Simple Shear Flow Research Articles

Role of surfactant-induced Marangoni effects in droplet dynamics on a solid surface in shear flow

We address the dynamics of a surfactant-laden droplet on a solid surface in simple shear flow numerically. Our analysis uses the front-tracking method to take surfactant transport into account. The interfacial tension and the slip coefficient, both of which depend heavily on the surfactant concentration, are fully integrated into the generalized Navier boundary condition to model the moving contact lines. Accurate prediction of droplet motion indicates that the surfactant can change droplet behavior drastically. Surfactant-induced effects, such as interfacial tension reduction, the Marangoni stress, and wettability alternation, are investigated for various capillary numbers, surface wettabilities, elasticity numbers, and surface Péclet numbers. Deformation and motion of a sliding droplet are enhanced by the Marangoni effect, which is associated with an interfacial tension gradient. When the capillary number reaches a critical value, the sliding-to-detachment and detachment-to-pinch-off transitions occur. Both transitions can be triggered and accelerated by a surfactant, especially when convection is dominant. As a result, the critical capillary number decreases, but exhibits a non-monotonic relationship with the elasticity number and Péclet number. The mechanisms that underlie the effect of Marangoni stress are discussed by analyzing the distributions of the surfactant concentration and the hydrodynamic forces exerted on the droplet. Accumulation of surfactants near the receding contact line reverses the local concentration gradient, attempts to change its direction along the interface, and delays droplet detachment. Furthermore, the strong surfactant dilution reduces both the surfactant concentration and the interfacial tension gradient, and thereby increasing the critical value for droplet pinch-off.

Critical comparison of polydisperse kinetic theories using bidisperse DEM data

Kinetic theories have been developed to describe the hydrodynamics of polydisperse granular flows under different theoretical assumptions. In this study, six species theories are assessed using the DEM data obtained from simple shear flow containing bidisperse particles with low and moderate solid volume fraction (Galvin, 2007). It was shown that (i) only the theories of Iddir and Arastoopour (2005) and Zhao and Wang (2021) can qualitatively capture all of the effects of various parameters on the granular temperature ratio and the normal and shear stresses; (ii) the granular temperature ratio can be predicted accurately either by Iddir and Arastoopour (2005) or Zhao and Wang (2021), depending on the input parameters; and (iii) the predictions of normal and shear stresses by Iddir and Arastoopour (2005) are superior in matching the DEM data for most tested cases. Present study not only discusses the fundamental differences between different species kinetic theories, but also offers a critical assessment of their suitability in modeling simple shear flow.

Birefringent strands drive the flow of viscoelastic fluids past obstacles

The flow of polymer solutions past solid obstacles or through porous media gives rise to rich physical phenomena over a wide range of spatial and temporal scales. Viscoelasticity, in particular, can induce a strong nonlinear response with an increase of flow resistance even for a solution whose viscosity decreases in simple shear flow. Various hypotheses have been proposed to explain this phenomenon but a clear picture of the pore-scale mechanisms involved and their impact upon larger scales is still lacking. Here, we show that localized zones of large polymeric stress, known as birefringent strands, drive the flow of an Oldroyd-B fluid through two-dimensional arrays of cylinders. Combining a recently developed numerical scheme with high performance computing, we find that these strands generate a complete reorganization of the flow with an increase of stagnation zones, a reinforcement of preferential paths and a splitting of flow channels. Furthermore, we show that this reorganization is the source of an increase in the viscous dissipation of the solvent and also that the stretching of polymer molecules in the strands is associated with entropy production. Both these phenomena yield a global increase in dissipation that can be directly linked to the increase of flow resistance. Our results demonstrate that the birefringent strands – not the elongational viscosity – drive the flow of viscoelastic fluids through porous media and that the increase of flow resistance can occur even at steady state, before the transition to elastic turbulence.

