Initial Shear Rate Research Articles

Yield Behavior of Moderately Filled Epoxy/Ni Suspensions

Epoxy/nickel (Ni) adhesives can be used as integrated circuit (IC) packaging materials due to their lower cost than epoxy/silver (Ag) adhesives with acceptable electrical conductivity. In this work, yield behavior was studied for moderately filled bisphenol-A based epoxy/Ni suspensions (10–60 wt% of Ni). Effects of the preshear history, resin viscosity, temperature, particle size, solid loading, as well as different yield stress determination methods were investigated. The preshear effect manifests itself in successive shear rate sweeps with the same sample. Consequently, an initial shear rate sweep was employed to serve as preshear conditioning and obtain reproducible results on all samples. Shear thinning generally occurs for epoxy/Ni suspensions. The fractal dimension (D f) may be employed to describe these flocculated structures, and a higher D f value was observed for Epon815C/Ni system as compared to Epon830/Ni system. The Arrhenius equation describes the temperature dependence of suspension viscositys adequately. Incorporation of Ni nanopowder significantly reduces flow and the activation energy for yielding. The stronger van der Waals attractions created within the nanoparticles lead to larger yield stress. Also, different yield stress values are calculated using different determination methods.

Experimental measurement and numerical simulation of viscosity reduction effects in HMMPE containing a small amount of exfoliated organoclay-modified TLCP composite

A small amount (1 wt%) of organoclay-modified thermotropic liquid crystalline polymer (TLCP) acting as a viscosity reduction agent in high molecular mass polyethylene (HMMPE) was characterized and compared with purified TLCP (1 wt%) in HMMPE at 190 °C and 230 °C, respectively, where the TLCP displayed nematic and nematic-isotropic biphase structures. In the TLCP/PE blend at 190 °C and 230 °C, dramatic reductions in viscosity were observed with significant improvement in extrudate surface smoothness and an enlarged processing window. For the organoclay-modified TLCP in PE, the viscosity reduction ability of TLCP was further enhanced with viscosity dropped by up to >98.5% and >97.4% at 190 °C and 230 °C and processing window enlarged to >700 s −1 and >900 s −1 respectively in comparison to that of PE. Moreover, yielding stress, initial transition shear rate and transition region decreased to lower magnitudes than those of the TLCP/PE blend. A phenomenological model was applied to elucidate the mechanism of organoclay, TLCP and PE conformation before and after yielding in the confined capillary environment. A binary flow pattern model was applied to successfully predict the rheological behavior of the blends at 190 °C.

Numerical Study of Shear-Induced Thrombus Formation Over Aterial Stent Struts

Thrombosis remains an important problem in both bare-metal and drug eluting stents. Platelet accumulation appears to be highly shear dependent in uniform parallel plate and stenosis models. This study was performed to evaluate thrombus formation location and size with respect to time for a stent. A three-dimensional laminar flow field was modeled via computational fluid dynamics through a stent-containing coronary sized vessel. Platelet deposition and accumulation was then simulated using a shear dependent accumulation function. The platelet deposition rate is given by the function: 3.2γ̇+67 platelets/mm2/s, where γ̇ is the shear rate, which comes from a linear regression to data presented in Ku and Flannery 2007. A three-dimensional stent with a helical strut matrix design and a pitch of 21 mm was designed around a 3 mm diameter vessel. Square strut designs of 0.15mm×0.15mm and 0.30mm×0.30mm were considered, with each strut embedded halfway into the vessel. A 30° section of the stent was modeled because of stent symmetry. The inlet was set at a mean Reynolds number of 200 by specifying a pressure differential across the length of the vessel. Thrombus growth based on shear rate was set through the equation: dΦ/dt=(3.2γ̇+67)(Vplatelet/V)∑n=0MAn. V is volume, Φ is the volume fraction of thrombus, M is the number of surrounding faces that are either a wall face or are neighboring a computational cell denoted as occluded by thrombus, associated with area, A. Each term without a subscript pertains to the local computational cell prescribed as undergoing thrombus growth. Thrombus cell occlusion was assumed to occur when thrombus filled 80% of the cell's volume. Maximum shear rates occur near the edges along the inner blood surface side of the stent struts. Thrombus growth increases more in the axial direction of the stent relative to the radial direction for the larger strut size. Conversely, the thrombus growth is more uniform in all directions along the smaller struts. The difference emanates from the two distinctly localized high shear contours near the edges of the larger stent struts, while the high shear regions were less distinct for the smaller strut size. Quadrupling the cross sectional area of a strut increases the initial maximum shear rate along the strut by 50%, in addition to doubling the available surface area for platelet deposition. Therefore, increasing strut size has a threefold effect on platelet deposition rate, leading to faster vessel occlusion. This computational technique may be extended to approximate where thrombus may grow to completely occlude a blood vessel and the length of time occlusion would take. The CFD modeling technique may also be used to evaluate thrombus deposition on medical devices such as heart valves and ventricular assist devices.

