles depositing at the contact line and others inside the droplet. In particular, we observe the changing migration directions of particles due to competing Marangoni and capillary flows. We further develop an analytical model that predicts the droplet internal flow, deposition patterns, and determines the deposition mechanisms depending on their initial locations and evolving internal flow. The model, validated using different types of droplets from our experiment and the literature, can be further expanded to other Newtonian and non-Newtonian droplets, potentially serving as a real-time assessment tool for particle deposition in various applications.

Parallel governing criteria for non-Newtonian droplet rebound suppression on superhydrophobic surfaces

Non-Newtonian droplets are known to suppress rebound on superhydrophobic (SH) surfaces. Our previous work (Dhar et al., Phys Rev Fluids, 2019, vol 4 [1]) showed that the polymer concentration and impact velocity must exceed a certain threshold to initiate the onset of rebound suppression. Analogous to drag reduction or elastic instabilities, we proposed that rebound suppression occurs only when the Weissenberg number exceeds unity (i.e., Wi >1) at the onset of retraction. In this study, we explore four different types of SH surfaces to examine the universality of the previous observation (the importance of Wi >1 for rebound suppression). We observed that rebound suppression does not occur on all types of SH surfaces. The surfaces where rebound suppression was observed are categorized as ‘Type-I’, while the remaining as ‘Type-II’. The non-uniformity in the rebound suppression phenomena is explained by the role of Cassie to Wenzel transformation (CWT) or impalement. We showed that for ‘Type-I’ surfaces, when the ratio of dynamic pressure (PD) to minimum capillary pressure (PC) exceeds unity (i.e., PD/PC > 1), the rebound is suppressed. The ‘Type-II’ surfaces have characteristic spacing in the order of nanometers, which is three orders of magnitude lower than the microtextured ‘Type-I’ surfaces. Thereby, the minimum capillary pressure is significantly higher for ‘Type-II’ surfaces. The dynamic pressure could not surpass the minimum capillary pressure for the impact velocities and polymer concentrations studied for the ‘Type-II’ surfaces. As PD/PC remained < 1, for ‘Type-II’ surfaces, rebound suppression was not observed. It must be noted that for the same values of PD/PC > 1 values, water droplets didn’t show rebound suppression on ‘Type-I’ surfaces. The non-Newtonian droplets are known to slow down the retraction dynamics due to normal stress, extensional viscosity and higher adsorption at the substrate. We have demonstrated the role of extensional viscosity in this study, particularly how strain stiffening of radial filaments emanating from the droplet aids in dissipating energy, which further aids in arresting drop rebound. Therefore, the existence of two parallel mechanisms: the role of fluid elasticity (manifested through Wi > 1), and the role of CWT or impalement (manifested through PD/PC> 1), are necessary conditions for non-Newtonian drop rebound suppression on superhydrophobic surfaces.

Experimental investigation of non-Newtonian droplet splitting mechanism in a cross-flow type microfluidic device

Experimental investigation of non-Newtonian droplet splitting mechanism in a cross-flow type microfluidic device

A universal rescaling law for the maximum spreading factor of non-Newtonian droplets with power-law fluids

The maximum spreading diameter of non-Newtonian fluid droplets impacting on the solid surface is a key concern in a variety of industrial and medical applications. In this work, we focus on the effect of the shear-thinning, one of the most important non-Newtonian properties, on the spreading dynamics of impacting droplets. A finite element scheme combined with a phase field method and dynamic contact angle model has been employed to perform extensive studies on the spreading process of power-law fluid droplets on solid surfaces with various rheological parameters, impact conditions and surface wettability. The simulation results show that on both hydrophilic and hydrophobic surfaces, impacting droplets exhibit two typical morphologies at the maximum spreading state: a spherical cap in the low-Weber-number range (capillary regime) and a thin-film form in the high-Weber-number range (viscous regime). The maximum spreading factor βmax, of droplets with different degrees of shear-thinning converges to the equilibrium spreading state for a droplet with U0=0 at the low-Weber-number limit. Furthermore, a theoretical relationship of βmax∼We1/2 has been derived in the capillary regime. In contrast, the effect of the shear-thinning property becomes significant in the high-Weber-number regime. We discussed the influence of the power-law coefficients K and n on the spreading process and βmax independently. Specifically, as the power-law index n decreases, the morphology of the shear-thinning droplet at the maximum spreading state tends to change from a spherical cap to a thin-film form. Considering the non-uniform distribution of shear rates in the spreading shear-thinning droplet, a new scaling relationship of βmax∼ln(Ren1/(2n+3)) has been proposed based on theoretical derivation and numerical simulations. By introducing an interpolation function on the scaling relationships between the capillary and viscous regimes, we obtained a universal rescaling model that agrees well with numerical and experimental results of non-Newtonian droplets with shear-thinning fluid over a wide range of We numbers, surface wettability and rheological parameters.

