Planar Flow Research Articles

Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid

We provide an explicit analytical solution of the planar Poiseuille flow of a viscoplastic fluid governed by the constitutive equation proposed by De Kee and Turcotte (1980). Formulae for the velocity and the flow rate are derived, making use of the Lambert W function. It is shown that a solution does not always exist because the flow curve is bounded from above and hence the rheological model can accommodate stresses only up to a certain limit. In fact, the flow curve reaches a peak at a critical shear rate, beyond which it exhibits a negative slope, giving rise to unstable solutions.

Dynamics of meniscus-bound particle clusters in extensional flow

Capillary suspensions are three-phase mixtures containing a solid particulate phase, a continuous liquid phase, and a second immiscible liquid forming capillary bridges between particles. Capillary suspensions are encountered in a wide array of applications including 3D printing, porous materials, and food formulations, but despite recent progress, the micromechanics of particle clusters in flow is not fully understood. In this work, we study the dynamics of meniscus-bound particle clusters in planar extensional flow using a Stokes trap, which is an automated flow control technique that allows for precise manipulation of freely suspended particles or particle clusters in flow. Focusing on the case of a two-particle doublet, we use a combination of experiments and analytical modeling to understand how particle clusters rearrange, deform, and ultimately break up in extensional flow. The time required for cluster breakup is quantified as a function of capillary number Ca and meniscus volume V. Importantly, a critical capillary number Cacrit for cluster breakup is determined using a combination of experiments and modeling. Cluster relaxation experiments are also performed by deforming particle clusters in flow, followed by flow cessation prior to breakup and observing cluster relaxation dynamics under zero-flow conditions. In all cases, experiments are complemented by an analytical model that accounts for capillary forces, lubrication forces, hydrodynamic drag forces, and hydrodynamic interactions acting on the particles. Results from the analytical models are found to be in good agreement with experiments. Overall, this work provides a new quantitative understanding of the deformation dynamics of capillary clusters in extensional flow.

Optimal wall shapes and flows for steady planar convection

We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer ( $Nu$ ) between hot and cold walls, for a given rate of viscous dissipation by the flow ( $Pe^2$ ), with no-slip boundary conditions at the walls. In the case of no flow, we show theoretically that the optimal walls are flat and horizontal, at the minimum separation distance. We use a decoupled approximation to show that flat walls remain optimal up to a critical non-zero flow magnitude. Beyond this value, our computed optimal flows and wall shapes converge to a set of forms that are invariant except for a $Pe^{-1/3}$ scaling of horizontal lengths. The corresponding rate of heat transfer $Nu \sim Pe^{2/3}$ . We show that these scalings result from flows at the interface between the diffusion-dominated and convection-dominated regimes. We also show that the separation distance of the walls remains at its minimum value at large $Pe$ .

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

AbstractWe parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable.

Effect of wheel speed on the microstructure and magnetic properties of Fe-3.0 wt %Si non-oriented silicon steel ultra-thin ribbons prepared by planar flow casting

Using the planar flow casting method to prepare ultra-thin silicon steel ribbons is an eco-friendly and efficient production method. However, the poor wettability between silicon steel and copper result in difficulties in formability by planar flow casting, which limits its application in production of silicon steel ultra-thin ribbons. The process parameters of planar flow casting are the key factors affecting the formability and magnetic properties of non-oriented silicon steel ribbons, in which the wheel speed determines the solidification rate of the silicon steel melt, which has an important influence on the surface quality and magnetic properties of silicon steel ultra-thin ribbons. Therefore, in this paper, the effect of wheel speed on microstructures and magnetic properties of Fe-3.0 wt %Si alloy are systematically investigated. The results indicate that as the wheel speed increases, the grain size and thickness gradually decrease. When the wheel speed is between 10 and 15 m/s, the surface of the ribbons is relatively flat. As the wheel speed increases, the surface quality of ribbons gradually deteriorates. The ribbons were in fragment with the wheel speed of 35 m/s. Compared with the ribbons before annealing, the magnetic induction B50 increased significantly and the iron losses P1.0/400 decreased sharply at 400 Hz after annealing. The magnetic induction of the ribbons after annealing with the wheel speed of 10 m/s reaches to 1.628 T as the wheel speed is 10 m/s with the corresponding iron loss is 16.171 W/kg. The lower lamination factor and micropores of the ribbons may cause the poorer magnetic properties.

