Uniaxial Extensional Flow Research Articles

Modulating droplet electrohydrodynamics via the interplay of extensional flow and an alternating current electric field

Electric fields can be used to exert controlled time-varying forces on a droplet under progressive stretching in an extensional flow, allowing for its precise manipulation in various industrial and scientific applications, including microfluidics, materials science, and biological studies. However, the interaction between the combined extensional flow field and electric field may trigger a complex electrohydrodynamic response, as determined primarily by the capillary and viscous forces and the convection of surface charge. Here, we theoretically and computationally analyze the deformation and breakup of a droplet subjected to an alternating current (AC) electric field and uniaxial extensional flow. Our asymptotic theory, applicable in the small-deformation limit, quantifies the contributions of each applied field to the shape oscillations. Numerical simulations are employed to explore the dynamical evolution of the droplet in the nonlinear regime of variation in the capillary number. Our theoretical and numerical results are in excellent agreement, demonstrating that an AC electric field can significantly alter transient deformation depending on its magnitude and frequency. We identify the threshold frequency, dependent on the ratios of electrical properties, which can induce periodic oblate-prolate shape transitions. The interaction between viscous and electric stresses driving these transients is discussed. Contrary to intuition, strong electric fields greatly suppress shape oscillations, leading instead to large continuous elongations that eventually result in an end-pinching breakup mode, forming elongated bulbous-ended droplets. The breakup state, characterized by droplet length and shape at the onset of breakup, is determined by the field parameters and the physical properties of the fluids. Notably, the breakup state length and total breakup time have a non-monotonic relationship with the applied electric field frequency. The insights gained into the physics of oscillatory stable deformation and non-oscillatory unstable deformation offer new means of droplet manipulation in droplet-based micro-mechano-electrical systems that remained unexplored thus far.

Experimental Analysis Of Flow Birefringence In Jeffery-Hamel Flow

The photoelastic method, a stress field measurement method in solid mechanics, is being considered for application to fluids. In previous studies, simple shear flow and uniaxial extensional flow experiments have shown a relationship between the measured phase retardation and the velocity field. However, no clear relationship has been shown for extensional and shear combined flow fields. The objective of the present study is to clarify the relationship between the velocity field and the measured phase retardation in an extensional-shear combined flow. For this objective, photoelastic measurements were conducted in a steady flow field using the Jeffery-Hamel flow, which is an extensional-shear combined flow with an analytical solution for the velocity field. Comparison with the analytical velocity field showed that birefringence was proportional to the 0.88 and 0.92 power of the deformation in the shear or extensional-dominated region, respectively. The results show that the birefringence Δ_n followed the power law of extensional rate ε^{0.95} where it is dominant. Whereas shear is dominant, Δ_n proportional to a power-law of γ^{0.88} holds. These results are consistent with previous studies using shear flow and uniaxial extensional flow. Furthermore, it is shown that in the extensional-shear combined flow, the sum-of-squares root of two equations suggests that the theory developed mainly for solids could also be applied to fluids.

Stable production of fluid jets with vanishing diameters via tip streaming

We study numerically the microjetting mode obtained when a fluid is injected through a tube submerged in a uniaxial extensional flow. The steady solution to the full nonlinear Navier–Stokes equations is calculated. We obtain the linear global modes determining the linear stability of the steady solution. For sufficiently large outer viscosity, the flow remains stable for infinitely small values of the injected flow rate. This implies that jets with vanishing diameters can be produced regardless of the jet viscosity and outer flow strength. For a sufficiently small inner-to-outer viscosity ratio, the microjetting instability is associated only with the flow near the entrance of the jet. The tapering meniscus stretches and adopts a slender quasiconical shape. Consequently, the cone tip is exposed to an intense outer flow, which stabilizes the flow in the cone–jet transition region. This work presents the first evidence that fluid jets with arbitrarily small diameters can be stably produced via tip streaming. The results are related to those of a droplet in a uniaxial extensional flow with its equator pinned to an infinitely thin ring. The pinning of the equator drastically affects the droplet stability and breakup.