Triggering of electro-elastic anti-superhydrophobicity during non-Newtonian droplet collision

The present article discusses the electrohydro-dynamics of impacting non-Newtonian dielectric droplets on superhydrophobic (SH) surfaces. The role of important parameters like electric Eotvos number ( Eo e ), Weber number ( We ), dielectric particle concentration ( TiO 2 ) and polymer concentration ( PEG-400 ) were elucidated in this experimental study. Due to the interplay of non-Newtonian effects and electric field, we had observed the suppression of drop rebound on SH surfaces at much lower Eo e compared to its Newtonian counterpart. It has been observed that with an increase in both polymer concentration or dielectric particle concentration, the suppression of drop rebounds was observed at lower Eo e. In order to encapsulate the combined effects of electric field and non-Newtonian dynamics on drop rebound suppression, we have introduced the ‘electro-elastic effect’. Contrary to the common observations of drop rebound on SH surfaces, this electro-elastic effect induces inhibition of drop rebound, thereby resulting in anti-superhydrophobicity. Subsequently, we also established a scaling relationship to show that the rebound suppression is observed as a manifestation of the onset of electro-elastic instability, when a proposed electric Weissenberg number ( Wi e ) exceeds unity. Finally, we demarcated the rebound and rebound suppression regimes of droplet dynamics through a detailed phase map.

Impinging blood droplets on different wettable surfaces: Impact phenomena, contact line motion, post-impact oscillation and dried stains

Understanding the underlying hydrodynamics of impinging blood droplets and finding out the physical parameters determining the bloodstain characteristics are of great importance in blood related forensic investigations. In this work, the impact of non-Newtonian blood droplets on solid surfaces ranging from lyophilic to superlyophobic was systematically investigated and compared to that of Newtonian droplets with a similar dynamic shear viscosity. We show that impinging blood droplets behave as low-viscosity Newtonian droplets in the short-time spreading, which is dominated by capillary and inertial forces, but their non-Newtonian viscoelasticity would notably affect the droplet retraction and post-impact oscillation occurring in large timescales. Whereas the strong liquid–solid adhesion and the non-Newtonian elongational viscosity hinder droplet recoiling and thus alter the impact phenomena on lyophobic and superlyophobic surfaces, the shear and elongational viscosities are coupled to result in higher damping coefficients of oscillating blood droplets after deposition, in comparison to that of impinging Newtonian droplets. The size of the dried bloodstain was found to be different from both the maximum spreading radius of the droplet that can reach during impact and the final radius of the deposited droplet after oscillation, and their correlations are highly dependent on the impact velocity and surface wettability. Moreover, the morphologic characteristics of the bloodstains would also be changed by varying either the impact velocity or the surface wettability. We envision that these findings can not only find applications in the bloodstain pattern analysis, but also provide useful information for medical diagnosis based on blood droplet test.

Shock-induced aerobreakup of a polymeric droplet

Droplet atomization through aerobreakup is omnipresent in various natural and industrial processes. Atomization of Newtonian droplets is a well-studied area; however, non-Newtonian droplets have received less attention despite their being frequently encountered. By subjecting polymeric droplets of different concentrations to the induced airflow behind a moving shock wave, we explore the role of elasticity in modulating the aerobreakup of viscoelastic droplets. Three distinct modes of aerobreakup are identified for a wide range of Weber number $({\sim }10^2\unicode{x2013}10^4)$ and elasticity number $({\sim }10^{-4}\unicode{x2013}10^2)$ variation: these modes are vibrational, shear-induced entrainment and catastrophic breakup modes. Each mode is described as a three-stage process. Stage I is droplet deformation, stage II is the appearance and growth of hydrodynamic instabilities and stage III is the evolution of liquid mass morphology. It is observed that elasticity plays an insignificant role in the first two stages but a dominant role in the final stage. The results are described with the support of adequate mathematical analysis.

