Apparent Shear Stress Research Articles

Hydraulic calculation of steady uniform flows in trapezoidal compound open channels

Hydraulic calculation of steady uniform flows in trapezoidal compound open channels is studied. Based on the force balance of water in each sub-section, the average velocities of the main channel, side slope, and floodplain are derived. The lateral momentum exchanges between the sub-sections are expressed by using the apparent shear stress. To verify the model, seven groups of UK Flood Channel Facility (UK-FCF) measured data with a relative water depth between the floodplain and the main channel varying from 0.057 to 0.4 are used for comparison. The result shows that the calculated velocity is larger than the measured data when the relative water depth is small, while it is less than or close to the measured value in the case of a larger relative water depth. The influence of the apparent shear stress on the calculation of velocity on the floodplain is not obvious, while it is much greater on the main channel. The three-stage model is compared with Liu’s two-stage model, showing that the former can give a better prediction for a three-stage trapezoidal compound channel. Finally, the apparent shear stress is calculated and compared with the measured data. The result shows that the chosen values of the momentum transfer coefficients are appropriate.

Rheological Properties of a Particulate-Filled Polymeric Composite through Fused Deposition Process

This paper presents an investigation on rheological properties of a new ABS (acrylonitrile-butadiene-styrene)-Iron composite for application in Fused Deposition Modelling rapid prototyping process. Test samples of ABS-Iron composites have been made by controlled centrifugal mixing and thermal compounding through a single-screw extruder and compression moulding. Rheological characterization was conducted using a capillary rheometer by measuring pressure drop at the die while varying the extrusion speed. Apparent shear rate and shear stress as well as viscosity of the melts were calculated. Modulated differential-scanning calorimetry (MDSC) techniques were used in order to characterize viscoelastic properties of these newly developed composites materials. Non-Newtonian behaviour of the composite melt has shown to follow a cross model of shear thinning characteristics.

복단면 개수로흐름에서 홍수터 식생의 흐름저항을 반영한 1차원 모형

본 연구에서는 식생이 포설된 홍수터를 포함하는 복단면 개수로 흐름의 수위를 예측하기 위하여 유효 전단응력기법에 근거한 일차원 모형을 제시하였다. 제안된 모형은 주수로와 홍수터 접합부에서 발생하는 운동량 교환효과를 와점성계수 개념을 이용하여 반영할 수 있다. 주수로와 홍수터의 경계에서 발생하는 경계와점성계수는 3차원 레이놀즈 응력 모형을 이용하여 결정하였다. 경계와점성계수의 영향을 파악하기 위하여 민감도분석을 수행하였다. 경계와점성계수의 변화에 대하여 배수곡선의 변화는 크지 않았으나, 홍수터에서 부담하는 유량은 경계와점성계수에 비례하여 증가하였다. 마지막으로 식생된 홍수터의 식생밀도 및 침수비에 따른 경계와점성계수의 변화를 살펴보았다. 계산된 경계와점성계수는 식생밀도와 침수비에 비례하며, 대략<TEX>$(2-5){\times}\;10^{-4}$</TEX> 정도의 값을 갖는 것으로 나타났다. In this study, the 1D apparent shear stress model for vegetated compound open-channel flows was suggested. To consider the effect of momentum exchange between main channel and floodplain, the eddy viscosity concept was used in the present model. The interfacial eddy viscosity in the interface of main channel and floodplain was determined from the 3D Reynolds stress model. The evaluated interfacial eddy viscosity appears to be good agreement with those proposed previously. To investigate the effect of interfacial eddy viscosity, sensitive analysis was carried out. the computed backwater profiles are nearly identical with respect to the value of the interfacial eddy viscosity. However, the discharge conveyed by the floodplain changes is proportional to the interfacial eddy viscosity. Finally, the changes of the interfacial eddy viscosity due to the vegetation density and vegetation height were examined. The computed results of interfacial eddy viscosity are in proportion to the vegetation density and vegetation height, and the interfacial eddy viscosity has a range of <TEX>$(2-5)\;{\times}\;10^{-4}$</TEX>.

