Development characteristics of drag-reducing surfactant solution flow in a duct

Development characteristics of dilute cationic surfactant solution flow have been studied through the measurements of the time characteristics of surfactant solution by birefringence experiments and of the streamwise mean velocity profiles of surfactant solution duct flow by a laser Doppler velocimetry system. For both experiments, the concentration of cationic surfactant (oleylbishydroxymethylethylammonium chloride: Ethoquad O/12) was kept constant at 1000 ppm and the molar ratio of the counter ion of sodium salicylate to the surfactants was at 1.5. From the birefringence experiments, dilute surfactant solution shows very long retardation time corresponding to micellar shear induced structure formation. This causes very slow flow development of surfactant solution in a duct. Even at the end of the test section with the distance of 112 times of hydraulic diameter form the inlet, the flow is not fully developed but still has the developing boundary layer characteristics on the duct wall. From the time characteristics and the boundary layer development, it is concluded that the entry length of 1000 to 2000 times hydraulic diameter is required for fully developed surfactant solution flow.List of abbreviations and symbols A₁, A₂ Coefficients for time constant fitting [-] - B Breadth of the test duct [m] - C₁, C₂ Coefficients for time constant fitting [-] - D Pipe diameter [m] - D_H Hydraulic diameter [m] - g Impulse response function [Pa] - H Width of the test duct [m] - n Index of Bird-Carreau model [-] - Re Reynolds number (=U_mD_H/) - Re_D Pipe Reynolds number (=U_mD/) - Re_x Streamwise distance Reynolds number (=U₀x/) - T Absolute temperature [K] - t Time [s] - t_a Retardation time [s] - t_b Build-up time [s] - t_x Relaxation time [s] - t_x1, t_x2 Relaxation time for double time constant fitting [s] - t Time constant in Bird-Carreau model [s] - U Time mean velocity [m/s] - U_m Bulk mean velocity [m/s] - U_max Maximum velocity in a pipe [m/s] - U₀ Main flow velocity [m/s] - u Friction velocity [m/s] - x, y Coordinates [m] - Shear rate [s^–1] - Mean shear rate [s^–1] - n Birefringence [-] - 99% boundary layer thickness [m] - Solution viscosity [Pa·s] - _P, _S Surfactant and solvent viscosity [Pa·s] - ₀, Zero and infinite viscosity of Bird-Carreau model [Pa·s] - Characteristic time in Maxwell model [s] - Water kinematic viscosity [m²/s] - Density [kg/m³] - Solution shear stress [Pa] - _P, _S Surfactant and solvent shear stress [Pa] - Time in convolution [s]     

Elastic properties of a dilute surfactant solution in the shear induced state

The first normal stress differences N ₁ of a highly dilute cationic surfactant solution are investigated in a cone-and-plate rheometer. In continuation of a previous paper (Nowak 1998), where the buildup of a shear induced structure in such a solution was attained after a reduced deformation, the N ₁ turned out to be in proportion to the square of the shear rate γ˙ reduced by a critical value γ˙ _c in a first range above γ˙ _c . At higher shear rates the N ₁ tend to lower values than predicted by this relation. Relaxation experiments were performed in the same geometry to determine the characteristic time scales of the shear induced state's decay. In the lower range above &γdot; _c the stress decay is a monoexponential process, while a second time constant has to be introduced to describe the relaxation in that range, where the N ₁ deviate from the parabolic dependence of the reduced shear rate. Received: 10 May 1999 Accepted: 15 November 2000     

Development characteristics of fluctuating velocity field of drag-reducing surfactant solution flow in a duct

Development behavior of the fluctuating velocity of surfactant solution in a duct has been studied experimentally. The concentration of surfactants was kept constant at 1,000 ppm, mean velocity at 0.78 m/s and fluid temperature at 15 °C. Using laser Doppler velocimetry, the fluctuating streamwise velocity distributions at six cross sections, which ranged from 14 to 112 times of hydraulic diameter of the duct, were measured. From the results, the fluctuating structures of surfactant solution flow are observed to have structures different from that of turbulent water flow in the developing field. The wavelet analysis reveals that the high-level fluctuation of surfactant solution flow is characterized by periodicity rather than irregularity around the position where the fluctuation intensity takes a peak value and that the period and the scale of periodic flow structures are related to the relaxation times of the fluid. This indicates that the high-level fluctuation is deeply related to the elastic instability and has a different generation mechanism from that of turbulence observed in a Newtonian turbulent flow.     

