Natural Convection Flow near a Vertical Plate that Applies a Shear Stress to a Viscous Fluid

The unsteady natural convection flow of an incompressible viscous fluid near a vertical plate that applies an arbitrary shear stress to the fluid is studied using the Laplace transform technique. The fluid flow is due to both the shear and the heating of the plate. Closed-form expressions for velocity and temperature are established under the usual Boussinesq approximation. For illustration purposes, two special cases are considered and the influence of pertinent parameters on the fluid motion is graphically underlined. The required time to reach the steady state in the case of oscillating shear stresses on the boundary is also determined.     

Shear-Induced Unfolding of Lysozyme Monitored In Situ

Conformational changes due to externally applied physiochemical parameters, including pH, temperature, solvent composition, and mechanical forces, have been extensively reported for numerous proteins. However, investigations on the effect of fluid shear flow on protein conformation remain inconclusive despite its importance not only in the research of protein dynamics but also for biotechnology applications where processes such as pumping, filtration, and mixing may expose protein solutions to changes in protein structure. By combining particle image velocimetry and Raman spectroscopy, we have successfully monitored reversible, shear-induced structural changes of lysozyme in well-characterized flows. Shearing of lysozyme in water altered the protein's backbone structure, whereas similar shear rates in glycerol solution affected the solvent exposure of side-chain residues located toward the exterior of the lysozyme α-domain. The results demonstrate the importance of measuring conformational changes in situ and of quantifying fluid stresses by the three-dimensional shear tensor to establish reversible unfolding or misfolding transitions occurring due to flow exposure.     

Physical degradation of proteins in well-defined fluid flows studied within a four-roll apparatus

In most applications of biotechnology and downstream processing proteins are exposed to fluid stresses in various flow configurations which often lead to the formation of unwanted protein aggregates. In this paper we present physical degradation experiments for proteins under well-defined flow conditions in a four-roll apparatus. The flow field was characterized numerically by computational fluid dynamics (CFD) and experimentally by particle image velocimetry (PIV). The local shear strain rate as well as the local shear and elongation rate was used to characterize the hydrodynamic stress environment acting on the proteins. Lysozyme was used as a model protein and subjected to well-defined fluid stresses in high and low stress environment. By using in situ turbidity measurements during stressing the aggregate formation was monitored directly in the fluid flow. An increase in absorbance at 350 nm was attributed to a higher content of visible particles (>1 μm). In addition to lysozyme, the formation of aggregates was confirmed for two larger proteins (bovine serum albumin and alcohol dehydrogenase). Thus, the presented experimental setup is a helpful tool to monitor flow-induced protein aggregation with high reproducibility. For instance, screening experiments for formulation development of biopharmaceuticals for fill and finish operations can be performed in the lab-scale in a short time-period if the stress distributions in the application are transferred and applied in the four-roll mill.     

Platelet lysis and aggregation in shear fields.

A rotational viscometer was used to study the effects of shear stress on platelets in human platelet-rich plasma (PRP). For 5-min exposure times, shear stresses above 160 dynes/cm2 induced platelet lysis (as determined by release of platelet lactic dehydrogenase). For 30-s exposure times, shear stresses greater than 600 dynes/cm2 were required to induce platelet lysis. The platelet counts of sheared PRP were decreased to as low as one-fifth the original count due largely to shear-induced aggregation. The count is a minimum at intermediate stress levels (200-400 dynes/cm2). Higher stresses induce disaggregation as well as lysis. The diminution in the counts was partially reversed in 2 h incubation after cessation of shearing. Experiments were carried out with three different viscometer configurations so that the shear stress and the solid surface area access could be varied independently. Surface access was not a significant variable in the conditions of the experiments. Thus aggregation and lysis may be induced by stress effects alone as well as by solid surface effects. The results also show that the response of platelets to shear stress is strongly dependent on exposure time. Platelets are much less resistant to shear stress than red cells for relatively long exposure times. However, the converse is true for very short exposure times.     