Effect of porous media models on rheological properties of suspensions

This work reports an experimental investigation of the flow of non-colloidal, non-Brownian suspensions via rheological tests over and through well-designed porous media models. We performed a series of simple shear flow experiments using a rheometer with a parallel-plate geometry where different porous structures were placed on the lower plate. The impact of various bulk particle volume fractions of suspensions φb, ranging from 0 to 0.4, was studied by considering four different porous microstructures with porosities of 0.7 and 0.9. We designed and built porous media models with known permeability and porosity, where the particles were either allowed to move or prevented from moving inside the porous structures. We examined the impact of viscosity by the existence of porous media. We found that, when particles move inside the porous layer, the slip velocity at the fluid-porous interface increases and varies with the porosity compared to when they do not flow into the porous layer. Additionally, with the increase in volume fraction of suspensions, the slip velocity decreases at a constant stress while the slip length rises. We then compared these data with the volume-averaged Navier-Stokes (VANS) equations for flow in the porous medium coupled with the Stokes equations in the free-flow region to further examine the slip velocity.

Analytical Solutions for Simple Turbulent Shear Flows on a Basis of a Generalized Newton's Law.

In the presented article a generalization of Newton’s formula for the shear stress in a fluid is carried out by giving it a power-law form. After the introduction of the corresponding strain rate tensor, a generalization is made to the spatial case of flow and the rheological relation is presented in tensor form. Depending on the power value in this rheological ratio, one can come either to a description of a laminar flow regime (in the form of Navier–Stokes equations), or to a description of the flow in turbulent regime. In the latter case, a set of differential equations with the no-slip boundary condition is specified, which is significantly different from that for the laminar flow regime, but which also allows one to obtain analytical solutions for simple shear flows and obtain the Blasius resistance law for the flow in a pipe. Therefore, the considered approach to solving problems of turbulent flows compares favorably with modern differential turbulence models. Solutions are given for simple shear flows of a fluid, when there is only one longitudinal component of the velocity, which depends on the transversal coordinate only. These solutions in terms of velocity profiles and resistance coefficients are in satisfactory agreement with the experimental data.

Long-Ranged Order and Flow Alignment in Sheared p-atic Liquid Crystals.

We formulate a hydrodynamic theory of p-atic liquid crystals, namely, two-dimensional anisotropic fluids endowed with generic p-fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of p-atic phases, allows us to unveil several unknown aspects of flowing p-atics, that previous theories, characterized by O(2) rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates.

Enhancement of heat and mass transfer by herringbone microstructures in a simple shear flow

The heat and mass transfer characteristics of a simple shear flow over a surface covered with staggered herringbone structures are numerically investigated using the lattice Boltzmann method. Two flow motions are identified. The first is a spiral flow oscillation above the herringbone structures that advect heat and mass from the top plane to herringbone structures. The second is a flow recirculation in the grooves between the ridges that advect heat and mass from the area around the tips of the structures to their side walls and the bottom surfaces. These two basic flow motions couple together to form a complex transport mechanism. The results show that when advective heat and mass transfer takes effect at relatively large Reynolds and Schmidt numbers, the dependence of the total transfer rate on Schmidt number follows a power law, with the exponent being the same as that in the Dittus–Boelter equation for turbulent heat transfer. As the Reynolds number increases, the dependence of the total transfer rate on the Reynolds number also approaches a power law, and the exponent is close to that in the Dittus–Boelter equation.

Computational Analysis of the Dynamics of Generalized-Viscoelastic-Fluid-Based Nanofluids Subject to Exothermic-Reaction in Shear-Flow