Numerical and experimental investigation of turbulent characteristics in a drag-reducing flow with surfactant additives

Cetyltrimethyl ammonium chloride (CTAC) surfactant additives, because of their long-life characteristics, can be used as promising drag-reducers in district heating and cooling systems. In the present study we performed both numerical and experimental tests for a 75 ppm CTAC surfactant drag-reducing channel flow. A two-component PIV system was used to measure the instantaneous streamwise and wall-normal velocity components. A Giesekus constitutive equation was adopted to model the extra stress due to the surfactant additives, with the constitutive parameters being determined by well-fitting apparent shear viscosities, as measured by an Advanced Rheometric Expansion System (ARES) rheometer. In the numerical study, we connected the realistic rheological properties with the drag-reduction rate. This is different from previous numerical studies in which the model parameters were set artificially. By performing consistent comparisons between numerical and experimental results, we have obtained an insight into the mechanism of the additive-induced drag-reduction phenomena.

Our simulation showed that the addition of surfactant additives introduces several changes in turbulent flow characteristics: (1) In the viscous sublayer, the mean velocity gradient becomes gentler due to the viscoelastic forces introduced by the additives. The buffer layer becomes expanded and the slope of the velocity profile in the logarithmic layer increases. (2) The locations where the streamwise velocity fluctuation and Reynolds shear stress attain their maximum value shifted from the wall region to the bulk flow region. (3) The root-mean-square velocity fluctuations in the wall-normal direction decrease for the drag-reducing flow. (4) The Reynolds shear stress decreases dramatically and the deficit of the Reynolds shear stress is mainly compensated by the viscoelastic shear stress. (5) The turbulent production becomes much smaller and its peak-value position moves toward the bulk flow region. All of these findings agree qualitatively with experimental measurements.

Regarding flow visualization, the violent streamwise vortices in the near wall region become dramatically suppressed, indicating that the additives weaken the ejection and sweeping motion, and thereby inhibit the generation of turbulence. The reduction in turbulence is accomplished by additive-introduced viscoelastic stress. Surfactant additives have dual effects on frictional drag: (1) introduce viscoelastic shear stress, which increases frictional drag; and (2) dampen the turbulent vortical structures, decrease the turbulent shear stress, and then decrease the frictional drag. Since the second effect is greater than the first one, drag-reduction occurs.     

Friction and heat transfer in drag-reducing surfactant solution flow through curved pipes and elbows

A study of drag-reducing flow in curved pipes was conducted. In contrast to earlier studies we show that if we use a modified definition of drag reduction that includes only the turbulence effects, we observe indeed the same level of drag reduction in both coiled and straight pipes. More complex results showing reduced drag reduction compared to curved pipes were achieved with elbows. Two elbows of different size and type were tested in turbulent flow of both water and drag-reducing surfactant solution. A more elaborate analysis was conducted for a half-inch threaded elbow with a ratio of curvature radius to diameter of 1.2. The pressure drop and heat transfer were measured in a section downstream from the elbow over a distance of x/D = 130 in order to investigate the hydrodynamic and thermal developments of the flow. The pressure drop coefficient of the elbow was calculated for water and a surfactant solution, based on the total increase in pressure drop in the system due to the presence of the elbow. For a larger welded elbow of 6″ diameter some drag reduction was measured for the surfactant solution.     

Characteristic turbulent structure of a modified drag-reduced surfactant solution flow via dosing water from channel wall

The modification of the near-wall structure is very important for the control of wall turbulence. To ascertain the effect of near-wall modulation on the viscoelastic drag-reduced flow, the modified characteristics of a surfactant solution channel flow were investigated experimentally. The modulation was conducted on the boundary of the channel flow by injecting water from the whole surface of one side of the channel wall. The diffusion process of the injected water was observed by using the planar laser-induced fluorescence technique. The velocity statistics and characteristic structure including the spatial distributions of instantaneous streamwise velocity, swirling strength, and Reynolds shear stress were analyzed based on the velocity vectors acquired in the streamwise wall-normal plane by using the particle imaging velocimetry technique. The results indicated that the disturbance of the injected water was constricted within a finite range very near the dosing wall, and the Reynolds shear stress was increased in this region. However, the eventual drag reduction rate was found to be increased due to a relatively large decrement of viscoelastic shear stress in this near-wall region. Moreover, the flow structure under this modulation presented obvious regional characteristics. In the unstable disturbed region, the mixing of high-speed and low-speed fluids and the motions of ejection and sweep occurred actively. Many clockwise vortex cores were also found to be generated. This characteristic structure was similar to that in the ordinary turbulence of Newtonian fluid. Nevertheless, outside this disturbed region, the structure still maintained the characteristics of the drag-reduced flow with non-Newtonian viscoelastic additives. These results proved that the injected Newtonian fluid associated with the modified stress distribution creates a diverse characteristic structure and subsequent enhanced drag reduction. This investigation can provide the experimental basis for further study of turbulence control.     