Impact Dynamics of Non-Newtonian Droplets on Superhydrophobic Surfaces

Droplet impact behavior on a solid surface is critical for many industrial applications such as spray coating, food production, printing, and agriculture. For all of these applications, a common challenge is to modify and control the impact regime and contact time of the droplets. This challenge becomes more critical for non-Newtonian liquids with complex rheology. In this research, we explored the impact dynamics of non-Newtonian liquids (by adding different concentrations of Xanthan into water) on superhydrophobic surfaces. Our experimental results show that by increasing the Xanthan concentration in water, the shapes of the bouncing droplet are dramatically altered, e.g., its shape at the separation moment is changed from a conventional vertical jetting into a "mushroom"-like one. As a result, the contact time of the non-Newtonian droplet could be reduced by up to ∼50%. We compare the impact scenarios of Xanthan liquids with those of glycerol solutions having a similar apparent viscosity, and results show that the differences in the elongation viscosity induce different impact dynamics of the droplets. Finally, we show that by increasing the Weber number for all of the liquids, the contact time is reduced, and the maximum spreading radius is increased.

Morphology and kinematics of a train of power-law droplets in a corrugated microchannel

We numerically investigate the deformation of a train of power-law droplets in a highly viscous suspending medium in nonlinear microfluidic geometry. We examine how viscous stresses conspire against surface tension in two-dimensional incompressible liquid–liquid flow in a corrugated microchannel using the finite volume technique with the volume of fluid method. To instill the influences of shear thinning, Newtonian, and shear-thickening fluids, the range of power-law indices (n) is varied from 0.7-1.3. We validate our numerical model with the available literature data in good agreement. Interestingly, the corrugated cavities are found to have an elongating effect on the non-Newtonian droplets, whereas literature delineates a compressive effect of the nonlinear geometry on bubbles. Specific orbital trajectories are found in the (droplet length A, spacing B) space with dispersed and synchronized orbitals at low and high capillary number for all power-law droplets, respectively. Furthermore, the hysteresis in the droplet shape is found to increase with the capillary number. Consequently, the hysteretic area Ap revealed that the slope increases with (n). An interesting finding is elucidated where the hysteresis loops are found to rotate from low capillary to high capillary number for all power-law droplets. A new finding is reported where the evolution of the droplet perimeter revealed the development of secondary peaks as the capillary number increases. The power-law droplets are found to pack themselves up in the corrugated section in two distinct regimes: smaller droplets obey the linear deformation regime. In contrast, large droplets lie in the flow-induced deformation regime. The instantaneous cap velocities produce a nonmonotonic behavior for the front velocity as the capillary number increases for all power-law droplets. We develop functional relationships between flow parameters of segmented flows at the pore scale for every non-Newtonian droplet. Given the implications of this setup with industrial and biomedical applications, the illustrations shown herein could be beneficial in tackling problems at the pore scale with nonlinear fluids.

Study on the Bouncing Behaviors of a Non-Newtonian Fluid Droplet Impacting on a Hydrophobic Surface

The control of a droplet bouncing on a substrate is of great importance not only in academic research but also in practical applications. In this work, we focus on a particular type of non-Newtonian fluid known as shear-thinning fluid. The rebound behaviors of shear-thinning fluid droplets impinging on a hydrophobic surface (equilibrium contact angle θeq ≈ 108°and contact angle hysteresis Δθ ≈ 20°) have been studied experimentally and numerically. The impact processes of Newtonian fluid droplets with various viscosities and non-Newtonian fluid droplets with dilute xanthan gum solutions were recorded by a high-speed imaging system under a range of Weber numbers (We) from 12 to 208. A numerical model of the droplet impact on the solid substrate was also constructed using a finite element scheme with the phase field method (PFM). The experimental results show that unlike the Newtonian fluid droplets where either partial rebound or deposition occurs, complete rebound behavior was observed for non-Newtonian fluid droplets under a certain range of We. Moreover, the minimum value of We required for complete rebound increases with xanthan concentration. The numerical simulations indicate that the shear-thinning property significantly affects the rebound behavior of the droplets. As the amount of xanthan increases, the high shear rate regions shift to the bottom of the droplet and the receding of the contact line accelerates. Once the high shear rate region appears only near the contact line, the droplet tends to fully rebound even on a hydrophobic surface. Through the impact maps of various droplets, we found that the maximum dimensionless height Hmax* of the droplet increases almost linearly with We as Hmax* ∼ αWe. In addition, a critical value Hmax,c* for the distinction between deposition and rebound for droplets on the hydrophobic surface has been theoretically derived. The prediction of the model shows good consistency with the experimental results.