Numerical simulation of fiber orientation kinetics and rheology of fiber-filled polymers in uniaxial extension

During processing of fiber composites, the fiber-induced stresses influence the local flow fields, which, in turn, influence the stress distribution and the fiber orientation. Therefore, it is crucial to be able to predict the rheology of fiber-filled polymer composites. In this study, we investigate the fiber orientation kinetics and rheological properties of fiber composites in uniaxial extensional flow by comparing direct numerical finite element simulations to experimental results from our previous study [Egelmeers et al., “In-situ experimental investigation of fiber orientation kinetics during uniaxial extensional flow of polymer composites,” J. Rheol. 68, 171–185 (2023)]. In the simulations, fiber–fiber interactions only occur hydrodynamically and lubrication stresses are fully resolved by using adaptive meshing. We employed a 7-mode and a 5-mode viscoelastic Giesekus material model to describe the behavior of, respectively, a strain hardening low-density polyethylene (LDPE) matrix and a non-strain hardening linear LDPE matrix, and investigated the influence of the Weissenberg number, strain hardening, and fiber volume fraction on the fiber orientation kinetics. We found that none of these parameters influence the fiber orientation kinetics, which agrees with our experimental data. The transient uniaxial extensional viscosity of a fiber-filled polymer suspension is investigated by comparing finite element simulations to a constitutive model proposed by Hinch and Leal [“Time-dependent shear flows of a suspension of particles with weak Brownian rotations,” J. Fluid Mech. 57(4), 753–767 (1973)] and to experimental results obtained in our previous study [Egelmeers et al., “In-situ experimental investigation of fiber orientation kinetics during uniaxial extensional flow of polymer composites,” J. Rheol. 68, 171–185 (2023)]. The simulations describe the experimental data well. Moreover, high agreement is found for the transient viscosity as a function of fiber orientation between the model and the simulations. At high strains for high fiber volume fractions, however, the simulations show additional strain hardening, which we attribute to local changes in microstructure.

Brownian dynamics simulations of bottlebrush polymers in dilute solution under simple shear and uniaxial extensional flows.

We study the dynamics of bottlebrush polymer molecules in dilute solutions subjected to shear and uniaxial extensional flows using Brownian dynamics simulations with hydrodynamic interaction (HI). Bottlebrush polymers are modeled using a coarse-grained representation, consisting of a set of beads interacting pairwise via a purely repulsive potential and connected by finitely extensible nonlinear springs. We present the results for molecular stretching, stress, and solution viscosity during the startup of flow as well as under steady state as a function of side chain length while keeping the backbone length fixed. In extensional flow, the backbone fractional extension and the first normal stress difference decrease with an increase in side chain length at a fixed Weissenberg number (Wi). Using simulation results both in the presence of and in the absence of HI, we show that this is primarily a consequence of steric interaction resulting from the dense grafting of side chains. In shear flow, we observe a shear-thinning behavior in all cases, although it becomes less pronounced with increasing side chain length. Furthermore, nonmonotonicity in the backbone fractional extension is observed under shear, particularly at high Wi. We contextualize our simulation results for bottlebrush polymers with respect to existing studies in the literature for linear polymers and show that the unique dynamical features characterizing bottlebrush polymers arise on account of their additional molecular thickness due to the presence of densely grafted side chains.

In situ experimental investigation of fiber orientation kinetics during uniaxial extensional flow of polymer composites

The demand for fiber-filled polymers has witnessed a significant upswing in recent years. A comprehensive understanding of the local fiber orientation is imperative to accurately predict the mechanical properties of fiber-filled products. In this study, we experimentally investigated the fiber orientation kinetics in uniaxial extensional flows. For this, we equipped a rheometer with a Sentmanat extensional measurement device and with an optical train that allows us to measure the fiber orientation in situ during uniaxial extension using small angle light scattering. We investigated an experimental system with glass fibers for the suspended phase (L/D=8−15), and for the matrix either low density polyethylene, which shows strain hardening in extension, or linear low density polyethylene, which shows no strain hardening. For these two polymer matrices, the fiber orientation kinetics were investigated as a function of fiber volume fraction (ϕ=1%, 5%, and 10%) and Weissenberg number (by varying the Hencky strain rate, ϵ˙H=0.01−1s−1). We found that all these parameters did not influence the fiber orientation kinetics in uniaxial extension and that these kinetics can be described by a multiparticle model, based on Jeffery’s equation for single particles. Our results show that, in uniaxial extension, fiber orientation is solely determined by the applied strain and that, up to the concentrated regime (ϕ≈D/L), fiber-fiber interactions do not influence the fiber orientation. The extensional stress growth coefficient of these composites, which is measured simultaneously with the orientation, shows high agreement with Batchelor’s equation for rodlike suspensions.