Dynamic shear stress in parallel-plate flow chambers

An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid shear stresses on various cell types exposed to dynamic fluid flow in their physiological environment. The metabolic response of cells in vitro is associated with the wall shear stress. However, parallel-plate flow chambers have not been characterized for dynamic fluid flow experiments. We use a dimensionless ratio h / lambda(v), in determining the exact magnitude of the dynamic wall shear stress, with its oscillating components scaled by a shear factor T. It is shown that, in order to expose cells to predictable levels of dynamic fluid shear stress, two conditions have to be met: (1) h / lambda(v) < 2, where h is the distance between the plates and lambda(v) is the viscous penetration depth; and (2) f(0) < f(c) / m, where the critical frequency f(c) is the upper threshold for this flow regime, m is the highest harmonic mode of the flow, and f(0) is the fundamental frequency of fluid flow.     

Dielectric approach to investigation of erythrocyte aggregation. II. Kinetics of erythrocyte aggregation-disaggregation in quiescent and flowing blood

A method based on dielectric properties of dispersed systems was applied to investigate the kinetics of RBC aggregation and the break-up of the aggregates. Experimentally, this method consists of measuring the capacitance at a frequency in the beginning of the beta-dispersion. Two experimental protocols were used to investigate the aggregation process. In the first case, blood samples were fully dispersed and then the flow was decreased or stopped to promote RBC aggregation. It was found that the initial phases of RBC aggregation are not affected by the shear rate. This finding indicates that RBC aggregation is a slow coagulation process. In the second case, RBCs aggregated under flow conditions at different shear rates and after the capacitance reached plateau levels, the flow was ceased. The steady-state capacitance of the quiescent blood and the kinetics of RBC aggregation after stoppage of shearing depend on the prior shear rate. To clarify the reasons for this effect, the kinetics of the disaggregation process was studied. In these experiments, time courses of the capacitance were recorded under different flow conditions and then a higher shear stress was applied to break up RBC aggregates. It was found that the kinetics of the disaggregation process depend on both the prior and current shear stresses. Results obtained in this study and their analysis show that the kinetics of RBC aggregation in stasis consists of two consecutive phases: At the onset, red blood cells interact face-to-face to form linear aggregates and then, after an accumulation of an appropriate concentration of these aggregates, branched rouleaux are formed via reactions of ends of the linear rouleaux with sides of other rouleaux (face-to-side interactions). Branching points are broken by low shear stresses whereas dispersion of the linear rouleaux requires significantly higher energy.     

Role of partial protein unfolding in alcohol‐induced protein aggregation

Proteins aggregate in response to various stresses including changes in solvent conditions. Addition of alcohols has been recently shown to induce aggregation of disease‐related as well as nondisease‐related proteins. Here we probed the biophysical mechanisms underlying alcohol‐induced protein aggregation, in particular the role of partial protein unfolding in aggregation. We have studied aggregation mechanisms due to benzyl alcohol which is used in numerous biochemical and biotechnological applications. We chose cytochrome c as a model protein, for the reason that various optical and structural probes are available to monitor its global and partial unfolding reactions. Benzyl alcohol induced the aggregation of cytochrome c in isothermal conditions and decreased the temperature at which the protein aggregates. However, benzyl alcohol did not perturb the overall native conformation of cytochrome c. Instead, it caused partial unfolding of a local protein region around the methionine residue at position 80. Site‐specific optical probes, two‐dimensional NMR titrations, and hydrogen exchange all support this conclusion. The protein aggregation temperature varied linearly with the melting temperature of the Met80 region. Stabilizing the Met80 region by heme iron reduction drastically decreased protein aggregation, which confirmed that the local unfolding of this region causes protein aggregation. These results indicate that a possible mechanism by which alcohols induce protein aggregation is through partial rather than complete unfolding of native proteins. Proteins 2010. © Wiley‐Liss, Inc.     

Helical swimming can provide robust upwards transport for gravitactic single-cell algae; a mechanistic model

In still fluid, many phytoplankton swim in helical paths with an average upwards motion. A new mechanistic model for gravitactic algae subject to an intrinsic torque is developed here, based on Heterosigma akashiwo, which results in upwards helical trajectories in still fluid. The resultant upwards swimming speed is calculated as a function of the gravitactic and intrinsic torques. Helical swimmers have a reduced upwards speed in still fluid compared to cells which swim straight upwards. However a novel result is obtained when the effect of fluid shear is considered. For intermediate values of shear and intrinsic torque, a new stable equilibrium solution for swimming direction is obtained for helical swimmers. This results in positive upwards transport in vertical shear flow, in contrast to the stable equilibrium solution for straight swimmers which results in downwards transport in vertical shear flow. Furthermore, for strong intrinsic torque, when there is no longer a stable orientation equilibrium, we show that the average downwards transport of helical swimmers in vertical shear flow is greatly suppressed compared to straight swimmers. We hypothesise that helical swimming provides robustness for upwards transport in the presence of fluid shearing motions.     

