Simplified Phan-Thien Tanner Research Articles

Elastic contribution of polymeric fluids augments salinity-gradient-induced electric potential across a microfluidic channel

HypothesisHarnessing electrical energy from salinity gradients, particularly for powering micro and nanoscale devices, has become a focal point of recent research attention, due to its renewable and biocompatible nature. Much of the reported research in that direction revolves around optimizing the membrane architecture and the charge distribution to maximize the induced electric potential, with no particular emphasis on the fluid rheology. However, many of the modern miniature systems, typically the bio-inspired ones, concern fluids with complex rheological characteristics, where the results for Newtonian solvents may not trivially apply. Here, we hypothesize that the interplay between interfacial electro-mechanics and the fluid rheology can influence the effectiveness of salinity-gradient-modulated electrokinetics significantly – an aspect that has largely remained overlooked. Theory and experimentsHere we report the first experiments supplemented by a theoretical model that unveil how that the addition of polymers in a solvent modulates the salinity gradient – induced electric potential in a microfluidic channel. Our theoretical framework considers the simplified Phan-Thien Tanner (sPTT) constitutive model, which represents the viscoelastic characteristics of fluids. Experiments were conducted with combined pressure driven and salinity gradient driven flow through microchannel involving dilute solutions of polyethylene oxide (PEO) of different molecular weights and concentrations to successfully validate the theoretical approach. FindingsOur findings indicate that the induced electrical potential increased non-linearly with the saline concentration ratio across the microchannel, as compared traditional linear response. Our results demonstrate how the elasticity of fluid may enable realizing an optimal benefit to this effect, by arresting the viscous resistance and uplifting the elastic response via utilizing polymeric inclusions of high relaxation times. These results provide specific insights on preferential windows of augmenting the induced streaming potential by harnessing the viscoelastic nature of the solution and the imposed salt concentration, bearing critical implications in miniature energy harvesting and desalination technology.

Thermally developing streaming potential-mediated pressure-driven flow of Phan–Thien–Tanner fluid in a microchannel

In this study, we have conducted a semi-analytical investigation into the streaming potential-mediated pressure-driven flow of hydrodynamically fully developed and thermally developing viscoelastic fluid in a parallel plate microchannel. We have utilized a simplified Phan–Thien–Tanner model to describe the rheology of the viscoelastic fluid. Our approach delved into the full Poisson–Boltzmann equation, deriving exact analytical solutions for the electrostatic potential distribution and velocity profile. Furthermore, we concurrently derived semi-analytical solutions for the temperature distribution and Nusselt number, accounting for the effects of heat generation from viscous dissipation and Joule heating in thermally developing flows. We have demonstrated that an increase in the degree of surface charge triggers the streaming potential field, while the volumetric flow rate escalates with the viscoelastic parameter εWik¯2. Moreover, we have observed that the magnitude of the dimensionless temperature decreases with increasing values of the effective Joule heating parameter Speff. Our analysis reveals that the streaming potential effect hampers fluid flow, resulting in an increase in the bulk fluid temperature and consequently reducing the heat transfer rate. We observe that the magnitude of the Nusselt number decreases with increasing Speff. The entropy generation analysis reveals that increasing the Peclet number amplifies flow and temperature gradients, leading to higher fluid irreversibility in microchannels. The Bejan number experiences a significant decrease across the channel, reaching its minimum at a specific axial location before stabilizing further downstream. We find that heat transfer irreversibility predominantly influences system irreversibility, except for the Brinkmann number Br = 0.01, where convective heat transfer dominates at the entrance region, transitioning to friction losses beyond the thermal entry zone.

