Dynamic Shear Stress Research Articles

A microfluidic generator of dynamic shear stress and biochemical signals based on autonomously oscillatory flow.

Biological cells in vivo typically reside in a dynamic flowing microenvironment with extensive biomechanical and biochemical cues varying in time and space. These dynamic biomechanical and biochemical signals together act to regulate cellular behaviors and functions. Microfluidic technology is an important experimental platform for mimicking extracellular flowing microenvironment in vitro. However, most existing microfluidic chips for generating dynamic shear stress and biochemical signals require expensive, large peripheral pumps and external control systems, unsuitable for being placed inside cell incubators to conduct cell biology experiments. This study has developed a microfluidic generator of dynamic shear stress and biochemical signals based on autonomously oscillatory flow. Further, based on the lumped-parameter and distributed-parameter models of multiscale fluid dynamics, the oscillatory flow field and the concentration field of biochemical factors has been simulated at the cell culture region within the designed microfluidic chip. Using the constructed experimental system, the feasibility of the designed microfluidic chip has been validated by simulating biochemical factors with red dye. The simulation results demonstrate that dynamic shear stress and biochemical signals with adjustable period and amplitude can be generated at the cell culture chamber within the microfluidic chip. The amplitudes of dynamic shear stress and biochemical signals is proportional to the pressure difference and inversely proportional to the flow resistance, while their periods are correlated positively with the flow capacity and the flow resistance. The experimental results reveal the feasibility of the designed microfluidic chip. Conclusively, the proposed microfluidic generator based on autonomously oscillatory flow can generate dynamic shear stress and biochemical signals without peripheral pumps and external control systems. In addition to reducing the experimental cost, due to the tiny volume, it is beneficial to be integrated into cell incubators for cell biology experiments. Thus, the proposed microfluidic chip provides a novel experimental platform for cell biology investigations.

Wetting mechanism and interfacial bonding performance of bamboo fiber reinforced epoxy resin composites

A polyacrylate-based wetting agent, BYK-358N, was used to improve the interfacial bonding between the bamboo fibers and epoxy matrix. Fourier transform infrared spectrometer and differential scanning calorimetry were used to study the curing process of epoxy resin. The wettability of the treated bamboo fiber, which by the untreated and wetting agent treated epoxy, was studied using the surface tension of epoxy and bamboo fiber. The analysis of dynamic contact angle and interfacial shear stress confirmed that the composite interface was improved. Finally, Vacuum-assisted resin transfer molding was used to prepare bamboo fiber reinforced epoxy resin (BF/EP) composites, and the tensile properties were measured. The results showed that the addition of the wetting agent could effectively improve the interface compatibility of BF/EP composites. The interfacial shear stress of BF/EP composites treated with 1% wetting agent was 24.36 MPa, tensile strength was 111.54 MPa, and Young's modulus was 3.90 GPa, which was 165.7%, 99.7%, and 66.7% higher than that of untreated BF/EP composites.

Microfluidic Obstacle Arrays Induce Large Reversible Shape Change in Red Blood Cells.

Red blood cell (RBC) shape change under static and dynamic shear stress has been a source of interest for at least 50 years. High-speed time-lapse microscopy was used to observe the rate of deformation and relaxation when RBCs are subjected to periodic shear stress and deformation forces as they pass through an obstacle. We show that red blood cells are reversibly deformed and take on characteristic shapes not previously seen in physiological buffers when the maximum shear stress was between 2.2 and 25 Pa (strain rate 2200 to 25,000 s−1). We quantify the rates of RBC deformation and recovery using Kaplan–Meier survival analysis. The time to deformation decreased from 320 to 23 milliseconds with increasing flow rates, but the distance traveled before deformation changed little. Shape recovery, a measure of degree of deformation, takes tens of milliseconds at the lowest flow rates and reached saturation at 2.4 s at a shear stress of 11.2 Pa indicating a maximum degree of deformation was reached. The rates and types of deformation have relevance in red blood cell disorders and in blood cell behavior in microfluidic devices.