Apparent friction coefficient in straight compound channels

In compound open channel flow, the strong interaction between the main channel and the shallow floodplains affects considerably the discharge capacity. Since this phenomenon was identified, many authors have estimated experimentally the flow interaction in terms of an apparent shear stress acting at the vertical interface between the main channel and the floodplains. Empirical formulae have been developed to quantify this apparent shear stress, yet without general applicability. Herein, a dimensionally sound expression, depending on the square of the velocity gradient between the main channel and the floodplains, and on the so called “apparent friction coefficient”, is proposed. Its variation with the geometrical and roughness ratios is analysed herein. A generalized formulation to predict the apparent shear stress is presented and validated for a wide range of laboratory data. These include small-scale flumes and the large-scale flood channel facility, with both smooth and rough floodplains.

Analysis of retinal circulation using an image-based network model of retinal vasculature

This paper presents the results of a circulation analysis using an image based network model of a murine retinal vasculature, which closely represents the 3D vascular distribution of the retina. The uneven distribution of the red blood cells at vascular network bifurcations (i.e., plasma skimming effect), the microvascular diameter effect (i.e., Fahraeus–Lindqvist effect) and the role of endothelium surface layer (i.e., in vivo viscosity) were considered in determining the viscosity of the blood in the retinal vessel segments. The study yielded detailed distributions of the hemodynamic quantities in the arterial and venous trees shown in various anatomical based contour plots. Quantitative analysis was also carried out based on statistical distributions. The analysis shows that the distribution of the blood hematocrit (HD) in the retinal network is very non-uniform, with lower values at the pre-equator region (near the optic disc) and higher values in the equator region of the retina. This has significant influence on the distribution of apparent viscosity, pressure and wall shear stress (WSS) in the vasculature. The viscosity is generally higher in smaller vessels (i.e., pre-capillary vessels) but exceptions occur in some vessels where the HD is small. WSS is greater in smaller vessels located near the optic disc than that in the mainstream retinal vessels. The results presented can be directly useful to ophthalmologists and researchers working with retinal vasculature.

APPARENT SHEAR STRESS IN A COMPOUND CHANNEL

ABSTRACT During the flow of in a compound channel section, there is always transfer of momentum between the deep main section and the adjoining shallow floodplains. This interaction mechanism has the effect of increasing floodplain shear and decreasing main channel shear. Experiments are carried out to measure the boundary shear around the wetted perimeter of a two-stage compound channel that helps to quantify the momentum transfer in terms of apparent shear stress along the assumed interfaces originating from the junction between main channel and flood plain. Analysis of the apparent shear is useful in deciding the choice of appropriate interface plains for developing stage-discharge relationship of a compound channel. In the present work, a modified expression to predict the boundary shear distribution in compound channels that is good for all width ratios is derived and is found to provide significant improved results, when validated using the well published data.

Study of Rheology of Flame-Retardant Copolyester Nanocomposites

A new type of nanocomposite was composited by the way of copolymerization of flame-retardant monomer DDP, PET monomer, terephthalic acid and ethylene dlycol. This article mainly researched the rheology behavior of different slices such as its apparent shear rate and shear stress and the relationship of the both in the use of capillary rheometer, and at the same time, the data of viscous flow activation energy of different sample were obtained. The result shows that under the same temperature, it is the PET/10%DDP/3% BaSO4 that is the best on the mobile performance that needs less shear stress and the temperature control in need is less strict than PFRP.

Correlation between polyethylene topology and melt flow instabilities by determining in-situ pressure fluctuations and applying advanced data analysis

Using three high sensitive pressure transducers located inside a slit-die of a capillary rheometer and applying a set of advanced mathematical tools to process the acquired time dependent pressure signals, we are able to detect in-situ pressure fluctuations associated with sharkskin instabilities. Other distortions, as spurt and gross melt fracture, can also be in-situ detected. This originates from a factor of 10 3 and 10 2 improvement in terms of time and pressure resolution achieved using the new set-up and data analysis that it will be described in detail in this article. Our approach quantifies the effect of polymer topology and shear rate on the characteristic frequency and amplitude of these pressure fluctuations inside the die. Depending on the polymer structure and the shear rate, different instabilities with large deviation in their main properties at melt-state, can be determined. Based on our results, a polymer-independent power law relationship between the characteristic frequency of the instability and the apparent shear stress has been found. Combining this new technique with the advanced mathematical analysis used, clear evidences concerning the origin and location of these instabilities, could be established. According to our analysis, the spurt instability starts in the entrance of the die and it propagates downstream while increasing its velocity along the die. This was confirmed by non-zero-time-lags in the cross-correlation function between the transducers located inside the slit-die. In case of sharkskin instability, pressure fluctuations inside the die indicate that its origin could also be already inside the die instead of being exclusively located at the die-exit region, as stated in earlier investigations.