Turbulent/non-turbulent interface of the turbulent boundary-layer over a spanwise-heterogeneous converging/diverging riblets rough wall

Turbulent boundary layer (TBL) flows over various spanwise-heterogeneous rough walls exhibit spanwise variations in turbulence statistics, implying modifications of the turbulent/non-turbulent interface (T/NTI). In this work, based on the datasets of TBL flows over a spanwise-alternating converging/diverging riblets wall, we investigate behavior of T/NTI, properties of ‘bubble’ and ‘drop’ that are associated with T/NTI, as well as connections between T/NTI and large-scale structures within the boundary layer. The flow datasets were obtained through stereoscopic particle image velocimetry measurements on the cross-stream plane of the TBL flow at a Reynolds number Reθ = 1.3 × 104. The T/NTI and associated ‘bubble’ and ‘drop’ are identified using a kinetic energy criterion, while the large-scale structures by a streak detection algorithm. It is observed that the T/NTI height and the occurrence of ‘bubble’ and ‘drop’ display a spanwise-heterogeneous feature, with lower T/NTI height and higher occurrence probability of ‘bubble’ over the diverging section of riblets than over the converging section of riblets. Results of conditional average show that the ‘bubble’ is associated with positive streamwise fluctuations, common-down flow and a pair of counter-rotating streamwise vortices, while the ‘drop’ with negative streamwise fluctuation, common-up flow and a pair of counter-rotating streamwise vortices. Probability density functions of the ‘bubble’ size and fractal dimensions of the T/NTI are found similar for both the riblets and smooth wall flows. Furthermore, it is observed that the large-scale low-speed structures occurring preferentially over the converging section of riblets play a role in elevating T/NTI while the large-scale high-speed ones over the diverging section of riblets lowering down T/NTI.

Deformation and breakup of a ferrofluid droplet in shear flow under magnetic field

Effects of magnetic field applied perpendicular to a shear plane in shear flow on the deformation of a ferrofluid droplet are numerically investigated. The boundary integral method is employed to solve the two-phase Stokes flow under a uniform magnetic field. When the magnetic field is applied perpendicular to the shear plane, the deformation of the droplet in the shear plane decreases. The magnetic field causes the droplet to elongate in the y-direction, and its cross-sectional radius in shear plane decreases. Consequently, the apparent capillary number in the shear plane decreases, thereby suppressing the droplet deformation. Droplet breakup is also suppressed by imposing a magnetic field perpendicular to the shear plane, thereby increasing the critical capillary numbers. The critical capillary numbers for the magnetic Bond numbers Bo = 2.0 and 4.0 increase to approximately 110% and 130%, respectively, than those without magnetic field. Furthermore, an equation for the theoretical prediction of the droplet deformation under a magnetic field in shear flow is presented, which is based on the small deformation theory, the decrease in the cross-sectional radius, and the boundary conditions at the droplet interface. The theoretical prediction agrees well with the numerical results for the variation in the magnetic susceptibility of the droplet as well as the viscosity ratio between the external fluid and the ferrofluid droplet under a small deformation. The critical capillary numbers under a magnetic field can also be predicted by using the numerical results without a magnetic field.

Study on the diffusion and deposition law of pore slurry in gangue filling zone based on CFD-DEM coupling.

In this study, the slurry diffusion in a cavity filled with coal gangue was studied by combining experimental and numerical simulation methods. By calibrating slurry and particle materials, the grouting process in coal gangue filling area is simulated successfully, and the change of slurry diffusion flow field and particle movement and settling process in different dimensions are deeply analyzed. Both experimental and numerical simulation results show that the particle settlement presents a bell-shaped curve, which is of great significance for understanding the particle movement and settlement behavior in the filling cavity. In addition, it is found that the grouting speed has a significant effect on the particle settlement during the slurry diffusion process. When the grouting speed increases from 0.1m /s to 0.2m /s, the particle settlement and diffusion range increases about twice. In the plane flow field, it is observed that the outward diffusion trend and speed of grouting are more obvious. It is worth noting that in the whole process of grouting, it is observed that with the increase of grouting distance and depth, both the velocity of slurry and particles show a trend of rapid initial decline and gradually slow down, and the flow velocity of slurry near the grouting outlet at a flow rate of 0.2m/s is 2-4 times that of 0.1m/s. This provides important enlightenment for the porous seepage effect at different grouting speeds.