Engineering collagen fiber templates with oriented nanoarchitecture and concerns on osteoblast behaviors

Nanostructure provides a closer structural support approximation to native bone architecture for cells and further regulates cell's behavior, resulting in the formation of functional tissues. In this work, three engineering collagen templates with oriented fiber architectures were fabricated via electrospinning (Es), plastic compression and tensile (PCT), and dynamic shear stress (SS) methods. Under the observation of POM, SEM, AFM and TEM, the PCT-template and SS-template are packed with well-oriented nanofibers with the native collagen architecture of 67 nm D-periodicity, and the mechanical properties conferred to the templates are better than that of the Es-template. When mentioning the cell's behavior, MC3T3-E1 adhered to grow along the alignment of collagen fiber orientation when cultured on the PCT-template and SS-template. The SS-template with nano- and micro-ordered architecture guided cells to stretch their plasma along with the orientation of collagen fiber, produce more aligned Type I collagen fibers and promote significantly higher osteogenic differentiation of MC3T3-E1 than the PCT-template and Es-template. Overall, it is strongly argued the feasibility of hierarchical collagen fiber architectures for bone tissue regeneration.

Correlations in rheological behavior between large amplitude oscillatory shear and steady shear flow of silica‐filled star‐shaped styrene‐butadiene rubber compounds: Experiment and simulation

AbstractThe large amplitude oscillatory shear (LAOS) and steady shear behavior of star‐shaped SSBR/silica 60 phr (21 vol%) compounds with various filler surface areas was measured and simulated. An SBR gum and SBR compounds containing four different silicas with surface areas of 55, 135, 160, and 195 m2/g were utilized. Rheological behavior indicated clear correlation with surface area. LAOS tests showed an increase in dynamic moduli, shear stress, and higher order harmonic contributions with surface area. Elastic and viscous Lissajous figures showed significant distortion at intermediate and higher strain amplitudes. Additionally, ratios of third and fifth order stress harmonics to the first stress harmonic (I3/1 and I5/1, respectively) showed a ''bump'' at intermediate strain amplitudes for the three highest surface area compounds. With regards to steady shear, all materials showed strong shear thinning behavior, and an increase in shear viscosity with surface area. The Cox‐Merz rule was shown to be valid for the SBR gum but not for the filled compounds. However, the complex viscosity as a function of shear rate amplitude at various frequencies at high strain amplitudes and the steady shear viscosity as a function of shear rate coincided. This correlation, referred to as the Philippoff approach, has important ramifications for the rubber industry, providing quick data for predicting processing behavior. The Simhambhatla‐Leonov model was successfully employed to simulate rheological behavior for the SBR gum and the lowest surface area silica compound, but the model yielded mixed results for the higher surface area silica compounds.

Regulation of gas-liquid Taylor flow by pulsating gas intake in micro-channel

Bubble formation mechanism and slug flow characteristics have been studied in a T-junction rectangular micro-channel under pulsating gas intake conditions. A high-speed camera is used to track the trajectory of gas-liquid interface by the Lagrangian method, while the numerical simulation is used to acquire the flow field distribution at different moments using the Euler method. The dynamic pressure, shear stress and pressure difference across the forming bubble at the T-junction increase with the pulsation frequency and liquid velocity. Under pulsating gas intake conditions, none of these three types of force can be neglected, indicating a transition regime between squeezing and dripping regime. The evolution of bubble length under pulsating conditions is similar to the general gas-liquid flow, but with a shorter value, while the liquid slug length is longer than the latter. The slug flow is transformed into wave flow when the pulsation energy inputted to the system reaches a critical value. The bubble velocity varies periodically over time with a main fluctuation frequency equal to that of pulsation. The present work proves that the technique of pulsating gas intake enables precise control the gas-liquid Taylor flow pattern, which would be useful for future application in gas-liquid reactions.

Experimental investigation on dynamic characteristics of sandy gravel in frozen region

In this study, a series of low-normal temperature triaxial tests and Computed Tomography scan (CT scan) tests are carried out to study the dynamic characteristics and micro-structural changes of sandy gravel in frozen region. The dynamic properties of sandy gravel at different temperatures and confining pressures are systematically discussed under the moisture content of 5.9% and frequency of 1 Hz through experimental tests combining with CT scan images. The variation of backbone curve, dynamic shear modulus and damping ratio under various mass ratios is explored. The average of CT numbers and standard deviation obtained from CT scan images of sandy gravel are evaluated. Meanwhile, internal structure and damage evolution process for sandy gravel are analyzed. The results derived from this study reveal that (i) the shear strength of specimen decreases with the temperature increase; (ii) within a certain dynamic shear strain interval, the dynamic shear modulus increases correspondingly with the growth of confining pressure; (iii) with the increase of mass ratio, the dynamic shear stress of specimen gradually decrease, and the dynamic shear modulus with high mass ratio is lower than that with low mass ratio.