Rheometric investigation on the temporal shear thickening of dilute micellar solutions of C14‐, C16‐, and C18TAB∕NaSal

The rheological behavior and especially the rheopexy phenomena of dilute self-assembled solutions in the presence of a counterion are examined in stationary and transient shear flows. In the first part, a continuous and gradually increasing strain is applied on the same sample. We study the effect of the initial shear rate, the temporal variation of the viscosity, and the hysterisis between charge and discharge curves. The results show that the properties of shear thickening are independent of the initial shear rate. In the second part, fresh samples are successively subjected to increasing shear strains; this method allows us to follow the evolution of the rheological characteristics during long measuring durations and gives us a distinct picture of the behavior per shear rate. In both cases, we confirm that the chain length has a strong influence on the emergence and amplitude of the shear thickening. It was also found by studying the start-up flow behavior that the structure at equilibrium is composed of bigger structures for longer chain lengths. The maximum of the viscosity in the shear thickening transition occurs in a range of lower shear rates when enough time is given to the system to undertake the formation of the shear induced structure. Considering this result, we introduce the concept of “temporal shear thickening transition.”

Rheological properties of veneer trial pastes relevant to clinical success

The porcelain veneer is a relatively conservative means of improving the appearance of teeth. As these restorations are usually highly visible it is essential to gain the approval of the patient before final cementation takes place. As a result a variety of trial pastes are available that match the shades of the resins that are used ultimately to finally cement the veneer in place. Such restorations, by virtue of their small size and fragility, are difficult to handle and position. It is therefore important that the application of trial paste does not impede placement and retention upon the tooth surface at try in whilst the patient assesses its appearance. To determine the rheological properties of three makes of trial pastes (Calibra - Dentsply Caulk, USA; Nexus - Kerr, USA; Rely X - 3M Espe, USA) and assess if temperature affected these. Design In vitro rheological measurement. For each product the rheological properties of three shades were determined at both 25 degrees C and 35 degrees C three times. Measurements of both the Initial Yield Stress and Shear Rate Index were undertaken using a controlled stress rheometer (Carri-med, Dorking, UK) in flow mode with a cone-and-plate test configuration. One way analyses of variance of the initial yield and shear rate index for each shade of material at 25 and 35 degrees C demonstrated no significant effects of temperature with the exception of the initial yield of Nexus (P = 0.0024) where the yield stress of the white shade was significantly (P <0.01) higher at 35 degrees C than at 25 degrees C. In all cases the yield stress for Nexus was of the order of ten times higher than the other materials. All materials demonstrated pseudoplastic behaviour. The variation in yield stress displayed by the materials will affect the handling of veneers and offers a potentially useful choice parameter to the clinician as to which paste bests suits their requirements.

Analytical modeling of the rheological behavior of semisolid metals and composites

The thixotropic nature of semisolid alloys and composites has been shown to be advantageous in semisolid metal processing. This effect can be highlighted by hysteresis experiments in the semisolid state where the shear rate is increased from zero to a maximum value and then decreased back to zero in a specific time period. The results presented in this article show that the rheological behavior of a semisolid material subjected to such a cycle depends strongly on the initial state of its microstructure. It is shown that the rheological behavior of the dissociated structure is reversible, while that of the agglomerated state is strongly thixotropic. The agglomeration of the structure is favored by a rest time and a low initial shear rate prior to the shear cycle. A model based on the assumptions of Moore was developed to describe our experimental results. It takes into account all the variables that influence the form of the hysteresis loops, i.e., the time to reach the maximum shear rate, the maximum shear rate attained during a cycle of shearing, the initial state of the microstructure, and the number of shearing cycles imposed. The results of our simulations show that we are able to reproduce the experimental results under various conditions in an analytical model, which take into account a set of experimentally determined constants and by varying the value of a structural parameter describing the initial state of agglomeration of the semisolid metal slug.

Evaluation of Platelet Thrombus Formation under Flow.