Electromagnetism - Properties of Erythrocytes

At the onset of blood flow, red blood cells (RBCs) align along the central plane of the vessels. In capillaries, RBCs transform from a biconcave disk into a parachute shape. As blood transitions from the arterial to the venous end, the hemoglobin in erythrocytes alters its magnetic susceptibility. Within approximately 0.6-0.8 seconds, oxygen is displaced from RBCs through diffusion. This study explores the fundamentals and interconnections of these processes.
 
 Blood samples from 35 different healthy individuals were analyzed. The research examined magnetic field induction in ferromagnetic toroids, formed by the alternative electric field with a square wave signal, and studied the AC in the secondary coil - a tube filled with blood. This study discusses the impact of RBC geometry and hemoglobin allosteric transitions on electric signal generation and its relevance to cellular metabolic activity in the body.
 
 The findings suggest that the AC field, originating from the heart's rotational dipole, can generate a magnetic field in RBCs, facilitating the allosteric transformations of hemoglobin. Hemoglobin's thermoelastic expansion and magnetostriction cause biconcave membrane oscillations at ultrasound frequencies. The resulting electroacoustic wave rotates charges at the cell's z-potential area, aids RBC migration into the flow plane, and enhances trans capillary diffusion of substances.
 
 An electroacoustic standing wave emerges between the oscillating RBCs, coinciding with the wavenumber of externally penetrating infrared light. The synergic influence on hemoglobin in capillaries causes the RBC membrane to create a temporally frequency-modulated wave, carrying resonance molecular frequencies. This wave regulates biochemical processes within and outside body cells.

Global dynamics and topology of two-phase mixing layer flow through simultaneous gas and liquid velocity measurements

This study reports the first time-resolved particle image velocimetry characterization of a planar two-phase mixing layer flow, whose velocity field is measured simultaneously in gas and liquid streams. Two parallel air and water flows meet downstream of a splitter plate, giving rise to an initially spanwise invariant configuration. The aim is to elucidate further the mechanisms leading to the flow breakup in gas-assisted atomization. The complete experimental characterization of the velocity field represents a database that could be used in data-driven reduced-order models to investigate the global behaviour of the flow system. After the analysis of a selected reference case, a parametric study of the flow behaviour is performed by varying the liquid ( $Re_l$ ) and gas ( $Re_g$ ) Reynolds numbers, and as a consequence also the gas-to-liquid dynamic pressure ratio ( $M$ ), shedding light on both time-averaged (mean) and unsteady velocity fields. In the reference case, it is shown that the mean flow exhibits a wake region just downstream of the splitter plate, followed by the development of a mixing layer. By increasing both $Re_l$ and $Re_g$ , the streamwise extent of the wake decreases and eventually vanishes, the flow resulting in a pure mixing layer regime. The spectral analysis of the normal-to-flow velocity fluctuations outlines different flow regimes by variation of the governing parameters, giving more insights into the global characteristics of the flow field. As a major result, it is found that at high $Re_g$ and $M$ values, the velocity fluctuations are characterized by low-frequency temporal oscillations synchronized in several locations within the flow field, which suggest the presence of a global mode of instability. The proper orthogonal decomposition of velocity fluctuations, performed in both gas and liquid phases, reveals finally that the synchronized oscillations are associated with a low-frequency dominant flapping mode of the gas–liquid interface. Higher-order modes correspond to interfacial wave structures travelling with the so-called Dimotakis velocity. For lower gas Reynolds numbers, the leading modes describe higher frequency fingers shedding at the interface.