Phase equilibria, physical and rheological properties of extracellular polymeric substances in the aqueous urea solutions at different temperatures and concentrations

Extracellular polymeric substances (EPS) were extracted from aerobic granule sludge (AGS) using 8 M aqueous urea solution. It seems that the knowledge of these multi-component systems properties and the ability to predict their phase behavior is necessary for the extraction units design as well as process optimization. In this regard, water activity using the Dynamic Vapor Sorption (DVS) method, viscosity and shear stress, pH, and conductivity were measured at 283.15–343.15 K and 0.0108 to 0.0375 wt fraction of EPS. The salting effects in ternary systems assessed and the results were interpreted in terms of solute-water and solute-solute interactions. It was found these systems were not semi-ideal and except at 283.15 K, had a positive deviation from ideal solution behavior and only at this temperature as the optimum extraction temperature, the salting-in effect was observed for each concentration of EPS. The ternary solutions behave like pseudo-plastic fluids while aqueous urea solution is a Newtonian fluid. Increasing the temperature causes a decrease and increase in pH and conductivity of ternary solutions, respectively and the presence of EPS increases those of 8 M urea solution significantly.

Effect of Non-metallic Inclusions on Subsurface Stress and Fatigue Life of High-speed Railway Bearings

The contact simulation model of high-speed railway train axle box bearing is simplified into a two-dimensional plane with an elastic semi-infinite body subjected to semi-elliptical cylindrical compressive stress in one direction. The ANSYS software was used to solve the effects of single inclusion size, the depth of the contact surface and the elastic modulus on dynamic shear stress and Von Mises stress of high-iron bearing subsurface, and compared with the calculation results of bearing material uniformity assumption. Using the modified Basquin equation, the relevant assumptions are made. The maximum Von Mises stress is used as the key stress for fatigue life calculation. The bearing fatigue life calculation method is established to study the influence of the inclusion size, the depth of the contact surface and the elastic modulus on the bearing fatigue life.

Experimental Study on the Dynamic Modulus and Damping Ratio of Compacted Loess under Circular Dynamic Stress Paths

Dynamic loads such as earthquakes and traffic will simultaneously generate vertical dynamic stress and horizontal shear stress in the foundation soil. When the vertical dynamic stress amplitude is twice the horizontal shear dynamic stress amplitude, and the phase difference between them is 90°, a circular dynamic stress path is formed in the τzθd ~ (σzd − σθd)/2 stress coordinate system. To simulate the stress state of soil in the area of the circular dynamic stress path caused by bidirectional dynamic stress coupling, a series of tests of compacted loess under the action of a circular dynamic stress path were carried out using a hollow cylindrical torsion shear apparatus. The effects of the mean principal stress, dry density, and deviatoric stress ratio (the ratio of deviator stress to average principal stress) on the dynamic modulus and damping ratio of compacted loess were mainly studied. The test results show that, under the action of the circular dynamic stress path, the larger the mean principal stress is, the larger the dynamic compression modulus and dynamic shear modulus are. The dynamic compression modulus increases obviously with increasing dry density, but the dynamic shear modulus increases only slightly. When the deviator stress ratio increases from 0 to 0.4, the dynamic compression modulus and dynamic shear modulus increase to a certain extent. In addition, the greater the dry density and deviatoric stress ratio are, the greater the initial dynamic compression modulus and initial dynamic shear modulus of the compacted loess. The dynamic compression damping ratio of compacted loess increases with increasing mean principal stress, but the dynamic shear damping ratio decreases with increasing mean principal stress. Dry density basically has no effect on the dynamic compression damping ratio and dynamic shear damping ratio of compacted loess. When the dynamic strain exceeds 1%, the greater the deviatoric stress ratio is, the smaller the dynamic compression damping ratio and the dynamic shear damping ratio are. The research results can provide reference for the study of dynamic modulus and damping ratio of loess under special stress paths.