Effect of solvent depletion on electrokinetic energy conversion in viscoelastic fluids

We analyze the electrokinetic energy conversion from the pressure-driven flow of viscoelastic fluids akin to dilute polymer solutions. In contrast to the previously reported results, we account for the reduced differential capacitance over the interfacial layer and the solvent-mediated non-electrostatic interactions, cumulatively represented in an extended continuum framework. We attribute a physical basis of our consideration from the perspective of the formation of a polymer-depleted layer at the channel interface, where the explicit role of the solvent appears to dictate the electromechanics–hydrodynamics coupling over the interfacial scales. By adapting a “box-model” depicting the alterations in the solvent permittivity across the interfacial layer and accommodating a non-electrostatic interaction coefficient concomitantly, the interfacial electrokinetics are coupled with the bulk flow of the polymer-rich medium using the simplified Phan-Thien–Tanner (sPTT) constitutive model. A closed-form theory is obtained that includes only two fitting parameters, namely, the span of the interfacial layer and the strength of the non-electrostatic interactions. These parameters are estimated from comprehensive molecular simulation data. The results of the investigation are analytically tractable and enable rationalizing the “electrokinetic” implications of the polymer-depleted interfacial layer and the possibility that the electrokinetic parameters can be extracted from measurements obtained from experiments. This paves the way toward optimizing the induced streaming potential for the conversion of hydraulic energy to electrical power in polymeric solutions.

A comparison between the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear

The finitely extensible nonlinear elastic with Peterlin closure (FENE-P) and simplified Phan-Thien–Tanner (sPTT) viscoelastic models are used widely for modelling of complex fluids. Although they are derived from distinct micro-structural theories, these models can become mathematically identical in steady and homogeneous flows with a particular choice of the values of the model parameters. However, even with this choice of parameter values, the model responses are known to differ from each other in transient flows. In this work, we investigate the responses of the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear (LAOS). In steady shear, the shear stress scales with the non-dimensional group $Wi/(aL)$ ( $Wi\,\sqrt {\epsilon }$ ) for the FENE-P (sPTT) model, where $Wi$ is the Weissenberg number, $L^2$ is the limit of extensibility in the FENE-P model ( $a$ being $L^2/(L^2-3)$ ), and $\epsilon$ is the extensibility parameter in the sPTT model. Our numerical and analytical results show that in LAOS, the FENE-P model shows this universality only for large values of $L^2$ , whereas the sPTT model shows it for all values of $\epsilon$ . In the strongly nonlinear region, there is a drastic difference between the responses of the two models, with the FENE-P model exhibiting strong shear stress overshoots that manifest as self-intersecting secondary loops in the viscous Lissajous curves. We quantify the nonlinearity exhibited by each constitutive model using the sequence of physical processes framework. Despite the high degree of nonlinearity exhibited by the FENE-P model, we also show using fully nonlinear one-dimensional simulations that it does not shear band in LAOS within the range of conditions studied.

Viscoelastic vapor bubble collapse near solid walls and corresponding shock wave formation

This study investigates the influence of viscoelasticity on the collapse of aspherical vapor bubbles near a solid boundary through numerical simulations. A fully compressible three-dimensional finite volume method is employed, incorporating a single-fluid homogeneous mixture cavitation model and the simplified linear Phan-Thien Tanner viscoelastic constitutive model. The collapse dynamics, liquid jetting, shock wave formation, and associated pressure impact are analyzed, and the viscous and viscoelastic stress fields are presented. A comparison of viscoelastic to Newtonian dynamics reveals significant differences in collapse behavior and shock wave formation due to viscoelasticity. Viscoelasticity can induce jet piercing, which is not observed in the Newtonian collapse, and increases vapor re-evaporation after the first collapse. The effect of changing the initial standoff distance is examined for both viscoelastic and Newtonian fluids, where a second jet formation is present only for the viscoelastic collapse, and the second collapse's intensity is increased due to increased vapor production during rebound. Additionally, the variation of elasticity in the viscoelastic case demonstrates a correlation between the amount of vapor produced during rebound and the relaxation time for the investigated cases.