Effects of fluid shear on immobilized enzyme kinetics.

There have been a number of reports concerning the damaging effects of shear on globular proteins in solution. Some recent work has indicated, however, that globular proteins in solution are relatively stable, but may be inactivated at air-liquid interfaces during shearing. This study investigated the effects of fluid shear on immobilized enzyme activity. Immobilized enzyme reactors were built to operate with the enzyme immobilized at the boundary of a fluid flow field. Two different enzymes, penicillinase and lactate dehydrogenase, were covalently bound to the interior surface of nylon tubes. Fluid shear rate was changed by varying the flow rate of substrate (reactant) solution through the tube, and fluid shear stresses were increased by increasing the viscosity of the recirculating solution. There were no observed effects of fluid shear on immobilized penicillinase or lactate dehydrogenase activity at shear rates of up to 10,350 s-1 or at shear stresses of up to 73 Pa.     

Quantified small-scale turbulence inhibits the growth of a green alga

1. Laboratory experiments were conducted to elucidate the effect of small-scale turbulent fluid motion on the growth of laboratory cultures of the freshwater algae Scenedesmus quadricauda . Turbulent flow was generated using an oscillating-grid apparatus. The experiments were performed under the range of fluid flow conditions similar to those occurring in nature. The only growth limiting factor was the effect of small-scale fluid motion; all other environmental factors, such as light, temperature and nutrients, were kept constant.
2. Growth of Scenedesmus quadricauda , measured in terms of chlorophyll a concentration, was inhibited when the level of turbulence in the water column was increased. Algal growth was maximum in a quiescent fluid. The inhibitory effect of fluid motion was observed independently of flow regime (laminar, transitional, turbulent) in the water column.
3. Cell destruction and aggregation of dead and living cells of algae were observed in a turbulent flow. High shear rates, estimated from the dissipation of turbulent kinetic energy, caused the cell destruction, algal collision and agglomeration of algae. Data on Scenedesmus responses to small-scale fluid motion will enhance and broaden our ability to develop predictive multispecies models for freshwater phytoplankton communities.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

The superposition of steady on oscillatory shear and its effect on the viscoelasticity of human blood and a blood-like model fluid

To understand the pulsatility of human blood flow in vivo, it is necessary to separately investigate (1) steady shear and oscillatory flow, and (2) the superposition of steady shear flow on oscillatory flow performed under in vitro conditions. In this study a variable steady shear rate was superimposed in parallel on oscillatory shear at a constant frequency (0.5 Hz) for human blood (45% hematocrit), and an aqueous polyacrylamide polymer solution (AP 30E, concentration 300 ppm). The effect of superposition of the above two shear flows on the viscoelasticity of blood was more pronounced for the elastic (η′') than for the viscous (η′) component of viscoelasticity. With increasing superimposed shear rate, both η′ and η′' decreased, especially at the low shear region. This behavior can be explained by the viscoelastic properties of blood and the phenomena of blood aggregation and disaggregation. Quantitatively, the dependence of the viscous component of complex viscosity on superimposed shear for both blood and polymer solution is described by a modified Carreau equation. The elastic component of complex viscosity decreased exponentially with increasing superimposed shear, and it is described by an exponential model. © 1997 Elsevier Science Ltd     

Experimental measurement of dynamic fluid shear stress on the aortic surface of the aortic valve leaflet