Fabrication of cyclic olefin polymer and polydimethylsiloxane co-bonded microfluidic device and its appliactions in terahertz biological effects on intestinal cells

<sec>The current research on the terahertz biological effects at a cellular level is limited by the conventional petri dishes used for cell culture, which cannot be directly used for confocal laser microscopy. In this research, the cycloolefin polymer (COP), a material that possesses low terahertz absorption rate but excellent optical property for microscopy, is bonded to polydimethylsiloxane (PDMS), thereby developing a novel COP-PDMS microfluidic device by using the techniques of soft etching, photolithography, plasma cleaning, high-temperature and high-pressure incubation. The bonding strength of resulting device is tested by using a push-tension meter. The results indicate that the developed device shows a bonding strength as strong as the device fabricated by quartz and PDMS, which is thought as the tightest binding in the multiple types of microfluidic device. In addition, by perfusing the device chamber at a high flow rate (200 μL/s) and long-term time-course (2 weeks), which simulates the dynamic shearing stress occurring in <i>in-vivo</i> organs and tissues, this COP-PDMS microfluidic device can still maintain the original shape and sealing property, indicating that this device qualifies the requirements of the following dynamic cell culture.</sec><sec>The biological effects of terahertz on the cells are explored by using this COP-PDMS microfluidic device mentioned above. In this device, we develop the dynamic culture of intestinal epithelial cells Caco-2 with a perfusion rate of 0.05 μL/s, which meets the findings of the <i>in-vivo</i> gastrointestinal lumen shearing stress. The Caco-2 cells are then irradiated with 0.1 THz wave with the power of 15 mW/cm<sup>2</sup> for 3 days, and the irradiation duration is 10 min per day. The biological effects of terahertz irradiation on the intercellular tight junction protein ZO-1, the Paxillin relating to the cell adhesion and migration, and the cytoskeletal microfilament protein F-actin of Caco-2 cells are detected in the device directly using the technique of immunofluorescence staining.</sec><sec>The results show that the morphology of cell adhesion as well as the level and distribution of ZO-1 and Paxillin are changed. In brief, the protein expression of ZO-1 and Paxillin are induced more by the terahertz irradiation, while the F-actin is not influenced by the irradiation. As can be seen from the F-actin results, the cells without terahertz irradiation show a spread and outward shape with regular smooth cell edge while a contraction and burr shape of cell edge are shown after irradiation, suggesting that the cell adhesion is weakened after irradiation. Even though the expression level of F-actin is consistent, the changed morphology indicates that terahertz may regulate the interaction and aggregation among actin proteins in cells. Interestingly, the ZO-1 presents diffuse distribution in the cells and its location on the cell membrane is not obvious, that is, a large amount of ZO-1 expresses not only on the cell membrane but also in the intracellular matrix after the irradiation. The expression of Paxillin is enhanced after terahertz irradiation, and some cells show local aggregation and distribution of Paxillin. These indicate that the terahertz irradiation might affect the biomolecular mechanism of synthesis and distribution of protein. The COP-PDMS co-bonded microfluidic device developed in this study provides a convenient and effective platform for exploring the biological effects of terahertz irradiation on cells, and is expected to be further used for real-time research on the effects of terahertz on cells and molecules in the future.</sec>

INSTABILITY OF A GRAVITY-DRIVEN LIQUID FILM CONFINED IN AN INCLINED RECTANGULAR DUCT

This study deals with the confinement effects due to top and side walls on the stability of a falling liquid film flowing down an incline. To this aim, we consider a liquid film flowing between two infinite plates and in rectangular ducts in the presence of an adjacent gas phase, focusing on the case of zero net gas flow rate. A rigorous linear stability analysis is conducted for three gas-liquid systems of particular interest in applications. This enables us to demonstrate the effect of the gas-liquid density ratio and viscosity ratio in small channels/ducts and shallow downward inclinations. Although the analysis considers all wave numbers, the neutral stability boundary is found to be defined mainly by long-wave perturbations in the two-plate (TP) geometry, as well as in the rectangular ducts. The decrease of the channel height for the considered liquid-gas systems always stabilizes the liquid film. However, the Kapitza criterion for the onset of Kapitza waves on the surface of a falling liquid film can either overpredict or underpredict the stability limits of the channel/duct flows, depending on the channel height, its aspect ratio, and the viscosity and density ratios of the phases. The falling liquid film, bounded by the side walls, becomes unstable at larger flow rates with the decrease of the duct aspect ratio. The presence of recirculating gas in the channel/duct is found to affect the stability through the dynamic shear stress components at the gas-liquid interface. Therefore, its presence must be taken into account.