We have used confocal laser microscopy and a novel “voxel”-based imaging software to study the dynamics of platelet aggregation and thrombus formation when anticoagulated blood was perfused over collagen-coated surfaces at shear rates simulating arterial flow. The objective was to evaluate the three-dimensional growth of platelet thrombi over time (“4-D” imaging). Blood from healthy donors, anticoagulated with either PPACK (80 μM) or, depending on the type of experiment, with trisodium citrate (11 mM), was incubated with mepacrine (10 μM) to render platelets fluorescent. Blood was aspirated with a syringe pump through a rectangular perfusion chamber (flow path height of 80 μm) at a flow rate of 160 or 480 μl per min to provide initial shear rates of 500 or 1,500 sec−1, respectively. Prior to perfusion, glass coverslips were coated with fibrillar type I collagen (Roche Diagnostics, Mannheim, Germany) prepared in 0.5 M acedic acid, pH 2.8, and blocked with 2 % BSA. The chamber was mounted on a Zeiss Axiovert 100M/LSM 510 invert laser scanning confocal microscope (Carl Zeiss, Oberkochem, Germany). Upon perfusion, a series of stacks, i.e. 30 confocal optical sections, from the bottom to the apex of the forming platelet aggregate or thrombus, were obtained every 25 sec with a 488-nm laser and a scanning time of < 500 msec on an area of 26,450 μm2. Images corresponding to an area of 0.202 μm2 were analyzed by a “voxel”-based procedure, whereby a voxel is defined by a volume of 0.202 μm3 (0.45 μm x 0.45 μm x 1 μm). For calibration, fluorescent beads (Invitrogen, Carlsbad, CA, USA) were used, and the volume coresponding to a 1.0 μm thick stack was calculated pursuant to the voxel technique. A threshold was applied to distinguish adherent platelets from the background. Using these procedures, a uniform profile of thrombus formation and volume was observed (n=7). With citrate anticoagulated blood at an initial shear rate of 500 sec−1, thrombus growth begun after a lag phase of 220 sec, and, after 420 sec, thrombus volume reached a maximum (mean ± SD, 5x104 ± 4.9x103 μm3). Thrombus progression occurred in a two-step way with an apical growth (height extension) at the interval of 220 and 300 sec, and a further growth in the plane section at the interval of 300 and 420 sec after perfusion. Prolonged perfusion resulted in markedly abnormal flow pattern due to thrombus growth and increased shear rates. Again at an initial shear rate of 500 sec−1, platelet aggregate formation and thrombus progression were completely suppressed in the presence of anti-αIIbβ3 antibody (abciximab, 4 μg/ml). Interestingly, the polymorphism (HPA-1, PlA) of the β subunit of αIIbβ3 had a dramatic effect on thrombus growth. Thus, when comparing blood from homozygous carriers of HPA-1b (n=8) and HPA-1a (n=8), thrombus formation and progression occurred more rapidly with HPA-1b than with HPA-1a platelets, resulting in significantly larger thrombi from HPA-1b than from HPA-1a individuals (p=0.001). In conclusion, the voxel-based determination of thrombus formation and progression in vitro provides an appropriate technique to assess volumina of thrombi. Moreover, this technique can detect phenotypic differences related to an αIIbβ3 polymorphism which is postulated to modulate platelet thrombogenicity.

Issues in Nanoimprint Processes: the Imprint Pressure

A technical thermoplastic polystyrene with broad molecular weight distribution was characterised with respect to its thermo mechanical behaviour. In comparison to two other polystyrenes with narrow molecular weight distribution its temperature behaviour was investigated and could be generalised making use of well-known basic common principles of polymer rheology. The role of the temperature and the molecular weight choice with respect to an imprint process was contrasted to the role of the imprint pressure, which is a free parameter without impact on polymer characteristics. Pressure determines the initial shear rate in the process. Correspondingly simulations of the course of an imprint were performed, where shear thinning was assumed and the viscosity changed throughout the process according to the measured polymer behaviour. Two different filling situations were investigated, bottom up filling of the stamp cavities and lateral filling of the stamp cavities. In both cases the simulations show a quick decrease of the polymer height within the first seconds of the imprint. Shear rate effects suggest being effective to end up with very short processing times during thermal imprint under appropriate pressure with medium molecular weight thermoplastics. This is an interesting approach towards high throughput nanoimprint processes.