Spur Dike Applications for the Sustainability of Channels in Incised Steep Bend Streams

Japan’s rivers are shaped by distinctive topography and abundant rainfall, and they face flooding and sediment supply escalation concerns under climate change. Small- and medium-sized rivers tend to catch unprecedented forces that exceed planned levels, leading to substantial widening and excavation. Thus, there is a demand for a method that is capable of managing significant flood flows over an extended period. The spur dike can maintain channel clearance by promoting erosion as well as providing bank protection. However, the effectiveness of this spur dike function has not been well studied in small- and medium-sized rivers and curved reaches. In this study, we evaluate the function of spur dikes in improving channel sustainability based on examples of small- and medium-sized rivers that have maintained their channel for more than ten years after spur dike installation. First, the applicability of the empirical rule was evaluated by comparing it with actual cases of erosion depths in curved sections in Japan. Next, one-dimensional simulations were performed to evaluate the sustainability of the section over a long period. Finally, a depth-averaged morphodynamic simulation, including the secondary flow effect, was applied to evaluate the location of the flow core and elevation changes due to the spur dike. The results showed that a slight difference in the ratio of river curvature radius to river width (r/B) caused the river channel to be erosive and sedimentary. The reasons for the difference were the cross-sectional expansion caused by the excavation of the bend and the difference in the plane flow regime caused by the shift of the flow core to the inside of the bend. Although it is structurally challenging to reproduce localized scour around a spur dike in a depth-averaged simulation, it is essential for designing to apply the simulation model and combine empirical knowledge.

Numerical Study of a Model and Full-Scale Container Ship Sailing in Regular Head Waves

In the present study, the added resistance, heave, and pitch of the KRISO Container Ship (KCS) in waves, at both model scale and full scale, are predicted numerically in regular head waves, for four wavelengths and three wave heights. The ISIS-CFD viscous flow solver, implemented in the Fidelity Fine Marine software provided by CADENCE, was employed for the numerical simulations. The spatial discretization was based on the finite volume method using an unstructured grid. The unsteady Reynolds-averaged Navier–Stokes (RANS) equations were solved numerically, with the turbulence modeled by shear stress transport (k-ω) (SST). The free-surface capturing was based on the volume-of-fluid method. The computed solutions were validated through comparisons with towing test data available in the public domain. To predict the uncertainties in the numerical solution, a systematic grid convergence study based on the Richardson extrapolation method was performed for a single wave case on three different grid resolutions. Specific attention was given to the free-surface and wake flow in the propeller plane. The purpose was to compare the numerical results from the model- and full-scale tests to examine the scale’s effect on the ship’s performance in regular head waves. The comparison between the model scale and full scale showed obvious differences, less accentuated for the free-surface topology and clearly observed in terms of boundary layer formation in the propeller’s vicinity.

Electrical Resistivity of Lead-Free Solders Reinforced by Carbon Nanospheres

Electrical resistivity of the nanocomposites Sn96.5Ag3Cu0.5 and Sn95,5Ag3,8Cu0,7 lead-free solder alloys with minor admixtures of carbon nanospheres (0.05 wt%) was measured in a wide temperature range, including a melting-solidification region. Influence of the carbon nanospheres content on electrical resistivity values has been analyzed. Carbon nanospheres were obtained by electrical discharge method from diesel fuel, cyclohexane, and aviation kerosene. The matrix samples were produced by planar flow casting technique in the form of thin ribbons. Electrical resistivity measurements were performed using four-probe method. Hysteresis between the heating and cooling electrical resistivity curves relates to the non-equilibrium solidification.