Mathematical study of viscoelastic polymer during roll-over-web coating

Roll-coating, also known as roll-to-roll coating or web coating is a continuous and high-speed method used in various industrial applications to apply a thin and uniform layer of material onto a substrate. This process is commonly employed in industries such as electronics, photovoltaic, printing, packaging, and other fields where precise and consistent coating is essential. Here we present an asymptotic analysis of forward roll coating over a rigid substrate for low Weissenberg number viscoelastic fluids. The analysis uses lubrication theory coupled with regular perturbation theory assuming a simplified Phan-Thien-Tanner (SPPT) constitutive equation and small values of the extensibility parameter ε. The analytical expressions of velocity fields, pressure gradient and pressure fields are obtained while the load carrying force, and power input are estimated by numerical solutions (4th order Runge-Kutta). Increases in both Wi and ε increases the pressure gradient in the nip region and increases in viscoelasticity reduce the overall force on the roll. Further, SPTT model predicts 14% lower pressure for [Formula: see text] in the nip region when compared to Newtonian model.

First and second laws analysis of viscoelastic fluid with temperature dependent properties for Couette-Poiseuille flow

The entropy analysis of viscoelastic fluid obeying the simplified Phan-Thien-Tanner (SPTT) model with variable thermophysical properties are obtained for laminar, steady state and fully developed Couette-Poiseuille flow. The homotopy perturbation method (HPM) allows us to solve nonlinear momentum and energy differential equations. The Reynold's model is used to describe the temperature dependency of thermophysical properties. Results indicate that the increase of the group parameter (Br/Ω) and the Brinkman number (Br) which show the power of viscous dissipation effect; increases the entropy generation while increasing fluid elasticity (εDe2) decreases the generated entropy. Increasing the Reynolds variational parameter (α) which control the level of temperature dependence of physical properties attenuate entropy generation when moving plate and applied pressure gradient have the opposite direction and decreases entropy generation when moving plate and applied pressure gradient have the same direction or both plates are at rest. Also, increasing elasticity reduces the difference between variable and constant thermophysical properties cases. These results may give guidelines for cost optimization in industrial processes.

Thermally developing combined electroosmotic and pressure-driven flow of Phan–Thien–Tanner fluids in a microchannel

We present semi-analytical solutions for the hydrodynamically developed and thermally developing flow of a non-Newtonian fluid through an isothermal rectangular microchannel. The fluid motion is actuated by the combined consequences of the electroosmotic and pressure-gradient forces. For the rheological behavior of the non-Newtonian fluid, we have used the simplified Phan–Thien–Tanner viscoelastic model. Going beyond the Debye Hückel linearization approximation, we have used the full-scale solution for the electrical double-layer potential equation to obtain the exact analytical solutions for the velocity, flow rate, and shear rate parameters. In contrast, the temperature distribution and heat transfer for the thermally developing flow have been obtained by solving the energy equation numerically considering the effects of volumetric heat generation due to Joule heating and viscous dissipation. We find that a larger value of the viscoelastic set ε̃Wĩk2 contributes toward the net gain in flow rate. Both the normal and shear stress increase for increasing ε̃Wĩk2, while the shear viscosity reduces with a degree of surface charging. The average shear viscosity reduces with the degree of surface charging and at higher ε̃Wĩk2 values. The heat transfer is enhanced for augmenting ε̃Wĩk2, although the thermal entrance region gets contracted for a pure electroosmotic flow at higher Peclet numbers. Our study reveals that the heat transfer rate can be amplified by effectively modulating the degree of surface charging and ε̃Wĩk2. We have also carried out an entropy generation analysis, which shows the dominance of heat transfer irreversibility over fluid friction irreversibility. We believe that the present research will offer essential approaches for designing advanced energy-efficient microchannels appropriate to modern industrial applications using viscoelastic fluids.

