Viscoelasticity in inkjet printing

We investigate the effects of viscoelasticity on drop generation in inkjet printing. In drop-on-demand printing, individual ink ‘drops’ are ejected from a nozzle by imposed pressure pulses. Upon exiting the nozzle, the shape of each ‘drop’ is that of a nearly spherical bead with a long thin trailing ligament. This ligament subsequently breaks up under the Rayleigh instability, typically into several small droplets (known as satellite drops). These satellite drops can create unwanted splash on the target substrate and a reduction in printing quality. Satellite drops can potentially be eliminated by adding polymer to the ink; elastic stresses can act to contract the trailing ligament into the main drop before capillary breakup occurs. However, elasticity can also reduce the drop velocity and can delay or even prevent the break-off of the drop from the ink reservoir within the nozzle. To achieve optimal drop shape and speed, non-Newtonian parameters such as the polymer concentration and molecular weight must be chosen correctly. We explore this parameter space via numerical simulations, using the Lagrangian–Eulerian finite-element method of Harlen et al. (J Non-Newtonian Fluid Mech 60:81–104, 1995). Results are compared with experimental observations taken from real printheads.     

A Study of the Behavior of Implicit Pressure Explicit Saturation (IMPES) Schedules for Two-phase Flow in Dynamic Pore Network Models

We focus on the numerical difficulties that typify implicit pressure explicit saturation (IMPES) schedules in dynamic “ball-and-stick” pore network models for two-phase flow. We show that a time stepping procedure based on a prescribed maximum variation of the local capillary pressure rather than on a (usual) maximum variation of the local saturation along with the addition in the solution algorithm of suitable “flow constraints” (in Koplik and Lasseter, Soc. Pet. Eng. J. 25(1):89–100, 1985) provide more stability and a significant run time speed up. In particular, the slow convergence and the oscillatory behavior that typify IMPES schemes at low Ca values due to capillary pinning are efficiently suppressed.     

In situ observations of unusual drop deformation and wobbling in simple shear flow

Deformation and wobbling of a liquid drop immersed in a liquid matrix were studied under mild shear conditions for various viscosity ratios. In situ visualization experiments were conducted on a homemade transparent Couette cell incorporated to the Paar Physica MCR500 shear rheometer. The effect of drop or matrix elasticity was examined and was found to play a major role in both deformation and wobbling processes. Experimental results were compared to Jackson and Tucker (J Rheol 47:659–682, 2003), Maffettone and Minale (J Non-Newton Fluid Mech 78:227–241, 1998) and Yu and Bousmina (J Rheol 47:1011–1039, 2003) ellipsoidal models. It was found that the agreement between the Newtonian models and the experimental results required an increase in the drop viscosity. Such increment in viscosity was found to scale with the first normal stress difference.     

Experimental investigation on splashing and nonlinear fingerlike instability of large water drops

The fluid physics of the splashing and spreading of a large-scale water drop is experimentally observed and investigated. New phenomena of drop impact that differ from the conventional Rayleigh–Taylor instability theory are reported. Our experimental data shows good agreement with previous work at low Weber number but the number of fingers or instabilities begins to deviate from the R–T equation of Allen at high Weber numbers. Also observed were multiple waves (or rings) on the spreading liquid surface induced from pressure bouncing (or pulsation) within the impacting liquid. The first ring is transformed into a radially ejecting spray whose initial speed is accelerated to a velocity of 4–5 times that of the impacting drop. This first ring is said to be “splashing,” and its structure is somewhat chaotic and turbulent, similar to a columnar liquid jet surrounded by neighboring gas jets at relatively high impact speed. At lower impact speeds, splashing occurs as a crown-shaped cylindrical sheet. A second spreading ring is observed that transforms into fingers in the circumferential direction during spreading. At higher Weber number, the spreading of a third ring follows that of the second. This third ring, induced by the pressure pulsation, overruns and has fewer fingers than the second, which is still in a transitional spreading stage. Several important relationships between the drop impact speed, the spray ejection speed of the first ring, and the number of fingers of the second and third rings are presented, based on data acquired during a set of drop impact experiments. Issues related to the traditional use of the R–T instability are also addressed.     