Steady-state simulation of the film-casting process for Newtonian and viscoelastic fluids

Thin polymeric films are usually produced in an extensional flow between an extrusion head and a chill roll. The final product is prone to several defects, such as reduced width and non-uniform thickness, and a better understanding of the whole process can improve the final product quality and reduce wastes. This work revisits the film-casting process by exploring the scaling relation between different variables, with particular focus on the width reduction (neck-in). The numerical simulations are carried out for Newtonian, Upper-Convected Maxwell and Giesekus fluids in isothermal and steady-state conditions, for varying film aspect ratio (AR; film width over length), draw ratio (DR) and Deborah number (De). The governing equations are discretized with finite-volumes in their full form (3D model) and using an approximate 2.5D model. However, the latter has been mainly used in this study, as it offered similar accuracy as the 3D model, at a much lower computational cost. The results show that the normalized film shape is independent of the aspect ratio for sufficiently high values of this parameter and that the film thickness scales with DR according to the theoretical prediction for planar and uniaxial extensional flows, in the centre and edge regions, respectively. The neck-in grows logarithmically with the draw ratio for high AR, with a De-dependent growth rate (higher De leads to lower neck-in and lower dependence on DR). There is a reasonable correlation between the neck-in and the ratio between the planar and uniaxial extensional viscosities, as well as between the neck-in and dimensionless variable M = ln(DR)/(De+δ), where δ is a constant which depends on the fluid rheology. However, none of the correlations offer a perfect fit to the neck-in and the search for such a correlation (or master curve) shall be pursued in future works.

Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar, and biaxial extensional rheology of dilute polymer solutions using numerically optimized stagnation point microfluidic devices

Part I of this paper [Haward et al., J. Rheol. 67, 995–1009 (2023)] presents a three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. Here, in Part II, the OUBER device is employed to examine the uniaxial and biaxial extensional rheology of model dilute polymer solutions, compared with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [OSCER, Haward et al. Phys. Rev. Lett. 109, 128301 (2012)]. In each case, micro-particle image velocimetry is used to measure the extension rate as a function of the imposed flow conditions, and excess pressure drop measurements enable estimation of the tensile stress difference generated in the fluid via a new analysis based on the macroscopic power balance for flow through each device. Based on this analysis, for the most dilute polymer sample tested, which is “ultradilute”, the extensional viscosity is well described by Peterlin’s finitely extensible nonlinear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, although the fluids remain dilute, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as the polymer chains unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, thereby limiting the utility of this flow type for extensional viscosity measurement.

Extensional rheometry of mobile fluids. Part I: OUBER, an optimized uniaxial and biaxial extensional rheometer

Numerical optimization of a “six-arm cross-slot” device yields several three-dimensional shapes of fluidic channels that impose close approximations to an ideal uniaxial (biaxial) stagnation point extensional flow under the constraints of having four inlets and two outlets (two inlets and four outlets) and for Newtonian creeping flow. One of the numerically designed geometries is considered suitable for fabrication at the microscale, and numerical simulations with the Oldroyd-B and Phan-Thien and Tanner models confirm that the optimal flow fields are observed in the geometry for both constant viscosity and shear thinning viscoelastic fluids. The geometry, named the optimized uniaxial and biaxial extensional rheometer (OUBER), is microfabricated with high precision by selective laser-induced etching of a fused-silica substrate. Employing a refractive index-matched viscous Newtonian fluid, microtomographic-particle image velocimetry enables the measurement of the flow field in a substantial volume around the stagnation point. The flow velocimetry, performed at low Reynolds number (<0.1), confirms the accurate imposition of the desired and predicted flows, with a pure extensional flow at an essentially uniform deformation rate being applied over a wide region around the stagnation point. In Part II of this paper [Haward et al., J. Rheol. 67, 1011–1030 (2023)], pressure drop measurements in the OUBER geometry are used to assess the uniaxial and biaxial extensional rheometry of dilute polymeric solutions, in comparison to measurements made in planar extension using an optimized-shape cross-slot extensional rheometer [OSCER, Haward et al., Phys. Rev. Lett. 109, 128301 (2012)].