On spherical vapor bubble collapse in viscoelastic fluids

Cavitating vapor bubbles, occur in variety of engineering applications, employing complex fluids as operating medium. Especially in biomechanics, biomedical applications as well as in polymer processing, fluids exhibit viscoelastic properties and fundamentally different behavior than Newtonian fluids. To explain the influence of viscoelasticity on cavitation a detailed understanding of the viscoelastic influence on bubble dynamics and of the underlying mechanisms is essential. With this study we provide in-depth numerical investigations of the spherical vapor bubble collapse in viscoelastic fluids. A compressible, density-based, 3D finite-volume solver with explicit time integration is used together with a conservative, compressible formulation for the constitutive equations of three different viscoelastic models, namely the upper convected Maxwell model, the Oldroyd-B model and the simplified linear Phan-Thien Tanner model. 3D simulations of the collapse dynamics are carried out to show the viscous and viscoelastic stress development during the collapse, and its relation to the occurring deformations. Collapse behavior is investigated for various elasticity, viscosity and constitutive models. It is demonstrated that viscoelasticity fundamentally alters the collapse behavior and evolution of stresses. It is observed that viscoelastic stresses develop with a time delay proportional to elasticity and show different spatial distributions as opposed to Newtonian stresses. Viscoelasticity introduces isotropic stress components even though the spherical collapse leads to purely deviatoric (elongational) deformation. Furthermore, the distinct influence of constitutive models is illustrated and the influence of viscoelastic models with solvent contribution is explained. For the upper convected Maxwell model, we show that for increased elasticity shock wave emission can be observed depending on the applied grid resolution.

Thermal entry flow problem for Rabinowitsch fluid subject to circular tube and flat channel with uniform heat flux boundary conditions

The heat exchangers, chemical reactors, cooling/heating systems and haemodialysis are specific areas due to which Graetz thermal problem is considered as fundamental flow in the duct along with heat and mass transfer aspects. Owing to its importance we examine the thermal entry flow problem for Rabinowitsch liquid in the pipe and channel ducts along with heat transfer aspects. The heat equation with uniform heat flux conditions is tackled via the superposition principle and separation of variable approach due to the involvement of non-homogeneous boundary conditions. The transformed boundary value problem is solved with the MATLAB algorithm for the calculation of eigenvalues and related eigenfunctions. The special cases for simplified Phan-Thien–Tanner (SPTT) fluid and finite extendable non-linear elastic peterline (FENE-P) fluids are also discussed. For SPTT and FENE-P models the controlling parameter can only take positive values and hence these models can only predict shear-thinning effects. The graphical illustrations of fully developed temperature, local and mean Nusselt numbers are displayed through the main effect brought by the controlling parameter.

Micro-imbibition electro-magneto-hydrodynamics of viscoelastic fluids with interactive streaming potential

• Imbibition electro-magneto-hydrodynamics of ionic viscoelastic fluid explored • Capillarity of a sPTT fluid with induced streaming potential solved semi-analytically • Roles of Hartmann number, Electroviscous number, and Deborah number investigated • The critical Hartmann number decreases with increase in Deborah number • Capillarity with rheology independent ( x ¯ ∼ t ¯ ), and later, rheology modulated regime ( x ¯ ∼ t ¯ ). Conjugated surface tension and electro-magneto-hydrodynamics driven micro-capillary imbibition of an ionic viscoelastic fluid, in presence of interacting streaming potential, has been investigated in this article. The rheology of the fluid is modelled by appealing to the linearized simplified Phan-Thien Tanner (sPTT) model. By taking into account the electrolytic nature of the fluid, additional electroviscous forces due to induced streaming potential is also considered in the model. Transverse electric and magnetic fields are applied externally to the fluid to investigate the possibility of achieving volumetric flow gain and/or fluidic control using body force manipulation. Considering all the participating mechanisms, we deduce a semi-analytical formalism and present a comprehensive picture on the dependence of various parameters on capillary imbibition dynamics. We explore the roles played by the governing non-dimensional parameters, viz. Hartmann number, Electroviscous number, and Deborah number. For low Hartmann number regimes, there is evidence of augmented imbibition, while at higher values the flow is suppressed. We also show that the critical Hartmann number decreases with increase in Deborah number, allowing for such viscoelastic fluids to achieve more efficient imbibition velocity with less strength of applied fields. The flow regime is noted to consist of two parts – a rheology independent regime ( x ¯ ∼ t ¯ ), and later, a rheology modulated regime ( x ¯ ∼ t ¯ ). These findings are expected to provide a significant understanding of the imbibition hydrodynamics of such complex fluids, and at the same time, provide means for flow augmentation and control in microfluidic devices.