Simplified model for mass diffusivity estimation based on dynamic pendant drop volume analysis

We present a simplified correlation for calculating the dissolved gas moles in a pendant drop during the diffusion time, for several drop shapes. After this correlation is determined, the Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) dynamic pendant drop volume analysis (DPDVA) method for calculation of mass diffusivity from the pendant drop volume variation against time can be used. We solved the differential equation in cylindrical coordinates for the mass transfer model of the gas diffusion into the liquid inside the pendant drop, using a different characteristic length (L_C), instead of the outer radius of the syringe needle (r_n) used in Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) for defining the dimensionless variables. L_C is the relationship between the pendant drop volume and its mass transfer surface area at the initial conditions. The generalized correlation saves time, simplifies the method application and the deviations in the diffusion coefficient calculation respect to the complete Yang and Gu model are below 6%.     

Development and characterization of a variable turbulence generation system

Experimental turbulent combustion studies require systems that can simulate the turbulence intensities [u′/U ₀ ~ 20–30% (Koutmos and McGuirk in Exp Fluids 7(5):344–354, 1989)] and operating conditions of real systems. Furthermore, it is important to have systems where turbulence intensity can be varied independently of mean flow velocity, as quantities such as turbulent flame speed and turbulent flame brush thickness exhibit complex and not yet fully understood dependencies upon both U ₀ and u′. Finally, high pressure operation in a highly pre-heated environment requires systems that can be sealed, withstand high gas temperatures, and have remotely variable turbulence intensity that does not require system shut down and disassembly. This paper describes the development and characterization of a variable turbulence generation system for turbulent combustion studies. The system is capable of a wide range of turbulence intensities (10–30%) and turbulent Reynolds numbers (140–2,200) over a range of flow velocities. An important aspect of this system is the ability to vary the turbulence intensity remotely, without changing the mean flow velocity. This system is similar to the turbulence generators described by Videto and Santavicca (Combust Sci Technol 76(1):159–164, 1991) and Coppola and Gomez (Exp Therm Fluid Sci 33(7):1037–1048, 2009), where variable blockage ratio slots are located upstream of a contoured nozzle. Vortical structures from the slots impinge on the walls of the contoured nozzle to produce fine-scale turbulence. The flow field was characterized for two nozzle diameters using three-component Laser Doppler velocimetry (LDV) and hotwire anemometry for mean flow velocities from 4 to 50 m/s. This paper describes the key design features of the system, as well as the variation of mean and RMS velocity, integral length scales, and spectra with nozzle diameter, flow velocity, and turbulence generator blockage ratio.     

Effect of wing–wake interaction on aerodynamic force generation on a 2D flapping wing

This paper is motivated by the works of Dickinson et al. (Science 284:1954–1960, 1999) and Sun and Tang (J Exp Biol 205:55–70, 2002) which provided two different perspectives on the influence of wing–wake interaction (or wake capture) on lift generation during flapping motion. Dickinson et al. (Science 284:1954–1960, 1999) hypothesize that wake capture is responsible for the additional lift generated at the early phase of each stroke, while Sun and Tang (J Exp Biol 205:55–70, 2002) believe otherwise. Here, we take a more fundamental approach to study the effect of wing–wake interaction on the aerodynamic force generation by carrying out simultaneous force and flow field measurements on a two-dimensional wing subjected to two different types of motion. In one of the motions, the wing at a fixed angle of attack was made to follow a motion profile described by “acceleration-constant velocity-deceleration”. Here, the wing was first linearly accelerated from rest to a predetermined maximum velocity and remains at that speed for set duration before linearly decelerating to a stop. The acceleration and deceleration phase each accounted for only 10% of the stroke, and the stroke covered a total distance of three chord lengths. In another motion, the wing was subjected to the same above-mentioned movement, but in a back and forth manner over twenty strokes. Results show that there are two possible outcomes of wing–wake interaction. The first outcome occurs when the wing encounters a pair of counter-rotating wake vortices on the reverse stroke, and the induced velocity of these vortices impinges directly on the windward side of the wing, resulting in a higher oncoming flow to the wing, which translates into a higher lift. Another outcome is when the wing encounters one vortex on the reverse stroke, and the close proximity of this vortex to the windward surface of the wing, coupled with the vortex suction effect (caused by low pressure region at the center of the vortex), causes the net force on the wing to decrease momentarily. These results suggest that wing–wake interaction does not always lead to lift enhancement, and it can also cause lift reduction. As to which outcome prevails depend very much on the flapping motion and the timing of the reverse stroke.     