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. Although exact causes and mechanisms of AV calcification are unclear, previous studies suggest that mechanical forces play a role. Since calcium deposits occur almost exclusively on the aortic surfaces of AV leaflets, it has been hypothesized that adverse patterns of fluid shear stress on the aortic surface of AV leaflets promote calcification. The current study characterizes AV leaflet aortic surface fluid shear stresses using Laser Doppler velocimetry and an in vitro pulsatile flow loop. The valve model used was a native porcine valve mounted on a suturing ring and preserved using 0.15% glutaraldehyde solution. This valve model was inserted in a mounting chamber with sinus geometries, which is made of clear acrylic to provide optical access for measurements. To understand the effects of hemodynamics on fluid shear stress, shear stress was measured across a range of conditions: varying stroke volumes at the same heart rate and varying heart rates at the same stroke volume. Systolic shear stress magnitude was found to be much higher than diastolic shear stress magnitude due to the stronger flow in the sinuses during systole, reaching up to 20 dyn/cm² at mid-systole. Upon increasing stroke volume, fluid shear stresses increased due to stronger sinus fluid motion. Upon increasing heart rate, fluid shear stresses decreased due to reduced systolic duration that restricted the formation of strong sinus flow. Significant changes in the shear stress waveform were observed at 90 beats/min, most likely due to altered leaflet dynamics at this higher heart rate. Overall, this study represents the most well-resolved shear stress measurements to date across a range of conditions on the aortic side of the AV. The data presented can be used for further investigation to understand AV biological response to shear stresses.     

Do protein molecules unfold in a simple shear flow?

Protein molecules typically unfold (denature) when subjected to extremes of heat, cold, pH, solvent composition, or mechanical stress. One might expect that shearing forces induced by a nonuniform fluid flow would also destabilize proteins, as when a protein solution flows rapidly through a narrow channel. However, although the protein literature contains many references to shear denaturation, we find little quantitative evidence for the phenomenon. We have investigated whether a high shear can destabilize a small globular protein to any measurable extent. We study a protein (horse cytochrome c, 104 amino acids) whose fluorescence increases sharply upon unfolding. By forcing the sample through a silica capillary (inner diameter 150-180 microm) at speeds approaching 10 m/s, we subject the protein to shear rates dv(z)/dr as large as approximately 2 x 10(5) s(-1) while illuminating it with an ultraviolet laser. We can readily detect fluorescence changes of <1%, corresponding to shifts of < approximately 0.01 kJ/mol in the stability of the folded state. We find no evidence that even our highest shear rates significantly destabilize the folded protein. A simple model suggests that extraordinary shear rates, approximately 10(7) s(-1), would be required to denature typical small, globular proteins in water.     

Response of a concentrated monoclonal antibody formulation to high shear

There is concern that shear could cause protein unfolding or aggregation during commercial biopharmaceutical production. In this work we exposed two concentrated immunoglobulin‐G1 (IgG1) monoclonal antibody (mAb, at >100 mg/mL) formulations to shear rates between 20,000 and 250,000 s^?1 for between 5 min and 30 ms using a parallel‐plate and capillary rheometer, respectively. The maximum shear and force exposures were far in excess of those expected during normal processing operations (20,000 s^?1 and 0.06 pN, respectively). We used multiple characterization techniques to determine if there was any detectable aggregation. We found that shear alone did not cause aggregation, but that prolonged exposure to shear in the stainless steel parallel‐plate rheometer caused a very minor reversible aggregation (<0.3%). Additionally, shear did not alter aggregate populations in formulations containing 17% preformed heat‐induced aggregates of a mAb. We calculate that the forces applied to a protein by production shear exposures (<0.06 pN) are small when compared with the 140 pN force expected at the air–water interface or the 20–150 pN forces required to mechanically unfold proteins described in the atomic force microscope (AFM) literature. Therefore, we suggest that in many cases, air‐bubble entrainment, adsorption to solid surfaces (with possible shear synergy), contamination by particulates, or pump cavitation stresses could be much more important causes of aggregation than shear exposure during production. Biotechnol. Bioeng. 2009;103: 936–943. © 2009 Wiley Periodicals, Inc.     

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Interstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman–Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.     