Peeling of linearly elastic sheets using complex fluids at low Reynolds numbers

We investigate the transient, fluid–structure interaction (FSI) of a non-Newtonian fluid peeling two Hookean sheets at low Reynolds numbers ( R e ≪ 1 ). Two different non-Newtonian fluids are considered – a simplified Phan–Thien–Tanner (sPTT) model fluid, and an inelastic fluid with shear-thinning viscosity (generalized Newtonian fluid). In the limit of small gap between the sheets, we invoke a lubrication approximation and numerically solve for the gap height between the two sheets during the start-up of a pressure-controlled flow. What we observe is that for an impulse pressure applied to the sheet inlet, the peeling front moves diffusively ( x f ∼ t 1 / 2 ) towards the end of the sheet when the fluid is Newtonian. However, when one examines a complex fluid with shear-thinning, the propagation front moves sub-diffusively in time ( x f ∼ t α , α < 0 . 5 ), but ultimately reaches the end faster due to an order of magnitude larger prefactor for the propagation speed. We provide scaling analyses and similarity solutions to delineate several regimes of peeling based on the sheet elasticity, flow Weissenberg number (for sPTT fluid), and shear-thinning exponent (for generalized Newtonian fluids). To conclude, this study aims to afford to the experimentalist a system of knowledge to a priori delineate the peeling characteristics of a certain class of complex fluids. • Modeled fluid–structure interaction of a complex fluid peeling two Hookean sheets. • Examined two different fluid constitutive rheological models. • Developed simulations and similarity solutions for the peeling front during start-up. • Quantified peeling time effects due to shear thinning. • Peeling time for a shear-thinning fluid is smaller than a Newtonian fluid.

On the similarities of the sPTT and FENE-P models for polymeric fluids

<h2>Abstract</h2> For many commonly used single mode viscoelastic constitutive equations of differential type, it is well known that they share many features. For example, in certain parameter limits the models due to Giesekus, Phan-Thien Tanner and FENE-type models approach the Oldroyd-B model. In this talk, I'll compare the response of the linear form of the simplified Phan-Thien Tanner model [due to Phan-Thien and Tanner, Journal of Non-Newtonian Fluid Mechanics, 2 (1977) 353–365] (the "sPTT") and the Finitely Extensible Nonlinear Elastic model that follows the Peterlin approximation [due to Bird et al., Journal of Non-Newtonian Fluid Mechanics, 7 (1980) 213–235] (the "FENE-P"). I'll show that for steady homogeneous flows such as steady simple shear flow or pure extension the response of both models is identical under certain conditions. For more general flows we show analytically that the results from the two models only formally approach each other when both the polymer concentration and Weissenberg number is small. We then use a numerical approach to investigate the response of the two models when the flow is "complex" under two different definitions: firstly, when the applied deformation field is homogenous in space but transient in time (so called "start-up" shear and planar extensional flow) and then for "complex" flows (through a range of geometries) which, although Eulerian steady, are unsteady in a Lagrangian sense. Under the limit that the flows remain Eulerian steady (so the Weissenberg number is typically small), we see once again a very close agreement between the FENE-P and sPTT models.

Thermally developed electrokinetic bi-layer flows of Newtonian and non-Newtonian fluids in a microchannel

In the present study, thermofluidic characteristics of a combined pressure-driven and electrical field mediated thermally fully developed flow of an immiscible Newtonian and a viscoelastic fluid bi-layer in a microchannel have been analyzed. The simplified Phan-Thien–Tanner model with a linear kernel for the stress coefficient function has been utilized to describe the complex fluid rheology for the non-Newtonian fluid. Disparate zeta potentials have been assumed at the interfaces. Accordingly, distinct zeta potential values have been used at the channel walls and interfaces between the fluids to derive the closed-form analytical expressions for the pertinent velocity, stress, and shear viscosity distributions in the fluid layers. For thermally developed flows, the temperature and entropy distributions are obtained along the microchannel for constant wall heat flux boundary conditions. Major findings from our research show that amplification of the viscoelastic parameter designated by the Weissenberg number exhibits an enhancement in the non-dimensional axial velocity, flow rate, and stress magnitudes. Furthermore, the present study indicates that Joule heating and viscous dissipation significantly vary the dimensionless temperature profiles along the fluid bi-layer. The Nusselt number values are found to decrease with the augmentation of the viscoelasticity, Joule heating, and viscous dissipation parameters. The total entropy generation for the fluid layer systems increases with the increasing Joule heating parameter.