A triple emulsion droplet in an extensional flow

In this theoretical report we analytically explore the deformation and breakup of an initially spherical triple emulsion drop undergoing an axisymmetric extensional creeping flow. The triple emulsion, suspended in an external fluid (fluid 1), is originally made from an inner spherical drop (fluid 4), engulfed by a spherical shell (fluid 3), which is subsequently engulfed by another spherical shell (fluid 2). The problem is described by eight dimensionless parameters: the external capillary number (Ca), three viscosity ratios (λ21, λ32, λ43), two radii ratios (K, k), and two surface tensions ratios (M, m). When the triple emulsion is subjected to an external uniaxial extensional flow (Ca > 0), the outer interface (21) and the inner drop interface (43) deform into prolate spheroids, while the interface between them (32) deforms into an oblate spheroid. The reverse occurs for an external biaxial flow (Ca < 0), the outer interface (21) and the inner drop interface (43) deform into oblate spheroids and the middle interface (32) becomes a prolate spheroid. Three types of breakup mechanisms are to be expected: when the outer and the middle interfaces are in contact, when the middle and the inner interfaces are in contact, and when the inner drop breaks while the two shell phases remain continuous. Finally, an analytical expression for the effective viscosity of a dilute emulsion containing spherical triple emulsion droplets is suggested. For a triple emulsion which behaves like a solid: a very viscous or a very thin outer shell (λ21→∞ or K→ 1), the effective viscosity reduces to Einstein’s formula, and when the triple emulsion behaves like a single drop: a very thick outer shell such that the inner shell and the inner drop disappear (K→ 0), Taylor’s expression is recovered.

3D manipulation and dynamics of soft materials in 3D flows

Flow-based manipulation of particles is an essential tool for studying soft materials, but prior work has nearly exclusively relied on using two-dimensional (2D) flows generated in planar microfluidic geometries. In this work, we demonstrate 3D trapping and manipulation of freely suspended particles, droplets, and giant unilamellar vesicles in 3D flow fields using automated flow control. Three-dimensional flow fields including uniaxial extension and biaxial extension are generated in 3D-printed fluidic devices combined with active feedback control for particle manipulation in 3D. Flow fields are characterized using particle tracking velocimetry complemented by finite-element simulations for all flow geometries. Single colloidal particles (3.4 μm diameter) are confined in low viscosity solvent (1.0 mPa s) near the stagnation points of uniaxial and biaxial extensional flow for long times (≥10 min) using active feedback control. Trap stiffness is experimentally determined by analyzing the power spectral density of particle position fluctuations. We further demonstrate precise manipulation of colloidal particles along user-defined trajectories in three dimensions using automated flow control. Newtonian liquid droplets and GUVs are trapped and deformed in precisely controlled uniaxial and biaxial extensional flows, which is a new demonstration for 3D flow fields. Overall, this work extends flow-based manipulation of particles and droplets to three dimensions, thereby enabling quantitative analysis of colloids and soft materials in complex nonequilibrium flows.

Fracture in elongational flow of two low-density polyethylene melts

Samples of two commercial low-density polyethylene melts were investigated with respect to their fracture behavior in controlled uniaxial extensional flow at constant strain rate in a filament stretching rheometer. In order to assess the possible influence of grain boundaries on fracture, the samples were prepared by three different types of pre-treatment: by compression molding of (1) virgin pellets used as received, (2) pellets homogenized in a twin-screw extruder, and (3) pellets that were milled into powder by cryogenic grinding under liquid nitrogen. The elongational stress growth data were analyzed by the Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model developed by Wagner et al. (Rheol. Acta 61, 281-298 (2022)) for long-chain branched (LCB) polymer melts. The EHMMSF model quantifies the elongational stress growth including the maximum in the elongational viscosity of LDPE melts based solely on the linear-viscoelastic relaxation spectrum and two nonlinear material parameters, the dilution modulus GD and a characteristic stretch parameter {overline{lambda}}_m. Within experimental accuracy, model predictions are in excellent agreement with the elongational stress growth data of the two LDPE melts, independent of the preparation method used. At sufficiently high strain rates, the fracture of the polymer filaments was observed and is in general accordance with the entropic fracture criterion implemented in the EHMMSF model. High-speed videography reveals that fracture is preceded by parabolic crack opening, which is characteristic for elastic fracture and which has been observed earlier in filament stretching of monodisperse polystyrene solutions. Here, for the first time, we demonstrate the appearance of a parabolic crack opening in the fracture process of polydisperse long-chain branched polyethylene melts.