A novel problem that describes laminar simple shear-flow of generalized-viscoelastic-fluid-based nanofluids (GVFBN) containing spherical shaped nano-particles under non-isothermal conditions but with isothermal walltemperature boundary-conditions is investigated. The GVFBN model is an extension of the VFBN to include shear-rate dependent viscosity effects. The Generalized non-isothermal Giesekus constitutive model (which is reducible to generalized Oldroyd-B model) with essential modifications for thermodynamics is used to account for the viscoelastic effects. Spherical shaped nano-particles are homogeneously mixed to the viscoelastic base fluid. To characterize the shear-thinning-viscosity, a viscosity-constitutive-model of the Carreau-type is employed. A temperature-dependent thermal conductivity is also considered. Additionally, empirical models are employed to account for to the nano-particle effects on the thermal conductivity. We use an efficient, semi-implicit, numerical scheme, based on finite difference methods (FDM), to obtain the numerical solutions of the model equations. The numerical scheme is computationally implemented in MATLAB. Results are graphically presented in both a qualitative and quantitative sense with regards to the various embedded parameters. Specifically, the thermodynamic and fluid-dynamical impacts of variations in the volume fraction of nano-particles are explored. In summary, we notice enhanced thermal conductivity and hence also increased temperature with increasing nano-particle volume fraction. The GVFBN model accounts for all four nanofluid types, Generalized-Newtonian-fluid-based nanofluids (GNFBN), Newtonian-fluid-based nanofluids (NFBN), Generalized-viscoelastic-fluid-based nanofluids (GNFBN), and viscoelastic-fluid-based nanofluids (VFBN). The comparative thermal runaway susceptibility of the four nanofluid types is presented and we demonstrate that the order of susceptibility from the most to the least susceptible is GNFBN, NFBN, GVFBN, VFBN.

The detachment of a wall-bound pendant drop suspended in a sheared fluid and subjected to an external force field

The phase field approach is applied to numerically simulate the detachment of an isolated, wall-bound 2D pendant drop suspended in a fluid in a simple shear flow. The model has been previously employed to simulate several two-phase flow phenomena, assuming that the system consists of a regular, partially miscible mixture, with the drop and the continuous phase being in thermodynamic equilibrium with each other. In addition, it is assumed that the two phases are separated by an interfacial region having a non-zero characteristic thickness â, i.e., the interface is diffuse. In the creeping flow regime, the problem is described in terms of three non-dimensional numbers: the fluidity number Nα as the ratio between capillary and viscous fluxes, the Bond number NBo as the ratio between external and capillary forces, and the Peclet number NPe as a non-dimensional shear rate. We find that, at large fluidity numbers and for small droplets (i.e., for d̃drop=ddrop/â≤45), the onset of the drop detachment can be described in terms of a master curve, with the critical macroscopic Bond number NBo(M)=NBo·d̃drop2 decreasing monotonously with NPe·d̃drop1.5 for five drop sizes in the micrometer range.

Hydrodynamic Behavior of Self-Propelled Particles in a Simple Shear Flow.

The hydrodynamic properties of a squirmer type of self-propelled particle in a simple shear flow are investigated using the immersed boundary-lattice Boltzmann method in the range of swimming Reynolds number 0.05 ≤ Res ≤ 2.0, flow Reynolds number 40 ≤ Rep ≤ 160, blocking rate 0.2 ≤ κ ≤ 0.5. Some results are validated by comparing with available other results. The effects of Res, Rep and κ on the hydrodynamic properties of squirmer are discussed. The results show that there exist four distinct motion modes for the squirmer, i.e., horizontal mode, attractive oscillation mode, oscillation mode, and chaotic mode. Increasing Res causes the motion mode of the squirmer to change from a constant tumbling near the centerline to a stable horizontal mode, even an oscillatory or appealing oscillatory mode near the wall. Increasing the swimming intensity of squirmer under the definite Res will induce the squirmer to make periodic and stable motion at a specific distance from the wall. Increasing Rep will cause the squirmer to change from a stable swimming state to a spiral motion or continuous rotation. Increasing κ will strengthen the wall’s attraction to the squirmer. Increasing swimming intensity of squirmer will modify the strength and direction of the wall’s attraction to the squirmer if κ remains constant.