On the similarities between the simplified Phan-Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows

For many commonly used viscoelastic constitutive equations, it is well known that the limiting behavior is that of the Oldroyd-B model. Here, we compare the response of the simplified linear form of the Phan-Thien–Tanner model (“sPTT”) [Phan-Thien and Tanner, “A new constitutive equation derived from network theory,” J. Non-Newtonian Fluid Mech. 2, 353–365 (1977)] and the finitely extensible nonlinear elastic (“FENE”) dumbbell model that follows the Peterlin approximation (“FENE-P”) [Bird et al., “Polymer solution rheology based on a finitely extensible bead—Spring chain model,” J. Non-Newtonian Fluid Mech. 7, 213–235 (1980)]. We show that for steady homogeneous flows such as steady simple shear flow or pure extension, the response of both models is identical under precise conditions (ε=1/L2). The similarity of the “spring” functions between the two models is shown to help understand this equivalence despite a different molecular origin of the two models. We then use a numerical approach to investigate the response of the two models when the flow is “complex” in a number of different definitions: first, when the applied deformation field is homogeneous in space but transient in time (so-called “start-up” shear and planar extensional flow), then, as an intermediate step, the start-up of the planar channel flow; and finally, “complex” flows (through a range of geometries), which, although being Eulerian steady, are unsteady in a Lagrangian sense. Although there can be significant differences in transient conditions, especially if the extensibility parameter is small L2&amp;gt;100,ε&amp;lt;0.01, under the limit that the flows remain Eulerian steady, we once again observe very close agreement between the FENE-P dumbbell and sPTT models in complex geometries.

A compressible 3D finite volume approach for the simulation of unsteady viscoelastic cavitating flows

We present a fully compressible, density-based finite volume solver for the simulation of 3D cavitating flows in viscoelastic Maxwell-/Oldroyd-like fluids. The upper-convected Maxwell model, the Oldroyd-B model and the linear and exponential simplified Phan-Thien Tanner models are implemented as viscoelastic constitutive equations in conservative formulation, and we identified the Truesdell rate as appropriate objective time derivative for compressible flows. Cavitation is modeled by a single-fluid homogeneous mixture equilibrium approach considering condensation and evaporation assuming volume averaged mixture quantities. The corresponding simplified quasilinear system is analyzed, and the wave speeds are calculated in order to adapt the employed four step Runge–Kutta explicit time stepping concerning the viscoelastic transport equations. We introduce a novel ghost cell boundary condition for the viscoelastic stress tensor. The approach is tested against (semi-)analytical unsteady and steady-state references and shows very good agreement. 3D simulations of the spherical vapor bubble collapse are performed for all implemented viscoelastic models and show a distinct influence compared to the Newtonian case. For the upper-convected Maxwell fluid a variation of the relaxation time exhibits its perspicuous influence on the dynamics of the collapse.

Numerical simulations for electro-osmotic flow of PTT fluids in diverging microchannel

In the current work, the electroosmotic coupled pressure driven flow through a diverging microchannel has been numerically investigated for the simplified Phan Thien Tanner (PTT) fluids. The Debye-Hückel approximation is used for the linearization of electric potential distribution in the electric double layer and the Debye length has been kept fixed (κH = 20). The pressure and electroosmotic forces are coupled and by, Г, the forcing ratio (the ratio of pressure to the electrokinetic gradient in the direction of flow), which is varied in the range of −4 ≤Г≤ 4. The viscoelastic fluid rheology has been modulated by the combined effect of the characteristic Deborah number and the PTT parameter as 0.1 ≤εDe≤ 5. The influence divergent angle (5° ≤α≤ 15°) has also been demonstrated to analyze the role of channel geometry on the resulting flow kinematics. The resulting variations in the flow field have been presented and discussed in the form velocity vectors, surfaces and velocity profiles at the outlet of the channel.