Complex flows of viscoelastic wormlike micelle solutions

Micelles are formed by the self-assembly of surfactants in solutions. Wormlike micelles or living polymers are a particularly interesting fluids because their long flexible cylindrical geometry can lead to entanglement even at relatively low concentrations. The non-linear rheological and flow response of wormlike micelles has proven to be incredibly rich and complex. In strong, steady-shear flows, some wormlike micelles have been shown to shear band. In uniaxial extensional flows, wormlike micelle solutions demonstrate enormous strain hardening of their extensional viscosity and under large extensional stresses, can break apart. This failure and the resulting morphological changes of the micelles in the flow have been linked to a number of interesting elastic instabilities that have been reported in flow of micelles past a falling sphere and/or a flexible cylinder. In this talk, we will primarily focus on flow of wormlike micelle solutions past a falling sphere and a flexible object, where both shear and extensional flow components are dominant. We will discuss how flow strength, detailed form of flow, micelle concentration, and micelle structure affect these complex flows.

Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution.

The transient elongational viscosity ηe(t) of the polymer melt is known to exhibit strain hardening, which depends on the strain rate ε˙. This phenomenon was elucidated by the difference of chain stretching in the entanglement network between extension and shear. However, to date, the microscopic evolution of polymer melt has not been fully statistically analyzed. In this work, the radial size distributions P(Rg,t) of linear polymers are explored by dissipative particle dynamics during the stretching processes. In uniaxial extensional flow, it is observed that the mean radius of gyration R¯g(t) and standard deviation σ(t) remain unchanged until the onset of strain hardening, corresponding to linear viscoelasticity. Both R¯g and σ rise rapidly in the non-linear regime, and bimodal size distribution can emerge. Moreover, the onset of strain hardening is found to be insensitive to the Hencky strain (ε˙Ht) and chain length (N).

Steady-state extensional rheology of a dilute suspension of spheres in a dilute polymer solution

It is well-known and intuitive that addition of a dilute volume concentration of spheres increases the viscosity of a Newtonian liquid. We find that a viscoelastic liquid undergoing uniaxial extensional flow at small $D\phantom{\rule{0}{0ex}}e$ (extension rate times the polymer relaxation time) experiences a larger increase in viscosity than the Newtonian case due to wakes of extra polymer stretch produced downstream of the spheres. However, when $D\phantom{\rule{0}{0ex}}e\ensuremath{\gtrsim}0.6$, the highly stretched polymer in the bulk fluid collapses near the particle surface and the suspension deforms more easily than the particle-free viscoelastic fluid.

The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow

The internal flow of a droplet in the nonlinear extensional flow field will exhibit more than two internal circulations with the variation of nonlinear intensity (E). In this paper, the effect of positions and sizes of internal circulations on internal mass transfer rate of a single spherical droplet in a nonlinear extensional flow field is studied and compared with that in a linear extensional flow field. The simulation results show that when E ≥ 0, there are two symmetrical internal circulations in the droplet, which is the same with that in a linear extensional flow. The limit value of mass transfer rate Sh is 15, which is equal to that in a linear extensional flow, no matter how large E is. When E ≤ –3/7, the number of internal flow circulation of a droplet increase to four and the transfer rate Sh increases. When E = –1, the maximum internal transfer rate Sh equals 30 which is twice of that in a linear extensional flow. The generation of new flow circulations in droplets and the circulation positions will enhance mass transfer when E ≤ –3/7, which provides a new idea for enhancing the internal mass transfer rate of droplets.