Effect of tall vegetation on sediment transport by channel flows

Results of an experimental study on sediment transport by channel flows with tall rigid stems are presented. The experiments were conducted for various stem areal densities, channel slopes and sediment sizes with uniformly distributed unsubmerged cylindrical rigid stems forming a regular square staggering pattern in plan. The rates of sediment transport in the presence of simulated vegetated surfaces were observed to be significantly smaller than those without the vegetation. A method is proposed to determine the effective (grain) shear stress in presence of vegetation under the condition that the apparent shear stress is available from easily measurable flow parameters. The present data along with literature data are used for quantification of the reduction in the rate of sediment transport by the rigid tall stems. The grain shear stress rather than the apparent shear stress is observed to better describe the variations in the rate of sediment transport by vegetated flows.

Application of the Shiono and Knight Method in compound channels with non-prismatic floodplains

The Shiono and Knight Method (SKM) is known as a capable tool to model flow in prismatic compound channels. This research explores whether SKM can be used to predict depth-averaged velocity and boundary shear stress in compound channels with non-prismatic floodplains. For this reason SKM was modified and used in combination with an extensive experimental data set of depth-averaged velocity and boundary shear stress measurement to investigate the issue over three various floodplain converging angles and relative depths. The modeling results indicate a good agreement between the experimental data and the modified SKM. Also, based on the momentum balance and using the experimental data on compound channel with non-prismatic floodplains lateral variations of the depth-averaged apparent shear stress, the Reynolds shear stress, and the secondary flow were investigated. The results reveal that the Reynolds shear stress is significant at the interface between the main channel and floodplains and secondary flow has linear variation.

Continuous extrusion production of microcellular rigid PVC

AbstractThis study examined the effect of Poly[vinyl chloride] (PVC) formulation on the cell morphology and density of rigid PVC foamed with supercritical CO2 in a continuous extrusion process. Cell morphology and the density of foamed samples were controlled by blending two acrylic‐based processing aids (all‐acrylic foam modifier K‐400 and acrylic‐based impact modifier KM‐334), using a mixture design. The effect of blend ratios on the fusion and die swell behaviors of PVC was investigated by means of a torque rheometer and on a single‐screw extrusion capillary rheometer, respectively. Fusion was promoted as the relative amount of the all‐acrylic foam modifier increased in the blends. Similarly, the elastic constant of PVC, derived from the linear relationship between the die swell and apparent shear stress, increased upon increasing the relative amount of the all‐acrylic foam modifier in the blends, thus suggesting an increase in the melt elasticity of PVC. Microcellular rigid PVC foams with densities of approximately 0.15 g/cm3 and a tenfold volume expansion were produced. An optimum ratio of impact modifier to all‐acrylic foam modifier of 1:3 was found to maximize the foam expansion. Using impact modifier alone or all‐acrylic foam modifier alone yielded expansions considerably lower than that achieved with the 1:3 blend. The experimental results indicated that fusion is not the only criterion to control the cell morphology and density achieved in microcellular rigid PVC foams. The melt must have a viscosity low enough to allow bubble formation and growth, as well as elasticity high enough to prevent cell coalescence. J. VINYL ADDIT. TECHNOL., 2009. © 2009 Society of Plastics Engineers

Partial replacement of silica with microcrystalline cellulose in rubber composites

Microcrystalline cellulose (MCC) was investigated to partially replace silica in rubber composites. The partial replacement of silica with MCC significantly reduced the energy required for dispersion of fillers in rubber matrix and lowered the internal temperature during the compounding. Moreover, the partial replacement of silica with MCC reduced Mooney viscosity, apparent shear stress, and apparent shear viscosity of the rubber composites, which facilitated the manufacturing process of the rubber composites. The replacement of up to 18% silica with MCC did not negatively affect the mechanical properties of the unaged and aged rubber composites. The partial replacement of silica with MCC also improved the heat resistance, did not significantly change the tan δ of rubber composites containing up to 11.8% of MCC at low temperature and decreased the tan δ of all rubber composites at high temperature. However, addition of MCC slightly decreased tear strength and hot tear strength of the rubber composites.