Crustal transpressional fault geometry influenced by viscous lower crustal flow

AbstractThe San Andreas fault (California, USA) is near vertical at shallow (<10 km) depth. Geophysical surveys along the San Andreas fault reveal that, at depths of 10–20 km, it dips ~50–70° to the southwest near the Western Transverse Ranges and dips northeast in the San Gorgonio region. We investigate the possible origin of along-strike geometric variations of the fault using a three-dimensional thermomechanical model. For two blocks separated by transpressional faults, our model shows that viscous lower crustal material moves from the high-viscosity block into the low-viscosity block. Fault plane-normal flow in the viscous lower crust rotates the fault plane due to the simple shear flow at the brittle-ductile transition depth. This occurs irrespective of initial fault dip direction. Rheological variations used to model the lower crust of Southern California are verified by independent observations. Block extrusion due to lower crustal viscosity variation facilitates the formation of the Garlock Fault and sustains the geometric complexity of the fault.

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.

The effect of thixotropy on deformation of a single droplet under simple shear flow

In this paper, the deformation of an isolated single two-dimensional droplet under simple shear flow is studied regarding the thixotropic behavior. In doing so, a modified consistent weakly compressible smoothed particle hydrodynamics method is employed. It is assumed that the thixotropic fluid obeys the Moore model, and the surface tension is modeled by the continuum surface tension (CST) method. After verifying the utilized paradigm, it is applied to novel cases in which one of the fluids exhibits thixotropic behavior. The effects of Moore's model constants are examined through several numerical simulations. It is shown that the drop deformation is dramatically affected by thixotropic behavior. Generally speaking, the deformation of the Newtonian droplet is decreased by increasing the destruction-to-rebuild ratio of the surrounding thixotropic liquid. The same trend is found when the thixotropic droplet is exposed to the shear flow of a Newtonian fluid. Also, it is demonstrated that the presence of another droplet in the vicinity of the first droplet could dramatically change the flow domain. To the best of the author's knowledge, the effect of thixotropy is investigated on droplet deformation for the first time.

A drop in a nonlinear shear flow

The fluid mechanics problem of an initially spherical drop subjected to a two-directional nonlinear cubic shear flow, under creeping flow conditions, is theoretically studied. This physical situation is described by four dimensionless numbers: the capillary number (Ca), the viscosity ratio (λ), the linear velocity ratio (G) and the nonlinear intensity of the flow (E). Analytical expressions for the external and internal flows of a spherical drop as well as for the shape of the deformed drop were obtained by applying Lamb's general solution to the Stokes equations. The internal and external streamlines of a spherical drop (Ca = 0) suggest interesting and unusual shapes which are sometimes also accompanied by many stagnation points. Whenλ = ∞, the drop becomes a solid sphere with an angular velocity$\omega ={-} (1 - G)/2$independent ofE. For the familiar simple shear flow in thex-direction (G = 0,E = 0), Taylor's theory, valid at$Ca \ll 1$andλ = O(1), predicts an ellipsoidal drop oriented at an azimuthal angleϕ = 45°; asCaincreases, the deformation increases and the drop attains a peanut shape. For other linear or nonlinear cases, the drop is aligned atϕ = ±45°, and a spherical drop with no deformation is possible atCa ≠ 0. In a highly viscous drop$(\lambda \gg 1)$, the drop remains almost spherical even atCa = O(1), oriented atϕ = 0° or 90° (G ≠ 1), and its deformation is independent ofCa.

A coarse-grained particle simulation on the capillary suspension and its rheological properties under the simple shear flow

A coarse-grained particle simulation on the capillary suspension and its rheological properties under the simple shear flow

Comparative Additional Factor for Diffraction Loss On (TEM01) Mode from That of (TEM00) Mode

Comparative Additional Factor for Diffraction Loss On (TEM01) Mode from That of (TEM00) Mode

Droplet deformation and breakup in shear-thinning viscoelastic fluid under simple shear flow