Collision of water drop on water

A series of experiments are performed to study the collision of a water drop with various impact velocities, ranged from 0 to 600 cm/s, onto a water surface. Three kinds of phenomena have been recorded. Two of them named “penetration” and “cleavage”, were observed for low impact velocity (up to 100 cm/s). Their common characteristics are that no obvious disturbances on the surface were observed during the colliding process. Namely no splashing jets nor obvious crater were observed. By penetration we mean that a drop fallen into water becomes a ring, which penetrates the water smoothly with a velocity of several centimeters per second. During the penetrating process no obvious change of its configuration was observed. The falling height corresponding to penetration is proportional to volume of the original drop. Some periodicity of the falling heights (corresponding to penetration) was revealed. The phenomenon named “cleavage” occurs when the impact velocity is other than that corresponding to penetration, then the drop cleaves into an “inverted cauliflower” after falling below the surface of water. It almost does not decend. By diffusing and slowly expanding it vanishes in the vessel water several minutes after. These two kinds of phenomena, as we know, have not been reported before. As the impact velocity approaches or exceeds 100 cm/s, the third kind of phenomena, the splash, appears. The diameter and depth of the crater occuring in the case of splash, together with the time for the crater to reach its maximum size, and the time for the rebounding column to begin to rise are given as functions of the falling height of the drop.     

Nonlinear dynamics and conformational changes of linear entangled polymers using the Rolie-Poly model with an “effective” maximum contour length

The extended Rouse-CCR tube model for linear entangled polymers recently proposed by the authors (Kabanemi and Hétu, J Non Newtonian-Fluid Mech 160:113–121, 2009), designed to capture the progressive changes in the average internal structure (kinked state) of polymer chains, is here used to analyze, by means of a time-dependent three-dimensional finite element method, chain segment dynamics, pressure drop, and stability of flow through a 4:1:4 constriction in a tube. The model predicts an enhancement of the pressure drop in the stretch-dominated flow regime, which is also observed experimentally. This excess pressure drop was not associated with the onset of flow instability. The model also predicts kinked configurations within chain segments in the entry section to the constriction tube, at the inception of flow, and prior to the development of upstream vortices. It is also shown how these kinked configurations within chain segments influence pressure drop transients.     

Motion and shape of an axisymmetric viscoplastic drop slowly falling through a viscous fluid

Slow sedimentation of a deformable drop of Bingham fluid in an unbounded Newtonian medium is studied using a variation of the integral equation method (Toose et al., J Eng Math 30:131–150, 1996, Int J Numer Methods Fluids 30:653–674, 1999). The Green function for the Stokes equation is used, and the non-Newtonian stress is treated as a source term. The computations are performed for a range of physical parameters of the system. It is demonstrated that initially deformed drop similar to Newtonian ones breaks up for high capillary number, Ca, and stabilizes to steady shapes at low Ca. Estimations of critical capillary number for specific initial deformations demonstrated its growth (increase in the stability of the drop) with the yield stress magnitude both for prolate and oblate initial shapes. Prolate initial shapes become more stable with the increase of the plastic viscosity. In contrast to this, for low yield stress, oblate shapes are destabilized with the growth of the plastic viscosity. This effect is similar to the effect of the viscosity of a Newtonian drop on its stability. However, at higher yield stress, the effect of plastic viscosity is reversed.     

On Mathematical Modeling and Simulation of the Pressing Section of a Paper Machine Including Dynamic Capillary Effects: One-Dimensional Model

This study presents the dynamic capillary pressure model (Hassanizadeh and Gray, Adv Water Resour 13:169–186, 1990; Water Resour Res 29:3389–3405, 1993) adapted for the needs of paper manufacturing process simulations. The dynamic capillary pressure–saturation relation is included in a one-dimensional simulation model for the pressing section of a paper machine. The one-dimensional model is derived from a two-dimensional model by averaging with respect to the vertical direction. Then, the model is discretized by the finite volume method and solved by Newton’s method. The numerical experiments are carried out for parameters typical for the paper layer. The dynamic capillary pressure–saturation relation shows significant influence on the distribution of water pressure. The behavior of the solution agrees with laboratory experiments (Beck, Fluid pressure in a press nip: measurements and conclusions, 1983).     

Use of high pressures for solving problems of hypersonic aerodynamics

The use of high pressures in a hypersonic aerodynamic experiment is founded on physical grounds. Calculation results of Mach and Reynolds numbers reachable at the line of gas condensation are given as functions of the temperature and pressure in the plenum chamber. Approaches to solving problems of designing ultrahigh-pressure facilities that ensure outflow with pressures up to20,000 atm are described. These problems include the stop of the first-stage piston at the point of maximum pressure, suppression of the reaction force, provision of normal operation of seals of the moving piston, and reduction of friction forces in the seals. The principles considered are used in an actually operating facility. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 103–114, September–October, 2000.     