Low-order planar pressure reconstruction of stalled airfoils using particle image velocimetry data

We present planar time-resolved particle image velocimetry (PIV) measurements of flow in the streamwise surface-normal plane of a NACA 0012 airfoil at chord-based Reynolds number Rec=7×104. The angles of attack α=13∘ and 15∘ correspond to transient stall and deep stall flow regimes, respectively. A Poisson solver is utilized to reconstruct the instantaneous planar pressure fields from the PIV with satisfactory comparison in the mean pressure compared with dynamically matched Reynolds-averaged Navier-Stokes (RANS) simulations. Using the proper orthogonal decomposition (POD), a systematic reduced-order reconstruction of the velocity fields and subsequent pressure fields is used to quantify the required number of velocity modes to achieve a desired accuracy in the instantaneous pressure. Further, a Galerkin projection of the Poisson equation onto the POD subspace is used as a framework to identify the relative contribution of each velocity mode on the resulting pressure field via quadratic stochastic estimation (QSE). In both cases, the zeroth mode (corresponding to the mean) is of leading-order importance. In addition, a tendency of the zeroth mode to interact with vortex-shedding modes is identified. Published by the American Physical Society 2024

Numerical Method for Calculating Plane Flows of Viscous Gas in a Cylinder

To solve scientific, technological and environmental problems in the field of road transport, it is necessary to develop new mathematical models. At this stage of development of internal combustion engines and their parts, it is necessary to model complex hydrodynamic technologies. This necessities revealing different forms of liquid and gas flows with arbitrary initial and boundary conditions for the region under consideration.The work is devoted to modelling a turbulent flow over a plate located in a cylinder. Reynolds-averaged Navier-Stokes equations were used as a mathematical model of the flow. Turbulent viscosity was calculated using the one-equation Spalart-Allmaras turbulence model. To solve the system of hydrodynamic equations, the finite difference method was used. A numerical method for calculating plane flows of viscous gas in a cylinder using turbulence models is presented. Suitable options were selected based on physical assumptions used to develop the models.Recommendations have been developed on the possibility of using the considered turbulence models.

Order–disorder transitions within deformable particle suspensions in planar Poiseuille flow

Three-dimensional simulations of the ordering of elastic capsule suspensions within planar Poiseuille flow channels are reported. The simulations utilize the immersed boundary method coupled with the lattice Boltzmann method to capture the complex flow-induced capsule deformations and hydrodynamic interactions within the suspensions. A parametric study is presented whereby the confinement ratio and the particle deformability are varied independently within a two-dimensional range relevant to this ordering phenomenon. The initial distribution of capsules is random, and the simulations evolve the system from a disordered state to an ordered one, while an order parameter that quantifies the fraction of capsules belonging to one-dimensional train assemblies is computed throughout time. A monotonic increase in ordering is observed with increasing deformability. However, an optimal confinement ratio is identified corresponding to a peak in the order parameter. This peak is attributed to the competition between increasing long-range capsule attractions and decreasing in-plane capsule density (with fixed volume fraction) as the confinement ratio increases. Simulations are also performed to understand how dispersity in capsule size and deformability impact the degree of ordering. It is shown that ordering is quite sensitive to dispersity in capsule size, and much less sensitive to dispersity in deformability. Overall, the results provide important insights for the design of microfluidic devices.

Single cavitation bubble dynamics in a stagnation flow

Jetting of collapsing bubbles is a key aspect in cavitation-driven fluid–solid interactions as it shapes the bubble dynamics and additionally due to its direct interaction with the wall. We study experimentally and numerically the near-wall collapse and jetting of a single bubble seeded into the stagnation flow of a wall jet, i.e. a jet that impinges perpendicular onto a solid wall. High-speed imaging shows rich and rather distinct bubble dynamics for different wall jet flow velocities and bubble-to-wall stand-off distances. The simulations use a volume-of-fluid method that allows us to numerically determine the microscopic and transient pressures and shear stresses on the wall. It is shown that a wall jet at moderate flow velocities of a few metres per second already shapes the bubble ellipsoidally inducing a planar and convergent jet flow. The distinct bubble dynamics allow us to tailor the wall interaction. In particular, the shear stresses can be increased by orders of magnitude without increasing impact pressures the same way. Interestingly, at small seeding stand-offs, the bubble during the final collapse stage can lift off the wall and migrate against the flow direction of the wall jet such that the violent collapse occurs away from the wall.