A three-dimensional lattice Boltzmann method, which couples the color-gradient model for two-phase fluid dynamics with a lattice diffusion-advection scheme for the elastic stress tensor, is developed to study the deformation and breakup of a Newtonian droplet in the Giesekus fluid matrix under simple shear flow. This method is first validated by the simulation of the single-phase Giesekus fluid in a steady shear flow and the droplet deformation in two different viscoelastic fluid systems. It is then used to investigate the effect of Deborah number De, mobility parameter α, and solvent viscosity ratio β on steady-state droplet deformation. We find for 0.025&amp;lt;α&amp;lt;0.5 that as De increases, the steady-state droplet deformation decreases until eventually approaching the one in the pure Newtonian case with the viscosity ratio of 1/β, which is attributed to the strong shear-thinning effect at high De. While for lower α, the droplet deformation exhibits a complex nonmonotonic variation with De. Under constant De, the droplet deformation decreases monotonically with α but increases with β. Force analysis shows that De modifies the droplet deformation by altering the normal viscous and elastic stresses at both poles and equators of the droplet, while α mainly alters the normal stresses at the poles. Finally, we explore the roles of De and α on the critical capillary number Cacr of the droplet breakup. By establishing both Ca–De and Ca–α phase diagrams, we find that the critical capillary number increases with De or α except that a plateau critical capillary number is observed in Ca–De phase diagram.

Gyrotactic trapping of micro-swimmers in simple shear flows: a study directly from the fundamental Smoluchowski equation

Thin phytoplankton layers with vertically compressed structures found in stratified lakes and coastal water bodies have been a hot-spot in marine science and fluid mechanics. Although extensive efforts have been made to explore gyrotactic trapping as a possible mechanism, obvious inconsistencies remain there between the generalised Taylor dispersion method and individual-based model. In this work, a study directly from the fundamental Smoluchowski equation is carried out on the gyrotactic trapping mechanism in representative simple shear flows. With no approximation made to the fundamental equation and applying a biorthogonal expansion to the local moments of the probability density function, the evolution and steady state of the transport process are in good agreement with results of individual-based model, thus removing the gap between the continuum approach and individual-based model. The influences of strongly varying shear rate and boundary effect are reasonably scrutinised. The average swimming orientation with fixed local shear is highlighted as time-dependent rather than steady as previously assumed. The variations of characteristic time of the transient thin layer as functions of the flow intensity, gyrotaxis intensity and swimming ability are characterised. Sedimentation of the micro-swimmers is considered in some cases to reflect that micro-organisms are possibly negatively buoyant, with corresponding boundary conditions devised. A steady thin layer can be realised in the solution by adding a small settling speed to counteract the gravitactic focusing at the upper surface.

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.

Discrete element modeling of strongly deformed particles in dense shear flows

The discrete element method (DEM) proposed by Cundall and Strack [1] is a widely used numerical approach to study the fundamentals of particulate matter at the particle scale. In our present study, the flow behavior of dense configurations of soft particles was studied by means of a new formulation of the multi-contact force closure for the DEM. The first step was to verify the response of the new force closure, and calibrate its parameters based on a comparison of the results for simple uniaxial compression with results from a reference simulation. This reference simulation used a highly accurate nonlocal formulation of contact mechanics in the quasi-static limit [2], which accounts for the interplay of deformations due to multiple contact forces acting on a single particle. The newly developed and calibrated model results show significant improvement over those derived via the existing multi-contact model. Also, the dependence of the stress in the sheared granular matter on the Poisson's ratio was unveiled when using the newly derived advanced multi-contact force closure. Therefore, an extensive campaign of simple shear flow simulations was performed (at a fixed volume of the simulation box) to probe the effect of particle volume fraction and the speed of shearing. These simulations show that the stress at particle volume fractions larger than a critical value depends not only on the friction coefficient and particle stiffness, but also on the Poisson's ratio of the material. Finally, we report a response surface for the pressure in a sheared particle bed as a function of all key influence parameters. This response surface is beneficial for calibrating DEM model parameters in extremely dense flow configurations.