Hysteresis phenomenon in turbulent convection

Coherent large-scale circulations of turbulent thermal convection in air have been studied experimentally in a rectangular box heated from below and cooled from above using Particle Image Velocimetry. The hysteresis phenomenon in turbulent convection was found by varying the temperature difference between the bottom and the top walls of the chamber (the Rayleigh number was changed within the range of 10⁷–10⁸). The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant (A=2–2.23). We found that the change of the sign of the degree of the anisotropy of turbulence was accompanied by the change of the flow pattern. The developed theory of coherent structures in turbulent convection (Phys Rev E 66:1–15, 2002, Boundary-Layer Meteorol, 2005) is in agreement with the experimental observations. The observed coherent structures are superimposed on a small-scale turbulent convection. The redistribution of the turbulent heat flux plays a crucial role in the formation of coherent large-scale circulations in turbulent convection.     

The MSF model: relation of nonlinear parameters to molecular structure of long-chain branched polymer melts

The elongational viscosity data of model PS combs (Hepperle J, Einfluss der Molekularen Struktur auf Rheologische Eigenschaften von Polystyrol- und Polycarbonatschmelzen. Doctoral Thesis, University Erlangen-Nürnberg, 2003) are reconsidered by including the interchain pressure term of Marrucci and Ianniruberto [Macromolecules 37:3934–3942, 2004] in the Molecular Stress Function model [Wagner et al., J Rheol 47(3):779–793, 2003, Wagner et al., J Rheol 49:1317–1327, 2005d]. Two nonlinear model parameters are needed to describe elongational flow, β and . The parameterβ determines the slope of the elongational viscosity after the inception of strain hardening. It is directly related to the molecular structure of the polymer and represents the ratio of the molar mass of the (branched) polymer to the molar mass of the backbone alone. β follows from the hypothesis of Wagner et al. [J Rheol 47(3):779–793, 2003] that side chains are compressed onto the backbone. We consider also the case that side chains are oriented by deformation, but not stretched, and found little difference in the model predictions. The parameter represents the maximum strain energy stored in the polymeric system and determines the steady-state value of the viscosity in extensional flows. The relation of this energy parameter to the molecular structure is discussed. Good correlations between the energy parameter and different coil contraction ratios, as determined either experimentally or calculated theoretically by considering the topology of the macromolecule, are found. The smaller the relative size of the polymer coil, the larger is the energy parameter and the more strain energy can be stored in the polymeric system. Presented at the 3rd Annual European Rheology Conference, AERC2006, Crete, Greece.     

Use of particle image velocimetry to study heterogeneous drag reduction

Large polymer filaments can form when drag reducing polymers are injected through wall slots. The presence of these structures enhances the performance of the drag reducing function by mechanisms which are not understood. This paper shows how particle image velocimetry (PIV) techniques can be used to study changes in the configuration of the injected polymer and in the structure of the velocity field with increasing drag reduction. The filaments are found to behave as solid bodies which break up in high shear regions close to a boundary. The breakup process provides an explanation of why the filaments are not observed close to a wall and offers the possibility of providing a heterogeneous distribution of small aggregates of polymers which could be more effective than uniformly distributed molecules as suggested by Hoyer and Gyr (J Non-Newton Fluid Mech 65:221–240, 1996; J Fluids Eng 120:818–823, 1998), Dunlop and Cox (Phys Fluids 20:203–213, 1977) and Vlachogiannis et al. (Phys Fluid 15:3786–3794, 2004). PIV measurements show dramatic qualitative changes in the velocity patterns at maximum drag reduction.     

The interchain pressure effect in shear rheology

Recently, the tube diameter relaxation time in the evolution equation of the molecular stress function (MSF) model (Wagner et al., J Rheol 49: 1317–1327, 2005) with the interchain pressure effect (Marrucci and Ianniruberto, Macromolecules 37:3934–3942, 2004) included was shown to be equal to three times the Rouse time in the limit of small chain stretch. From this result, an advanced version of the MSF model was proposed, allowing modeling of the transient and steady-state elongational viscosity data of monodisperse polystyrene melts without using any nonlinear parameter, i.e., solely based on the linear viscoelastic characterization of the melts (Wagner and Rolón-Garrido 2009a, b). In this work, the same approach is extended to model experimental data in shear flow. The shear viscosity of two polybutadiene solutions (Ravindranath and Wang, J Rheol 52(3):681–695, 2008), of four styrene-butadiene random copolymer melts (Boukany et al., J Rheol 53(3):617–629, 2009), and of four polyisoprene melts (Auhl et al., J Rheol 52(3):801–835, 2008) as well as the shear viscosity and the first and second normal stress differences of a polystyrene melt (Schweizer et al., J Rheol 48(6):1345–1363, 2004), are analyzed. The capability of the MSF model with the interchain pressure effect included in the evolution equation of the chain stretch to model shear rheology on the basis of linear viscoelastic data alone is confirmed.     