Modeling flocculation of biological cells

Biotechnological manufacturing processes often include a bioreactor harvesting step which involves separation of cells, cell debris and other particulate matter from the suspending medium which frequently contains the product of interest. Tangential flow microfiltration is used to separate the particulate matter from the suspending medium. The efficiency of this microfiltration step is often improved by increasing the particle size through flocculation prior to microfiltration. Here flocculation of yeast suspensions using a cationic polyelectrolyte has been investigated. A self-similar steady state floc size distribution is obtained experimentally. The experimental results may be modeled using a population balance approach. The dimensionless floc size distribution is found to be independent of the particulate volume fraction, initial particle size and shear rate during flocculation for the ranges of these variables considered. However, the actual floc size distribution does depend upon these parameters. In addition, the approach to the self-similar steady state floc size distribution depends upon the particulate volume fraction. At higher particulate volume fractions, the volume average floc size is found to increase during flocculation, pass through a maximum and then decrease to the final steady state value. However, at lower particle volume fractions, a maximum in the volume average floc size is not observed. Flocculation of cells leads to an increase in the volume average particle diameter. However, it also leads to a broadening of the particle size distribution. Consequently, when determining the improvement in permeate flux for tangential flow microfiltration, it is essential to include the effects of an increased average particle diameter and a broadened particle size distribution.

Application of in situ adaptive tabulation to CFD simulation of nano-particle formation by reactive precipitation

Reactive precipitation involves four fundamental processes: mixing-limited reaction, nucleation, growth, and aggregation. A novel algorithm, in situ adaptive tabulation (ISAT), has been implemented in a code for micromixing simulations, which is often applied together with computational fluid dynamics (CFD), using full probability density function (PDF) methods to incorporate these fundamental processes in the formation of nano-particles by reactive precipitation in a plug-flow reactor. The quadrature method of moments is applied to solve population balance equations for turbulent aggregation of the growing particles. The various performance issues (error control, accuracy, number of records, speed-up) for ISAT are discussed. Based on a large number of simulations, an error tolerance of 10 −4–10 −5 is found to be satisfactory for carrying out time-evolving full PDF simulations of nano-particle formation by reactive precipitation. Our results show that CFD simulation of reactive precipitation requires a much smaller computational effort when the ISAT algorithm is implemented than when direct integration is used. Finally, the effects of initial species concentrations, micromixing time, and turbulent shear rate on the reactive precipitation of barium sulfate are studied.

Particle size distributions and viscosity of suspensions undergoing shear-induced coagulation and fragmentation

The dynamic behavior of concentrated suspensions (up to a solids volume fraction of 20%) of non-spherical particles is investigated theoretically by coupling a rheological law to a population balance model accounting for coagulation and fragmentation of the detailed particle size distribution. In these suspensions, the immobilization of matrix liquid renders the viscosity dependent on the particle aggregation state. The effect of initial solids volume concentration and shear rate on the transient behavior of particle size distribution and suspension viscosity is examined. Power law correlations for the equilibrium flow curves of aggregating suspensions are deduced and compared to experimental data. Steady-state or equilibrium particle size distributions are found to be self-preserving with respect to solids volume fraction and shear rate.

Response of semi-solid Sn-15 pct Pb to rapid shear-rate changes

Semisolid metal alloys, used in thixoforming, are thixotropic. The slurry viscosity is shear-rate- and time dependent provided the microstructure in the semisolid state is nondendritic and consists of solid spheroids surrounded by liquid. Thixoforming takes less than 1 second, during which time the structure of the material breaks down. This breakdown can be studied by viscometry, using rapid data-collection rates, by imposing rapid increases in shear rate on the slurry. An initial rapid (<1 second) structural breakdown during a shear-rate jump is followed by a more gradual decrease in viscosity, lasting several minutes. The slurry breaks down more rapidly with a higher final shear rate, but the first breakdown time is independent of the initial shear rate. The reverse is found with the shear-rate drops: recovery times increase with increasing final shear rate. Again, this time is independent of the starting shear rate. The shear stress and viscosity during initial breakdown and initial recovery can be described by single exponential equations. Build-up processes were examined by performing jumps after allowing the slurry to rest at a zero shear rate for different times. The increase in peak stress with rest time reflects the evolving degree of particle agglomeration. Microstructural examination confirms this phenomenon.

Transient response of concentrated suspensions after shear reversal

We have examined the transient stress response under shear flow of concentrated suspensions of non-Brownian spheres. We focused on the experiment where the shearing is momentarily stopped and restarted in the opposite direction. We found that the normalized stress recovery curves for different values of the initial and subsequent shear rates could be collapsed quite well if plotted against the strain. This behavior agrees with the basic concept that the transient stress behavior is a function only of the imposed strain, as predicted by some recent constitutive models of concentrated suspensions. We also found that the transient behavior of the normal stress difference showed similar data collapse. Further, there appeared to be little qualitative difference in the behavior of particulate systems with a high degree of size monodispersity and those more polydisperse.