Binary coalescence of non-Newtonian droplets under an electric field: A numerical study

We numerically investigate the effect of electrohydrodynamics on a non-Newtonian droplet pair suspended in a Newtonian medium. The leaky dielectric model is implemented to study the response of emulsion drops in an externally applied electric field. Subsequently, the non-Newtonian drop behavior is incorporated using the power law model, whereby three different fluid behaviors are considered for the drops: Newtonian, Shear thinning, and Shear thickening. We validated our numerical model with the available literature data, and the results are in good agreement. The droplets' deformation and net motion are investigated for a range of electrical permittivity ratios of the droplet medium with respect to the surrounding fluid. In this study, four distinct regimes are identified based on the net drop pair motion and the circulation pattern that develops due to the electric stresses inside and around the drops. Furthermore, it is observed that the droplet deformation and their net motion are fastest for the pseudo-plastic drops and slowest for dilatant drops. We devised a simple ratio-based model to understand this behavior. The inferences drawn from this study will help contribute to a better understanding of the behavior of nonlinear fluids under an electric field.

Viscoelastic Particle Encapsulation Using a Hyaluronic Acid Solution in a T-Junction Microfluidic Device

The encapsulation of particles and cells in droplets is highly relevant in biomedical engineering as well as in material science. So far, however, the majority of the studies in this area have focused on the encapsulation of particles or cells suspended in Newtonian liquids. We here studied the particle encapsulation phenomenon in a T-junction microfluidic device, using a non-Newtonian viscoelastic hyaluronic acid solution in phosphate buffer saline as suspending liquid for the particles. We first studied the non-Newtonian droplet formation mechanism, finding that the data for the normalised droplet length scaled as the Newtonian ones. We then performed viscoelastic encapsulation experiments, where we exploited the fact that particles self-assembled in equally-spaced structures before approaching the encapsulation area, to then identify some experimental conditions for which the single encapsulation efficiency was larger than the stochastic limit predicted by the Poisson statistics.

Non-Newtonian droplet breakup in a T-junction microdevice containing constriction induced asymmetric parallel branches

Here, we describe the breakup and post-breakup dynamics of a non-Newtonian droplet of xanthan gum aqueous solution in asymmetric parallel branch microdevices. Our experimental results reveal that the droplet breakup regimes, namely, obstruction, tunnel, combined, non-breakup, and parallel, are the functions of xanthan gum concentration and the continuous phase flow rate. We examined the influence of fluid properties on droplet breakup stages by varying the xanthan gum concentration in an aqueous solution that exhibited increasing shear-thinning and elastic properties with its concentration. Four sequential stages (squeezing, transition, pinch-off, and filament thinning) are identified during the droplet breakup process. We found that upstream pressure controlled the squeezing stage, and fluid properties mainly steered the filament rupture stage. A complex interaction between elastic, capillary, and inertial forces further divided the final stage into the stretching and fluid-drainage stages. The Hencky strain characterized the formation of a persistent cylindrical filament in the stretching stage that decayed exponentially in the fluid-drainage stage. Eventually, this study highlights the significance of parallel branches with asymmetric geometric confinements on droplet splitting. Enhanced asymmetry is observed for the elongated filament, emphasizing the dominance of feedback from the downstream confinement.

Numerical simulation of secondary breakup of shear-thinning droplets

The breakup of non-Newtonian droplets is ubiquitous in numerous applications. Although the non-Newtonian property can significantly change the droplet breakup process, most previous studies consider Newtonian droplets, and the effects of non-Newtonian properties on the breakup process are still unclear. This study focuses on the secondary breakup of shear-thinning droplets by numerical simulation. The volume of fluid method is used to capture interface dynamics on adaptive grids. To compare shear-thinning droplets and Newtonian droplets, a new definition of the Ohnesorge number is proposed by considering the characteristic shear rate in the droplet induced by the airflow. The results show that compared with the Newtonian fluid, the shear-thinning properties can change the apparent viscosity distribution inside the droplet, alter the local deformation, change the droplet morphology, and affect the transition in the droplet breakup regime.

Impingement and mixing between two shear-thinning droplets on the solid surface

The impingement and the following mixing between non-Newtonian droplets on the solid surface are a common phenomenon in industry, where reasonably controlling the mixing is always of vital importance. In this work, Many Body Dissipative Particle Dynamics method is used to reveal the law of this process with two non-Newtonian droplets. Firstly, the variation of droplets morphology with the Weber number of the impinging droplet is studied. Then, by dividing this mixing process into convection-dominated and molecular diffusion-dominated stages, the relationship between duration of the former stage and Weber number is quantitatively determined. In the latter stage, it is found a special phenomenon in the mixing which results from the difference in particle diffusion coefficients. Finally, the mixing time for the two droplets and its variation with the Weber number is proposed, which can be helpful in the design of the related device when mixing is between non-Newtonian droplets.