Experimental investigation of hydrodynamic loads and pressure distribution during a pyramid water entry

In the maritime environment slamming is a phenomenon known as short duration impact of water on a floating or sailing structure. Slamming loads are local and could induce very high local stresses. This paper reports a series of impact test results and investigate the slamming loads and pressures acting on a square based pyramid. In this study the slamming tests have been conducted at constant velocity impact with a hydraulic high speed shock machine. This specific experimental equipment avoids the deceleration of the structure observed usually during water entry with drop tests. Three velocities of the rigid pyramid have been used (10, 13 and 15 m s⁻¹). Time-histories of local pressures, accelerations and slamming loads were successfully measured. The relationship between the pressure magnitude and the impact velocity is obtained and the spatial distribution of pressures on pyramid sides is characterized. The impact velocity was found to have a negligible influence in predicting the maximum pressure coefficient.     

The Minimal Speed of Traveling Fronts for the Lotka–Volterra Competition System

We study the minimal speed for a two species competition system with monostable nonlinearity. We are interested in the linear determinacy for the minimal speed in the sense defined by (Lewis et al. J Math Biol 45:219–233, 2002). We provide more general cases for the linear determinacy than that of (Lewis et al. J Math Biol 45:219–233, 2002). For this, we study the minimal speed for the corresponding lattice dynamical system. Our approach gives one new way to study the traveling waves of the parabolic equations through its discretization which can be applied to other similar problems.     

Large Eddy Simulation and PIV Measurements of Unsteady Premixed Flames Accelerated by Obstacles

In gas explosions, the unsteady coupling of the propagating flame and the flow field induced by the presence of blockages along the flame path produces vortices of different scales ahead of the flame front. The resulting flame–vortex interaction intensifies the rate of flame propagation and the pressure rise. In this paper, a joint numerical and experimental study of unsteady premixed flame propagation around three sequential obstacles in a small-scale vented explosion chamber is presented. The modeling work is carried out utilizing large eddy simulation (LES). In the experimental work, previous results (Patel et al., Proc Combust Inst 29:1849–1854, 2002) are extended to include simultaneous flame and particle image velocimetry (PIV) measurements of the flow field within the wake of each obstacle. Comparisons between LES predictions and experimental data show a satisfactory agreement in terms of shape of the propagating flame, flame arrival times, spatial profile of the flame speed, pressure time history, and velocity vector fields. Computations through the validated model are also performed to evaluate the effects of both large-scale and sub-grid scale (SGS) vortices on the flame propagation. The results obtained demonstrate that the large vortical structures dictate the evolution of the flame in qualitative terms (shape and structure of the flame, succession of the combustion regimes along the path, acceleration-deceleration step around each obstacle, and pressure time trend). Conversely, the SGS vortices do not affect the qualitative trends. However, it is essential to model their effects on the combustion rate to achieve quantitative predictions for the flame speed and the pressure peak.     

Characteristics of liquid sheets formed by splash plate nozzles

An experimental study was conducted to identify the effect of viscosity on the characteristics of liquid sheets formed by a splash plate nozzle. Various mixtures of corn syrup and water are used to obtain viscosities in the range 1–170 mPa.s. Four different splash plates with nozzle diameters of 0.5, 0.75, 1, and 2 mm, with a constant plate angle of 55° were tested. Liquid sheets formed under various operating conditions were directly visualized. The sheet atomization process for the range of parameters studied here is governed by two different mechanisms: Rayleigh–Plateau (R–P) and Rayleigh–Taylor (R–T) instabilities. R–P occurs at the rim and R–T occurs on the thin sheet. The rim instability can be laminar or turbulent, depending on the jet Reynolds number. The R–T instability of the sheet is observed at the outer edges of the radially spreading sheet, where the sheet is the thinnest. It can also occur inside the sheet, due to formation of holes and ruptures.