Comparison of Rheological Properties between DoS and Liquid Dropping Methods in Uniaxial Extensional Flow of Dilute Polymer Aqueous Solutions

Comparison of Rheological Properties between DoS and Liquid Dropping Methods in Uniaxial Extensional Flow of Dilute Polymer Aqueous Solutions

Wrinkling and multiplicity in the dynamics of deformable sheets in uniaxial extensional flow

The processing of thin-structured materials in a fluidic environment, from nearly inextensible but flexible graphene sheets to highly extensible polymer films, arises in many applications. So far, little is known about the dynamics of such thin sheets freely suspended in fluid. In this work, we study the dynamics of freely suspended soft sheets in uniaxial extensional flow. Elastic sheets are modeled with a continuum model that accounts for in-plane deformation and out-of-plane bending, and the fluid motion is computed using the method of regularized Stokeslets. We explore two types of sheets: "stiff" sheets that strongly resist bending deformations and always stay flat, and "flexible" sheets with both in-plane and out-of plane deformability that can wrinkle. For stiff sheets, we observe a coil-stretch-like transition, similar to what has been observed for long-chain linear polymers under extension as well as elastic sheets under planar extension: in a certain range of capillary number (flow strength relative to in-plane deformability), the sheets exhibit either a compact or a highly stretched conformation, depending on deformation history. For flexible sheets, sheets with sufficiently small bending stiffness wrinkle to form various conformations. Here, the compact-stretched bistability still occurs, but is strongly modified by the wrinkling instability: a highly-stretched planar state can become unstable and wrinkle, after which it may dramatically shrink in length due to hydrodynamic screening associated with wrinkling. Therefore, wrinkling renders a shift in the bistability regime. In addition, we can predict and understand the nonlinear long-term dynamics for some parameter regimes with linear stability analysis of the flat steady states.

Flow-induced crystallization of polylactides

In this work, the flow-induced crystallization of two polylactides (PLAs) with different microstructures (different l-lactic acid contents) is studied using simple shear, uniaxial extension and capillary flow experiments. In a simple shear and capillary flow, an increase in shear rate and a decrease in temperature were found to enhance the crystallization kinetics particularly for Weissenberg numbers (based on the reptation relaxation time, Wi) greater than 1 (strong flow causing chain stretching). On the other hand, in a uniaxial extensional flow, once a critical Hencky strain is achieved, crystallization starts independently of strain rate and temperature. The amount of mechanical work per unit volume imposed/dissipated onto the polymers during flow to initialize crystallization was also calculated in the simple shear, capillary, and extensional flow. The critical mechanical work for the onset of flow-induced crystallization was found to be independent of temperature and degree of molecular chain stretch (Wi) as Wi becomes greater than 1. The critical mechanical work for the onset of flow-induced crystallization in an extensional flow was found to be much smaller than that in a shear flow. The PLA sample with higher content of PLLA showed slightly higher zero-shear viscosity and a smaller thermodynamic barrier for the onset of crystallization. Finally, the degree of crystallinity increases linearly from 0% at the start of the flow-induced crystallization region and reaches a plateau at Wi equals to around 1.

Stability and tip streaming of a surfactant-loaded drop in an extensional flow. Influence of surface viscosity

We study numerically the nonlinear stationary states of a droplet covered with an insoluble surfactant in a uniaxial extensional flow. We calculate both the eigenfunctions to reveal the instability mechanism and the time-dependent states resulting from it, which provides a coherent picture of the phenomenon. The transition is of the saddle-node type, both with and without surfactant. The flow becomes unstable under stationary linear perturbations. Surfactant considerably reduces the interval of stable capillary numbers. Inertia increases the droplet deformation and decreases the critical capillary number. In the presence of the surfactant monolayer, neither the droplet deformation nor the stability is significantly affected by the droplet viscosity. The transient state resulting from instability is fundamentally different for drops with and without surfactant. Tip streaming occurs only in the presence of surfactants. The critical eigenmode leading to tip streaming is qualitatively the same as that yielding the central pinching mode for a clean interface, which indicates that the small local scale characterizing tip streaming is set during the nonlinear droplet deformation. The viscous surface stress does not significantly affect the droplet deformation and the critical capillary number. However, the damping rate of the dominant mode considerably decreases for viscous surfactants. Interestingly, shear viscous surface stress considerably alters the tip streaming arising in the supercritical regime, even for very small surface viscosities. The viscous surface stresses alter the balance of normal interfacial stresses and affect the surfactant transport over the stretched interface.