Characterization of micellar structure dynamics for a drag-reducing surfactant solution under shear: normal stress studies and flow geometry effects

Some surfactant solutions have been observed to exhibit a strong drag reduction behavior in turbulent flow. This effect is generally believed to result from the formation of large cylindrical micelles or micellar structures. To characterize and understand better these fluids, we have studied the transient rheological properties of an efficient drag-reducing aqueous solution: tris (2-hydroxyethyl) tallowalkyl ammonium acetate (TTAA) with added sodium salicylate (NaSal) as counter ion. For a 5/5 mM equimolar TTAA/NaSal solution, there is no measurable first normal stress difference (N ₁) immediately after the inception of shear, but N ₁ begins to increase after a well-defined induction time — presumably as shear-induced structures (SIS) are formed — and it finally reaches a fluctuating plateau region where its average value is two orders of magnitude larger than that of the shear stress. The SIS buildup times obtained by first normal stress measurements were approximately inversely proportional to the shear rate, which is consistent with a kinetic process during which individual micelles are incorporated through shear into large micellar structures. The SIS buildup after a strong preshear and the relaxation processes after flow cessation were also studied and quantified with first normal stress difference measurements. The SIS buildup times and final state were also found to be highly dependent on flow geometry. With an increase in gap between parallel plates, for example, the SIS buildup times decreased, whereas the plateau viscosity increased.     

Viscosity of a Newtonian fluid calculated from the deformation of droplets covered with a surfactant under a linear shear flow

The viscosity of small fluid droplets covered with a surfactant is determined using drop deformation techniques. This method, proposed by Hu and Lips, is here extended to the case of the presence of a surface-active adsorpted at the liquid–liquid interface, to consider more general scenarios. In these experiments, a droplet is sheared by another immiscible fluid of known viscosity, both Newtonian liquids. From the steady-state deformation and retraction mechanisms, the droplet viscosity is calculated using an equation derived from the theories of Taylor and Rallison. Although these theories were expressed for surfactant-free interfaces, they can be applied when a surfactant is present in the system if the sheared droplet reaches reliable steady-state deformations and the surfactant attains its equilibrium adsorption concentration. These determinations are compared to bulk viscosities measured in a rheometer for systems with different viscosity ratios and surfactant concentrations. Very good agreement between both determinations is found for drops more viscous than the continuous phase.     

Time dependent flow in equimolar micellar solutions: transient behaviour of the shear stress and first normal stress difference in shear induced structures coupled with flow instabilities

Recently we studied time dependent structural changes that are coupled with flow instabilities (Fischer 1998; Wheeler 1998; Fischer 2000). Within a stability analysis, a classification scheme for the feedback circuit of coupled shear-induced structure and flow instabilities was derived by Schmitt et al. (1995) and applied to our samples. Here, inhomogeneous flow layers of different concentration and viscosity are generated by shear-induced diffusion (spinodal demixing) and, as consequence, one no longer observes a homogeneous solution but a type of shear banding that is seen here for the first time. In this paper we present the behaviour of the first normal stress difference observed in the critical shear-rate regime where transient shear-induced structure is coupled with flow instability. Similar to the oscillations of the shear stresses (strain-controlled rheometer) one observes oscillations in the first normal stress difference. This behaviour indicates that elastic structures are built up and destroyed while the shear-induced structures occur and that the induced phase is more elastic than the initial one. Oscillations of shear stress and first normal stress difference are in phase and indicate that both phenomena are caused by the same mechanism. Received: 30 June 1999/Accepted: 14 December 1999     