Flow resistance of one-line emergent vegetation along the floodplain edge of a compound open channel

Experiments have been conducted in straight compound channels with and without one-line emergent vegetation along the floodplain edge, in which stream-wise velocities and boundary shear stresses have been measured. The experimental results show that the velocity distribution in the vegetation case is considerably different from that in the no vegetation case and the boundary shear stress is also significantly reduced by the additional flow resistance caused by the vegetation at a similar relative water depth. The apparent shear stress distribution which has been calculated with the boundary shear stress and weight component in the vegetation case is totally different from that in the no-vegetation case. New formulae for friction factors for the with and without vegetation cases are developed using vegetation density and flow parameters. The drag force caused by the vegetation is obtained for two different vegetation density cases and the magnitude of its effect on total flow resistance is then investigated. The force balance method is used to predict discharge and this is compared with the discharge predicted by the new formula. A further analysis of the selection of vegetation spacing is carried out, determining its effect on stage-discharge.

Transverse velocity distributions in channels with emergent bank vegetation

AbstractDefining hydraulic habitat conditions in rivers requires prediction of local flow velocities, which are strongly influenced by the presence of emergent vegetation along the banks. Previously proposed methods for describing the transverse variation of depth‐averaged velocity away from the vegetation edge are shown by comparison with independent laboratory data to be inadequate. One of the methods is modified on the basis of new data to provide realistic descriptions over a wide range of conditions. The new method enables prediction of the maximum velocity in both wide and relatively narrow channels, the apparent shear stress at the vegetation interface, and the variation of velocity from the vegetation boundary to the point where the maximum velocity occurs. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Directional adhesion of gecko-inspired angled microfiber arrays

Arrays of angled microfibers with a gecko-inspired structure were fabricated from a stiff thermoplastic polymer (polypropylene) with elastic properties similar to those of β-keratin of natural setae. Friction experiments demonstrated that this fibrillar polymer surface exhibits directional adhesion. Sliding of clean glass surfaces against and along the microfiber direction without applying an external normal force produced an apparent shear stress of 0.1 and 4.5 N/cm2, respectively. This directional adhesion is interpreted in the context of a nonlinear elastic bending model of an angled beam. Shearing and normal contact experiments yielded further evidence of the anisotropic adhesion of the fibrillar polymer and revealed the occurrence of a pull-off (adhesive) force at the instant of surface detachment, unlike vertically aligned microfiber arrays of the same material that exhibited a zero pull-off force. The results of this study provide impetus for the design of gecko-inspired adhesives with angled structures that demonstrate directional adhesion against different material surfaces.

Effect of grafted maleic anhydride content and recyclability of dynamically cured maleated natural rubber/polypropylene blends

AbstractMaleated natural rubbers (MNRs) were prepared using various levels of maleic anhydride (MA) at 4, 6, 8, 10, and 12 phr. Dynamically cured 60/40 MNR/PP blends with phenolic‐modified polypropylene (Ph‐PP) compatibilizer at a loading level of 5 wt % of PP were prepared by melt mixing process using sulfur vulcanization system. The influence of the level of MA on properties of the thermoplastic vulcanizates (TPVs) was studied. It was found that the mixing torque, apparent shear stress, shear viscosity, tensile strength, and hardness properties increased with increasing levels of the MA or grafted succinic anhydride groups in the MNR molecules. This is attributed to an increase in chemical interaction and reaction between methylol groups in the Ph‐PP molecules and polar functional groups in the MNR molecules upon increasing levels of the grafted succinic anhydride groups. As a consequence, compatibilizing block copolymers of MNR and PP blocks were formed. The block copolymers were capable of compatibilizing with MNR and PP blend components via the respective blocks. Recyclability of the MNR/PP TPVs was also studied. It was found that, after processing through a number of cycles by injection molding and extrusion processing, the TPV exhibited marginal decreases in mechanical properties. This corresponded to slightly increasing size of the dispersed vulcanized rubber domains. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Reliable plate–plate MRF magnetorheometry based on validated radial magnetic flux density profile simulations