Influence of cell deformation on leukocyte rolling adhesion in shear flow

Blood cell interaction with vascular endothelium is important in microcirculation, where rolling adhesion of circulating leukocytes along the surface of endothelial cells is a prerequisite for leukocyte emigration under flow conditions. HL-60 cell rolling adhesion to surface-immobilized P-selectin in shear flow was investigated using a side-view flow chamber, which permitted measurements of cell deformation and cell-substrate contact length as well as cell rolling velocity. A two-dimensional model was developed based on the assumption that fluid energy input to a rolling cell was essentially distributed into two parts: cytoplasmic viscous dissipation, and energy needed to break adhesion bonds between the rolling cell and its substrate. The flow fields of extracellular fluid and intracellular cytoplasm were solved using finite element methods with a deformable cell membrane represented by an elastic ring. The adhesion energy loss was calculated based on receptor-ligand kinetics equations. It was found that, as a result of shear-flow-induced cell deformation, cell-substrate contact area under high wall shear stresses (20 dyn/cm2) could be as much as twice of that under low stresses (0.5 dyn/cm2). An increase in contact area may cause more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy input may decrease due to the flattened cell shape. Our model predicts that leukocyte rolling velocity will reach a plateau as shear stress increases, which agrees with both in vivo and in vitro experimental observations.     

Viscoelasticity of rigid macromolecules with irregular shapes in the limit of overwhelming Brownian motion

We consider viscoelastic properties of complex rigid macromolecules in fluids undergoing steady or sinusoidal linear shearing. An arbitrary body is hydrodynamically described by six tensors to allow for irregular shapes that couple rotational and translational motions to each other and to the shear field. The viscosity increment ν is obtained for infinitely dilute suspensions in the limit of overwhelming Brownian motion by balancing drag forces and torques with entropic forces and torques. For sinusoidal shearing, ν is a complex number that exhibits five resonances at frequencies matching the j = 2 eigenvalues of the rotational diffusion equation for a stationary fluid. The resonance amplitudes are conveniently expressed in terms of a second-rank body-fixed tensor χ that characterizes alignment by the shear field, and special cases of symmetry are considered which reduce the number of contributing terms. Steadyshear methods, which assume a body matches the translational and rotational motions of the fluid element it replaces, are shown to slightly overestimate ν when complex shapes are involved. An algebraic criterion is found to locate the center of viscosity needed in these other methods although our treatment is independent of the choice of position in the body used for calculations. Bead-model expressions are derived in order to provide numerical treatments of complicated structures. As an example, we examine a long bent rod.     

A novel in vitro loading system to produce supraphysiologic oscillatory fluid shear stress

A multi-well fluid loading (MFL) system was developed to deliver oscillatory subphysiologic to supraphysiologic fluid shear stresses to cell monolayers in vitro using standard multi-well culture plates. Computational fluid dynamics modeling with fluid-structure interactions was used to quantify the squeeze film fluid flow between an axially displaced piston and the well plate surface. Adjusting the cone angle of the piston base modulated the fluid pressure, velocity, and shear stress magnitudes. Modeling results showed that there was near uniform fluid shear stress across the well with a linear drop in pressure across the radius of the well. Using the MFL system, RAW 264.7 osteoclastic cells were exposed to oscillatory fluid shear stresses of 0, 0.5, 1.5, 4, 6, and 17 Pa. Cells were loaded 1 h per day at 1 Hz for two days. Compared to sub-physiologic and physiologic levels, supraphysiologic oscillatory fluid shear induced upregulation of osteoclastic activity as measured by tartrate-resistant acid phosphatase activity and formation of mineral resorption pits. Cell number remained constant across all treatment groups.     

Critical stresses for cancer cell detachment in microchannels

We present experiments involving cancer cells adhering to microchannels, subjected to increasing shear stresses (0.1–30 Pa). Morphological studies were carried out at different shear stresses. Cells exhibit spreading patterns similar to those observed under static conditions, as long as the shear stress is not too high. At critical wall shear stresses (around 2−5 Pa), cell-substrate contact area decreases until detachment at the larger stresses. Critical shear stresses are found to be lower for higher confinements (i.e. smaller cell height to channel height ratio). Fluorescent techniques were used to locate focal adhesions (typically 1 μm² in size) under various shearing conditions, showing that cells increase the number of focal contacts in the region facing the flow. To analyze such data, we propose a model to determine the critical stress, resulting from the competition between hydrodynamic forces and the adhesive cell resistance. With this model, typical adhesive stresses exerted at each focal contact can be determined and are in agreement with previous works.