Electroosmotic flow of viscoelastic fluid through a microchannel with slip-dependent zeta potential

We investigate flow characteristics for an electroosmotic flow of viscoelastic fluids through a hydrophobic plane microchannel, considering the coupled effect of interfacial slip and zeta potential. We employ a simplified Phan–Thien–Tanner model to describe the constitutive behavior of the fluid. The governing equations are solved analytically to obtain electric double layer (EDL) potential distribution, flow velocity, flow rate, stresses, and viscosity. We have compared the obtained analytical flow field with the established theoretical and experimental works at the limiting cases. We demonstrate that ignoring the effect of the interfacial slip on zeta potential will lead to underprediction of the flow rate, and this underprediction is amplified with the increase in the Deborah number, decrease in the EDL thickness, and increase in the slip coefficient. Moreover, the relative flow rate augmentation by the rheological behavior strictly depends on the range of slip coefficients with the change in the EDL thickness. Accordingly, we have identified three regions of the slip coefficient. In addition, the viscosity near the wall decreases with the slip coefficient for the slip dependent zeta potential model. In contrast, the normal and shear stresses are augmented with the slip coefficient. Outcomes of the present investigation may help one to understand the enhanced flow behavior for the transport of complex fluids through a hydrophobic microchannel.

Fluid structure-interaction in a deformable microchannel conveying a viscoelastic fluid

We theoretically analyze the interaction between a viscoelastic fluid flow, whose constitutive equation is the simplified Phan–Thien–Tanner model, and a deformable slender shallow microchannel. The microchannel top wall displacement is analyzed considering two cases: a) as a thin plate, using the Kirchhoff–Love theory, and b) as a thick plate, based on the Reissner–Mindlin theory. The mathematical model is nondimensionalized, and dimensionless parameters related to problem physics arise that control the fluid–structure interaction. The governing equations that describe the hydrodynamic field are simplified using the lubrication theory, and the displacement of the top wall is analyzed for each plate theory, relating the hydrodynamic pressure and the volumetric flow rate. These equations are implicit in the pressure and are solved numerically. The effect of dimensionless parameters on the pressure drop-volumetric flow rate relationship is analyzed, showing that for a viscoelastic fluid flowing through deformable channels, the volumetric flow rate is higher than the case of a Newtonian fluid under the same pressure. Our results are compared against those published in the specialized literature, showing an excellent agreement.

Investigations into the Complete Spreading Dynamics of a Viscoelastic Drop on a Spherical Substrate.

We study the spreading dynamics of a sphere-shaped elastic non-Newtonian liquid drop on a spherical substrate in the capillary-driven regime. We use the simplified Phan-Thien-Tanner model to represent the rheology of the elastic non-Newtonian drop. We consider the drop to be a crater on a flat substrate to calculate the viscous dissipation near the contact line. Following the approach compatible with the capillary-viscous force balance, we establish the evolution equation for describing the temporal evolution of the contact line during spreading. We show that the contact line velocity obtained from the theoretical calculation matches well with our experimental observations. Also, as confirmed by the present experimental observations, our analysis deems efficient to capture the phenomenon during the late stage of spreading for which the effect of line tension becomes dominant. An increment in the viscoelastic parameter of the fluid increases the viscous dissipation effect at the contact line. It is seen that the higher dissipation effect leads to an enhancement in the wetting time of the drop on the spherical substrate. Also, we have shown that the elastic nature of the fluid leads to an increment in the dynamic contact angle at any temporal instant as compared to its Newtonian counterpart. Finally, we unveil that the phenomenon of the increasing contact angle results in the time required for the complete wetting of drop, which becomes higher with increasing viscoelasticity of the fluid. This article will fill a gap still affecting the existing literature because of the unavailability of experimental investigations of the spreading of the elastic non-Newtonian drop on a spherical substrate.