Dissipation induced instability in porous medium using Brinkman model: Thermal non-equilibrium effect

The convective instability that arises in a porous layer solely because of dissipative energy in the medium is studied. The thermal non-equilibrium model is considered for energy equation. The boundary at top is kept at constant temperature, and an adiabatic lower boundary is considered. The momentum equation is written according to the Brinkman model. A basic flow in the horizontal plane is considered, and the basic velocity and temperature profile have been derived. A comparison between the basic temperature profiles for solid and fluid of the porous medium is presented for Darcy and Brinkman models. Infinitesimal disturbance is introduced to the basic flow. A linear stability analysis has been carried out to study the stability of the basic flow. The parameters influencing the stability of the system are critical Rayleigh number (RaC), Gebhart number (Ge), ξ associated with the Darcy number (Da), and interphase heat transfer coefficient (H). The values of the critical Rayleigh number and wavenumber are compared by varying other variables. The flow is more stable when the Brinkman medium is considered. With the increase in interphase heat transfer coefficient, the critical Rayleigh number increases in both Darcy and Brinkman media. The longitudinal rolls appear as the most unstable rolls for all cases. The variation of convective rolls with respect to ξ and heat transfer coefficient is presented.

Simulation of fiber-induced melt pressure fluctuations within large scale polymer composite deposition beads

The process-structure-property relationship in Large Area Additive Manufacturing (LAAM) technology is an ongoing area of research as the inherent microstructural properties (chiefly fibers and voids) affect the performance of printed parts. Unfortunately, we currently lack adequate understanding of micro void nucleation and evolution during the LAAM and fused deposition modelling (FDM) processes. Modeling of the polymer melt flow during the extrusion process is important in understanding the underlying microstructural formation and associated properties of the print, that determines the part performance in service conditions. In this paper we compute fiber-induced local pressure fluctuations which may promote void formation in the bead’s microstructure. On a macro-scale, we determine flow fields of a purely viscous, Newtonian planar polymer deposition flow through a LAAM nozzle which are utilized on a micro-scale model where we simulate the evolution of a single ellipsoidal fiber along streamlines obtained from the macro-model. On the micro-scale, we determine instantaneous values of the translational and rotational velocities of the rigid ellipsoidal fiber that satisfies a balance of hydrodynamic forces and couples on the fiber’s surface based on a Newton Raphson algorithm and we track the fiber’s motion along the flow path via an explicit numerical iterative algorithm. Model verification is achieved by benchmarking results with solutions from well-known Jeffery’s equation of motion of a particle in homogeneous simple shear flow. We account for rotary diffusivity due to short-range fiber-fiber interaction in the FEA simulation by determining an effective fluid domain size representative of the interaction coefficient of the melt flow through a correlation analysis that yields an equivalent steady state orientation based on the Advani-Tucker equation. We also consider different possible motions of the fiber along individual LAAM flow paths from a given set of random initial fiber conditions to determine pressure bounds on the fiber surface along each streamline. For improved computational efficiency, calculations are carried out with respect to the fiber’s local coordinate axes to overcome the rigor of adaptive remeshing during the quasi-transient analysis. Results show low pressure extremes near the fiber’s surface which varies across the printed bead as well as through its thickness. Discussion is provided to gain insight into the effect of low-pressure extremes on micro void formation, particularly at the nozzle exit and during die swell/expansion.

Drop deformation in a planar elongational flow: impact of surfactant dynamics.

Drops in extensional flow undergo a deformation, which is primarily fixed by a balance between their surface tension and the viscous stress. This deformation, predicted and measured by Taylor on millimetric drops, is expected to be affected by the presence of surfactants but has never been measured systematically. We provide a controlled experiment allowing us to measure this deformation as a function of the drop size and of the shear stress for different surfactants at varying concentrations. Our observation is that the deformation predicted by Taylor is recovered at zero and high surfactant concentration, whereas it is smaller at concentrations close to the critical micellar concentration. This is in contradiction to the existing analytical models. We develop a new analytical model, taking into account the surfactant dynamics. The model predicts a transition between a deformation similar to that of a pure liquid and a smaller one. We show that the transition is driven by a parameter KL, which compares adsorption and desorption dynamics. Finally, the concentration C*, at which we observe this transition in the extensional flow is in good agreement with the one predicted by independent measurements of KL.