Numerical and experimental study of influence function in magnetorheological finishing of oxygen-free high conductivity (OFHC) copper

Study of influence function of finishing process is very important for setting the process parameters. In this article, influence function of magnetorheological finishing (MRF) process is investigated numerically and experimentally by studying the flow behaviour of magnetorheological (MR) fluid. A 3D computational fluid dynamics simulation is performed considering MR fluid as a Herschel–Bulkley fluid. Dynamic pressure and wall shear stress on the workpiece surface are determined for different working gaps and rotational speeds. Variable depth of indentation by abrasive particle on oxygen-free high conductivity copper is calculated numerically and correlated with the experiments. Depth and area of influence function increase with spindle speed and reducing working gap. Dynamic pressure decides the indentation depth which is related to normal force, whereas wall shear stress removes the material up to the indentation depth which is related to the tangential force. Influence function shows two separate regions at the edge of magnet due to variable magnetic flux density. Contact length of MR fluid with workpiece and squeezing of MR fluid play significant role in material removal. Experiments are carried out to study forces acting on the workpiece, indentation depth and validation of simulation results.

Feasibility of Linear Relationship between Failure and Non-failure Rheological Properties as Functions of Salt and pH

Effects of pH and salt concentration on rheological and thermal properties of Pacific whiting surimi were investigated. As pH increased from 6 to 7.5, failure shear stress and strain values increased from 15.4 to 31.32 kPa, whereas lightness values (L*) decreased from 86.22 to 78.86. Storage modulus (G'') followed a trend similar to failure shear stress. A linear relationship (r 2 =0.89) was found between G'' and failure stress values as a function of pH. Increasing salt concentration up to 1% increased failure shear stress to 27.14 kPa without salt to 34.30 kPa, and strain values from 1.73 to 1.91, whereas further increase had a negative effect. The relationship between dynamic rheological data and failure shear stress was not linear, indicating that salt concentration cannot be used as an index for estimating final gel quality. The transition temperatures obtained from temperature sweep measurements of Pacific whiting surimi at different salt concentrations showed similar peak temperatures as DSC thermograms, indicating lower stability due to increased salt concentration.

A micromechanical vibration damping model of fiber-reinforced ceramic–matrix composites considering interface debonding

A micromechanical vibration damping model of fiber-reinforced ceramic–matrix composites is developed considering interface debonding. The relationship between the stress-dependent composite damping and interface debonding is established. Effects of material properties and damage-related parameters on the vibration damping of fiber-reinforced CMCs are discussed. Experimental vibration damping with interface debonding of C/SiC composites is predicted. When the vibration frequency increases from f = 1–5 Hz, the vibration damping decreases due to the increasing dynamic interfacial shear stress and low frictional dissipated energy in the debonding region. The composite vibration damping decreases with increasing fiber volume, matrix crack spacing and interface shear stress, and increases with fiber radius and fiber elastic modulus. When the interface debonding energy increases, the vibration damping decreases when the interface partial debonding and approaches the same value when the interface complete debonding, and the vibration stress for complete interface debonding increases.

Liquefaction Analysis using Shear Wave Velocity

The Andrus and Stokoe curves developed based on shear wave velocity case history databases, are the most widely used in the context of the Seed and Idriss simplified procedure as a deterministic model. Theses curves were developed from the database according to the calculate cyclic stress ratio (CSR) proposed by Seed and Idriss in 1971 with the assumption that the dynamic cyclic shear stress (τd) is always less than the simplified cyclic shear stress (τr) deduced by Seed and Idriss based on their simplifying hypotheses (rd= τd / τr <1). Filali and Sbartai in 2017, showed that rd can in many cases be greater than 1, and they have proposed a correction for the CSR in the range where rd >1. In this paper, we will present a probabilistic study based on the Bayesian method for the evaluation of the liquefaction potential of a soil deposit using a case history database based on shear wave velocity measurement. The result of this analysis shows that by using the corrected version of the simplified method, the boundary curve is moved to a new position. Then, the objective of this study is to present an adjusted mathematical model which characterizes the new position of the boundary curve (CRR) and a new formulation for computing the probability of liquefaction based on the probabilistic shape of the CRR curves using the corrected and the original version of the simplified method.