Viscoelasticity of a surfactant and its drag-reducing ability

There is considerable interest in the use of viscoelastic cationic surfactant-counterion mixtures in district heating and cooling systems to reduce pressure losses. A recent field test in a secondary system near Prague showed a 30+% reduction in pumping energy requirements.We have studied a number of commercial surfactants and we report here results of rheological, drag reduction and turbulence measurements on Arquad 18–50 (octadecyl trimethyl ammonium chloride (AR 18)) with an excess of sodium salicylate (NA). The concentration studied was 1.6 mM AR 18 and 4.0 mM NA which is about one third the concentration for excellent drag reduction in this surfactant's effective temperature range 30–90°C.Viscosity, , vs. shear rate,D, first normal stress difference,N ₁, vs. shear rate, drag reduction (as pressure drop,i=P/1) vs. average velocity,U _ave, in a 39.4 mm tube for AR 18, and turbulence intensity data for three drag reducing surfactants are reported.Of particular interest are the generally low turbulence intensities in all three directions which correspond to reduced heat, mass and momentum transfer rates compared to water, and the existence of large normal stress differences at 20°C for AR 18, a temperature at which no drag reduction occurs with this surfactant, indicating that normal stress effects do not correlate directly with drag reduction.The effect of time of pumping on increasing drag reduction demonstrates that this factor overwhelms the expected increase in drag reduction as temperature is raised from 18–19°C to 40.5°C.     

Analysis of an organized turbulent structure using a pattern recognition technique in a drag-reducing surfactant solution flow

This work presents the investigation for an organized turbulent structure in a drag-reducing flow of dilute surfactant solution by utilizing a particle image velocimetry system to perform the pattern recognition technique on a trajectory in four quadrants of streamwise and wall-normal velocity fluctuations. The pattern recognition is added to a new algorithm in order to directly capture the spatial rotation motion. The Reynolds number based on the channel height and bulk mean velocity was set to 1.5 × 10⁴. Surfactant solution with a weight concentration of 150 ppm was employed and the drag reduction rate was 65%. In the drag-reducing flow, we observe increased frequencies of occurrence of the flow events that correspond to a meandering motion in the wall-normal direction of the high-and low-speed regions. Three findings from investigation of the ensemble-averaged Reynolds shear stress and vortex structure are as follows: (i) the Reynolds shear stress in the large fluctuation range occurs in the narrow region; (ii) Size, strength, arrangement and inclination in the spatial vortex structure in the drag-reducing flow differ from those of the water; and (iii) all trajectory contributions for the wall friction coefficient decrease. Finally, we interpreted that the viscoelasticity characterizing the viscoelastic stress and relaxation time in rheological properties of the flow changes specific elementary vortex for the drag-reducing flow, and the trajectories of each flow pattern change drastically.     

The effects of salts on the rheological characteristics of a drag-reducing cationic surfactant solution with shear-induced micellar structures

The effect of the counterion salt sodium salicylate (Nasal) on the transient rheological properties of a drag-reducing surfactant system tris (2-hydroxyethyl) tallowalkyl ammonium acetate (TTAA) has been studied with both rheometric and rheo-optical methods. Three types of transient behavior for N₁ and viscosity were identified in 5 mM TTAA solutions depending on the counterion concentration: induction and growth (below equimolar concentration); overshoot and growth (above equimolar concentration); and overshoot then plateau (at high concentrations of Nasal). The transient flow birefringence and orientation angle show trends similar to those of the viscosity and N₁. The second type of transient behavior suggests a two-stage alignment and shear thickening process. The SIS buildup time from the quiescent state, the rebuilding time after a strong preshear, and the relaxation time were also obtained from N₁ measurements, and show a maximum around equimolar conditions. The initial N₁ and viscosity immediately after the flow startup, on the other hand, show a maximum around a ratio of 2.5 to 3 Nasal/TTAA. For solutions with a Nasal concentration in the ratio 1.5 to 3, the steady state values of N₁ and viscosity do not show much variation with Nasal concentration over the shear rate range covered, however. The effect of an addition of sodium chloride (NaCI) to an equimolar Nasal/TTAA solution on the characteristic times and steady state values was also quantified. These rheological results provide us with tools to determine the optimal concentration ratio for practical drag reduction applications.     

Recent experimental probes of shear banding

Recent experimental techniques used to investigate shear banding are reviewed. After recalling the rheological signature of shear-banded flows, we summarize the various tools for measuring locally the microstructure and the velocity field under shear. Local velocity measurements using dynamic light scattering and ultrasound are emphasized. A few results are extracted from current works to illustrate open questions and directions for future research.