The apparent shear stress from plate–plate magnetorheometry, using the commercial magnetocell MRD180/1T (Physica/Anton Paar) in standard configuration, is distinctly overestimated. The effect is due to a flux density maximum near the sample rim and radial migration of iron particles towards the rim. Radial magnetic flux density profiles were investigated by finite element simulations using the Maxwell®2D code and by direct Hall probe measurements. The reliability of the finite element method results, both for the empty magnetocell and with magnetorheological fluid (MRF) in the measuring gap, allows conclusions on the true flux density within the MRF, which cannot be accessed by Hall probe measurements. If the MRF sits on top of the bottom yoke (standard configuration), the flux density maximum reaches twice the plateau value (0.74 T for 3 A coil current and 0.3 mm gap height of the investigated MRF). This yields a higher effective flux density and causes radial iron particle migration, resulting in an additional magnetic flux increase near the rim due to augmented MRF magnetisation. As a result, the rotor torque at constant rotary speed increases with time. Reliable results are achieved by a modification of the magnetocell, such that the MRF sits on a non-magnetic Hall disc of 1.5 mm thickness, allowing an online flux density measurement by a FW Bell Hall probe. In this configuration, the radial flux density profile near the rim remains sufficiently flat and no iron particle migration is detected.

Numerical modeling of turbulent compound channel flow using the lattice Boltzmann method

AbstractThe flow of water in a straight compound channel with prismatic cross section is investigated with a relatively new tool, the lattice Boltzmann method. The large eddy simulation model is added in the lattice Boltzmann model for nonlinear shallow water equations (LABSWETM) so that the turbulence, caused by lateral exchange of momentum in the shear layer between the main channel and floodplain, can be taken into account and modeled efficiently. To validate the numerical model, a symmetrical compound channel with trapezoidal main channel and flat floodplain is tested. Similar to most natural watercourses, the floodplain has higher roughness values than the main channel. Different relative depths, Dr (the ratio of the depth of flow on the floodplain to that in the main channel), are considered. The Reynolds number is set at 30 000 in the main channel. The lateral distributions of the longitudinal velocity, the boundary shear stress, the Reynolds stress and the apparent shear stress across the channel are obtained after the large eddy simulation is performed. The results of numerical simulations are compared with the available experiment data, which show that the LABSWETM is capable of modeling the features of flow turbulence in compound channels and is sufficiently accurate for practical applications in engineering. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Rheological behavior of a microcellular, oil‐extended ethylene–propylene–diene rubber compound: Effects of the blowing agent curing agent, and conductive carbon black filler

AbstractThe rheological behavior of microcellular, oil‐extended ethylene–propylene–diene rubber (EPDM) compounds was studied in extrusions containing a blowing agent. The cell morphology development and rheological properties were studied for unfilled and conductive carbon black (Vulcan XC72, Cabot Corp., Ltd., Alpharetta, GA) filled compounds with variations of the blowing agent, extrusion temperature, and shear rate. The apparent shear stress, apparent viscosity, die swell (%), and total extrusion pressure of the Vulcan XC72 filled, oil‐extended EPDM compounds were determined with a Monsanto processability tester (St. Louis, MO). The effects of the curing agent and blowing agent on the rheological properties of the compounds were also studied. A significant reduction in the stress and viscosity with the blowing agent was observed in the compound in the presence of the curing agent in comparison with those without the curing agent. The viscosity reduction factor was found to be dependent on the blowing agent loading, shear rate, and temperature. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Rheological Behavior, Tensile Properties, Morphology, and Thermal Stability of Recycled Poly(vinyl chloride)/Acrylonitrile Butadiene Rubber (PVCr/NBR) Blends: The Effect of Maleic Acid

Blends of recycled poly(vinyl chloride) (PVCr) and acrylonitrile butadiene rubber (NBR) modified by addition of maleic acid (MAc) are prepared by using a Haake Rheomix. The effect of MAc on melt Rheological behavior, tensile properties, morphology, and thermal stability of PVCr/NBR blends are investigated. The recorded data obtained from the Haake Rheomix are converted into values of apparent shear rate, apparent shear stress, and apparent viscosity. The apparent viscosity of the blends is found to decrease with increase in the shear rate and follow the pseudoplasticity behavior. At a similar shear rate, the presence of MAc in PVCr/NBR blends exhibits higher apparent viscosity than PVCr/NBR blends without MAc. Activation energy, Ea decreases with increasing shear rate, obviously due to the strong non-Newtonian behavior of PVCr/NBR blends. The addition of MAc in PVCr/NBR blends exhibits higher stress at peak and stress at 100% elongation but lower elongation at break and thermal stability than PVCr/NBR blends without the addition of MAc. Scanning electron microscopic (SEM) examination of extracted surfaces of PVCr/NBR+MAc blends indicates the increase of the interfacial interaction between PVCr and NBR phases with the presence of Mac.