Influence of Polymer Reagents in the Drilling Fluids on the Efficiency of Deviated and Horizontal Wells Drilling

Improving the efficiency of well drilling process in a reservoir is directly related to subsequent well flow rates. Drilling of deviated and horizontal wells is often accompanied by an increase in pressure losses due to flow resistance caused by small size of the annular space. An important role in such conditions is played by the quality of borehole cleaning and transport capacity of drilling fluid, which is directly related to the rheological parameters of the drilling fluid. The main viscosifiers in modern drilling fluids are polymer reagents. They can be of various origin and structure, which determines their features. This work presents investigations that assess the effect of various polymers on the rheological parameters of drilling fluids. Obtained data are evaluated taking into account the main rheological models of fluid flow. However, process of fluid motion during drilling cannot be described by only one flow model. Paper shows experimentally obtained data of such indicators as plastic viscosity, dynamic shear stress, non-linearity index and consistency coefficient. Study has shown that high molecular weight polymer reagents (e.g., xanthan gum) can give drilling fluid more pronounced pseudoplastic properties, and combining them with a linear high molecular weight polymer (e.g., polyacrylamide) can reduce the value of the dynamic shear stress. Results of the work show the necessity of using combinations of different types of polymer reagents, which can lead to a synergetic effect. In addition to assessing the effect of various polymer reagents, the paper presents study on the development of a drilling fluid composition for specific conditions of an oil field.

Effect of Elevated Temperature on Harmonic Interlaminar Shear Stress in Graphite/Epoxy FRP Simply Supported Laminated Thin Plate Using Finite Element Modeling

Graphite/Epoxy Fiber Reinforced Polymer (FRP) plates are used widely due to their high strength to weight ratio. Current work is concerned about investigating the harmonic interlaminar shear stresses existing between laminates in a simply supported composite Graphite/Epoxy FRP plate under elevated temperatures and for different fiber orientation schemes using finite element modeling. Interlaminar shear stress which is affected by temperature plays a major role in composite material delamination. The simply supported composite plate under study consists of eight laminated layers with different orientation schemes ([0°]8, [0°/15°]4, [0°/30°]4, [0°/45°]4, [0°/60°]4, [0°/75°]4, and [0°/90°]4). Modal analysis is performed to find the natural frequencies for all fiber orientations and temperatures considered. However, harmonic analysis is carried out to study the transverse deflection and interlaminar dynamic shear stress for orientation schemes and temperatures considered at the interfacial of the 7th ply. It is found that increasing temperature leads to slight drop in natural frequency at each orientation scheme but leads to higher deflection and shear stress. Furthermore, it is observed that orientation scheme [0o/45o]4 is the best case for all the temperatures considered since minimum transverse deflection and interfacial shear stress are obtained for almost all the driving frequency range.

Development of the drilling mud composition for directional wellbore drilling considering rheological parameters of the fluid

Article presents investigations on the development of a drilling mud composition for directional wells in an oil field located in the Republic of Tatarstan (Russia). Various rheological models of fluid flow and their applicability for drilling muds are analyzed. Laboratory experiments to measure the main rheological parameters of a solution, such as plastic viscosity, dynamic shear stress, as well as indicators of non-linearity and consistency are presented.
 On the basis of laboratory investigations, it was concluded that high molecular weight polymer reagents (for example, xanthan gum) can give tangible pseudoplastic properties to the washing fluid, and their combination with a linear high molecular weight polymer (for example, polyacrylamide) reduces the value of dynamic shear stress. Thus, when selecting polymer reagents for treating drilling muds at directional drilling, it is necessary to take into account their structure, molecular weight and properties. Combination of different types of reagents in the composition of the drilling mud can lead to a synergistic effect and increase the efficiency of the drilling process as a whole.

Platelet activation via dynamic conformational changes of von Willebrand factor under shear.

Shear-induced conformational changes of von Willebrand factor (VWF) play an important role in platelet activation. A novel approach describing VWF unfolding on the platelet surface under dynamic shear stress is proposed. Cumulative effect of dynamic shear on platelet activation via conformational changes of VWF is analysed. The critical condition of shear-induced platelet activation is formulated. The explicit expression for the threshold value of cumulative shear stress as a function of VWF multimer size is derived. The results open novel prospects for pharmacological regulation of shear-induced platelet activation through control of VWF multimers size distribution.