Simultaneous measurements of velocity and temperature fluctuations in thermal boundary layer in a drag-reducing surfactant solution flow

The mechanism of turbulent heat transfer in the thermal boundary layer developing in the channel flow of a drag-reducing surfactant solution was studied experimentally. A two-component laser Doppler velocimetry and a fine-wire thermocouple probe were used to measure the velocity and temperature fluctuations simultaneously. Two layers of thermal field were found: a high heat resistance layer with a high temperature gradient, and a layer with a small or even zero temperature gradient. The peak value of was larger for the flow with the drag-reducing additives than for the Newtonian flow, and the peak location was away from the wall. The profile of was depressed in a similar manner to the depression of the profile of in the flow of the surfactant solution, i.e., decorrelation between v and compared with decorrelation between u and v. The depression of the Reynolds shear stress resulted in drag reduction; similarly, it was conjectured that the heat transfer reduction is due to the decrease in the turbulent heat flux in the wall-normal direction for a flow with drag-reducing surfactant additives.List of symbols ensemble averaged value - (·)⁺ normalized by the inner wall variables - (·) root-mean-square value - C concentration of cetyltrimethyl ammonium chloride (CTAC) solution - c _p heat capacity - D hydraulic diameter - f friction factor - H channel height - h heat transfer coefficient - j _H Colburn factor - l length - Nu Nusselt number, h - Pr Prandtl number, c _p/ - q _w wall heated flux - Re Reynolds number, U _b/ - T temperature - T _b bulk temperature - T _i inlet temperature - T _w wall temperature - T friction temperature, q _w /c _p u - U local time-mean streamwise velocity - U ₁ velocity signals from BSA1 - U ₂ velocity signals from BSA2 - U _b bulk velocity - u streamwise velocity fluctuation - u1 velocity in abscissa direction in transformed coordinates - u friction velocity, - v wall-normal velocity fluctuation - v1 velocity in ordinate direction in transformed coordinates - var(·) variance - x streamwise direction - y wall-normal direction - z spanwise direction - _j junction diameter of fine-wire TC - _w wire diameter of fine-wire TC - angle of principal axis of joint probability function p(u,v) - _f heat conduction of fluid - _w heat conduction of wire of fine-wire TC - kinematic viscosity - local time-mean temperature difference, T _w –T - temperature fluctuation - standard deviation - density - _w wall shear stress     

Experimental study on swirling flow of dilute surfactant solution with deformed free-surface

An experimental investigation was performed on a swirling flow of dilute surfactant solution with deformed free-surface in a cylindrical container driven by the constantly rotating bottom wall. The purpose of the experiment was to estimate weak viscoelasticity in the tested surfactant solutions as well as to investigate the flow characteristics. The tested fluid was an aqueous solution of CTAC (CTAC: cetyltrimethyl ammonium chloride), which is a cationic surfactant. Water, 40 ppm, 60 ppm and 200 ppm CTAC solution flows were tested at Froude numbers ranging from 2.59 to 16.3. Particle image velocimetry (PIV) was used to measure the secondary velocity field in the meridional plane. The deformed free-surface level was extracted from the PIV images. At a similar Froude number, the depth of the dip formed at the center region of the free surface was decreased for CTAC solution flow compared with water flow. The inertia-driven vortex at the up-right corner in the meridional plane becomes more and more weakened with increase of the solution concentration or viscoelasticity. Through analyzing the overall force balance compared with water flow, the first normal stress difference characterizing the viscoelasticity was estimated for the dilute CTAC solution flows. The result supports the viscoelasticity-based turbulent drag-reduction mechanism of surfactant solution flow.     

Shear-banding structure orientated in the vorticity direction observed for equimolar micellar solution