A dynamic study of onion phases under shear flow: size changes

It has been shown that lyotropic lamellar phases under shear flow form structures corresponding to a close packed assembly of monodisperse multilamellar vesicles (onions). The size, which is fixed by the shear rate, can vary from a few microns to a tenth of a micron. In this study, we investigate for the first time the transient behaviour of size changes of onions under shear flow by means of small angle light scattering, direct microscopic observations, and conductivity measurements. We evidence two regimes: continuous and discontinuous. The nature of which (continuous or discontinuous) depends on the initial and final shear rate, and can be described by a dynamic phase diagram.

Decay of Flow Birefringence in Dispersions of Charged Colloidal Rods: Effect of Double-Layer Interactions

The rotational diffusion of charged colloidal boehmite needles in aqueous dispersions was assessed from the decay rate of optical birefringence after cessation of a shear flow. The strong dependence of the characteristic relaxation time τ r on the ionic strength and the boehmite rod concentration can be described by a rescaling of the particle concentrations in terms of an effective rotational volume which takes the electric double layers into account. This dynamic rescaling is obeyed over a wide range of initial shear rates. Rotational relaxation times diverge when the effective particle concentration approaches the threshold density for the formation of a space-filling gel.

Computer Simulation of Steady Shear Flow of Liquid Crystals with the Gay-Berne Potential

Computer simulations of steady shear flow of nematic phases are performed using a non-equilibrium molecular dynamics. The SLLOD-type algorithm is applied to the shear flows of Gay-Berne fluids which are nematic in the equilibrium states. Two Gay-Berne potentials with μ = 1, v = 2 and μ = 2, v = 1 are used and both molecular aspect ratios are set equal to 3. In the initial stage of shearing various patterns of the transient behavior are found in the order parameter and orientation angle, according to the initial conditions and shear rate. In the steady state the director is inclined to the flow at a constant angle regardless of the shear rate and the system becomes more highly oriented state. The fluids exhibit shear-thinning in viscosity and non-zero first and second normal stress differences.

Acicular particle orientation in a shear-centrifuge filter

Acicular particles of potassium hexatitanate (K 2Ti 6O 13), 5 to 40 μm long with an aspect ratio of between 10 and 100, were dispersed in aqueous solutions of poly(vinyl alcohol) (PVA). The slurries were cast by using a shear-centrifuge filter (SCF) with a cylindrical stator, to obtain a green sheet with a preferred orientation of the particles. The green sheet obtained by SCF from a slurry with a solid volume fraction of 0.005 in a 1 wt.% PVA solution showed a degree of orientation of 73%. A two-step process with a low, initial shear rate followed by a higher one brought about better orientation. The importance of controlling the balance of the rate of shear and the rate of filtration was discussed.

Finite-volume computation of merging parallel channel flows by a second-moment turbulence closure model

The mixing process of turbulent shear layer developing in a plane two-dimensional channel has been numerically investigated. Under the condition of various initial shear rates as accomplished by varying the mass flow rate of the two oncoming parallel channel flows, the performance of a second-moment closure model and the k- ϵ model has been examined in terms of representing the overall streamwise flow development as well as the profiles of individual variables. It is shown that the difference between the two models is largely attributable to the evaluation of the production rate of turbulent kinetic energy, the second-moment closure model ensuring a slightly more realistic simulation of the flows out of the equilibrium state of turbulent kinetic energy.

Scaling laws for homogeneous turbulent shear flows in a rotating frame

The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier–Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E*(k*,0), initial dimensionless shear rate SK0/ε0, initial Reynolds number K20/νε0, and the ratio of the rotation rate to the shear rate Ω/S are identical. Consequently, if universal equilibrium states exist at high Reynolds numbers, they will only depend on the single parameter Ω/S. The commonly assumed dependence of such equilibrium states on Ω/S through the Richardson number Ri=−2(Ω/S)(1−2Ω/S) is proved to be inconsistent with the full Navier–Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier–Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on Ω/S is discussed in detail, along with the implications for turbulence modeling.

Flow optical detection and analysis of vortices and principle of a flow optical determination of viscosities

Monodisperse sols of β-FeOOH crystals are used for the detection and structural analysis of vortices formed prior to the transition of laminar into turbulent flow, the experimental tools used being both characteristic qualitative periodicities observed in flow light scattering and quantitative variations in its intensity as a function of shear rate. The proportionality between viscosity and initial shear rate, expressed in the classical equation of Taylor, is taken advantage of for the determination of viscosities in dilute dispersed systems using discontinuities in flow light scattering at the critical shear rate as a very sensitive argument which is under certain circumstances applicable also to dispersions of spherical particles.