 The non-monotonic shear flow of a viscoelastic equimolar aqueous surfactant solution (cetylpyridinium chloride-sodium salicylate) is investigated rheologically and optically in a transparent strain-controlled Taylor Couette flow cell. As reported before, this particular wormlike micellar solution exhibits first a shear thinning and then a pronounced shear-thickening behavior. Once this shear-thickening regime is reached, a transient phase separation/shear banding of the solution into turbid and clear ring-like patterns orientated perpendicular to the vorticity axis, i.e., stacked like pancakes, is observed (Wheeler et al. 1998; Fischer 2000). The solution exhibit several unique features as no induction period of the shear induced phase, no structural build-up at the inner rotating cylinder, jumping pancake structure of clear and turbid ringlike phases, and oscillating shear stresses appear once the pancake structure is present. According to our analysis this flow phenomenon is not purely a mechanical or rheological driven hydrodynamic instability but one has to take into account structural changes of the oriented micellar aggregates (flow induced non-equilibrium phase transition) as proposed by several authors. Although this particular flow behavior and the underlying mixture of shear induced phases and mechanical instabilities is not fully understood yet, some classification characteristics based on a recent theoretical approach by Schmitt et al. (1995) and Porte et al. (1997) where a strong coupling between the flow instability (non-homogeneous flow profile due to the bands) and the structural changes causes the observed transient phenomena can be derived. In reference to the presented model the observed orientation of the rings is typical for complex fluids that undergo a spinodal phase separation coupled with a thermodynamic flow instability. In contrast to other shear banding phenomena, this one is observed in parallel plate, cone-plate, and Couette flow cell as well as under controlled stress and controlled rate conditions. Therefore, it adds an additional aspect to the present discussion on shear banding phenomena, i.e., the coupling of hydrodynamics and phase transition of rheological complex fluids. Received: 8 January 2001 Accepted: 15 May 2001     

Effect of surfactant concentration on saturated flow boiling in vertical narrow annular channels

Saturated flow boiling of environmentally acceptable nonionic surfactant solutions of Alkyl (8–16) was compared to that of pure water. The concentration of surfactant solutions was in the range of 100–1000 ppm. The liquid flowed in an annular gap of 2.5 and 4.4 mm between two vertical tubes. The heat was transferred from the inner heated tube to two-phase flow in the range of mass flux from 5 to 18 kg/m² s and heat flux from 40 to 200 kW/m². Boiling curves of water were found to be heat flux and channel gap size dependent but essentially mass flux independent. An addition of surfactant to the water produced a large number of bubbles of small diameter, which, at high heat fluxes, tend to cover the entire heater surface with a vapor blanket. It was found that the heat transfer increased at low values of relative surfactant concentration C/C₀, reaches a maximum close to the value of C/C₀ = 1 (where C₀ = 300 ppm is the critical micelle concentration) and decreased with further increase in the amount of additive. The dependence of the maximal values of the relative heat transfer enhancement, obtained at the value of relative concentration of C/C₀ = 1, on the boiling number Bo may be presented as single curve for both gap sizes and the whole range of considered concentrations.     

Effects of surfactant and salt concentrations on capillary flow and its entry flow for wormlike micelle solutions

Dynamic viscoelasticities and flow properties were measured for aqueous solutions of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) to examine the effects of surfactant (C _D) and salt (C _S). The relaxation time λ of a single mode Maxwell model was obtained, and the relationship between λ and free NaSal concentration was discussed. The relation between λ and was applied to the classification of flow curves, which were obtained using a capillary rheometer. In the flow curves, a shear rate jump occurred at low shear rates for the solutions with low , while bending was seen at high shear rates for all the flow curves. On the other hand, vortex growth at the salient corner in the entrance region of the capillary was also investigated. Four different flow patterns were identified: Newtonian-like flow (A), steady vortex flow (B), periodically oscillated flow (C), and perfectly unstable flow (D). In the steady vortex of the flow pattern B, the vortex length increased with increasing shear rate. In the flow patterns C and D, white turbidity was observed. Furthermore, the relation between λ and was also applied to the discussion on the development of the vortex.     

An experimental investigation on vortex induced vibration of a flexible inclined cable under a shear flow

In the present study, an experimental investigation was performed to characterize the vortex induced vibration (VIV) of a flexible cable in an oncoming shear flow. The VIV tests were conducted in a wind tunnel with a flexible cable model. It was found that, under different oncoming velocity profiles, the cable model behaved in single-mode and multi-mode VIVs. The displacement amplitudes of the single mode VIVs were found to be larger than those of multi-mode VIVs, and the cross-flow (CF) response was larger than that of in-line (IL) direction for either the single mode or multi-mode VIVs. For a single mode vibration, the largest CF response occurs in the 1st mode VIV, and the motion trajectory of the 1st mode VIV was found to be an inclined figure of eight shape, while other single mode VIVs behaved in ellipse or straight line trajectories. For multi-mode VIVs, no stable vibration trajectories were found to exist since the vibration frequency bands covered two or more vibration modes. The vortex-shedding frequencies in the wake behind the inclined cable were also characterized in the present study. The shedding frequencies of the wake vortices were found to coincide well with the vibration modes: for a single mode VIV, they were close to the dominant vibration mode; for a multi-mode VIV, they could also cover the appearing vibration modes.     

Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.