Alignment of spherical particles in rheologically complex fluid under torsional flow

Transcription

1 Korea-Australia Rheology Journal, Vol.26, No.2, pp (May 2014) DOI: /s Alignment of spherical particles in rheologically complex fluid under torsional flow Jungmi Yoo and Chongyoup Kim* Department of Chemical and Biological Engineering, Korea University, Sungbuk-ku, Seoul , Republic of Korea (Received December 2, 2013; final revision February 13, 2014; accepted March 27, 2014) The microstructures of suspensions of spherical particles under the torsional flow between two parallel plates are studied by using the optical microscopy and the small angle light scattering technique (SALS) along the velocity gradient direction. The particle diameter is 2.2 micrometer and the gap distance between two parallel plates is 200 micrometer. The dispersing media are glycerin, aqueous solution of 4% xanthan gum and 1500 ppm polyacrylamide solution in glycerin. The xanthan gum solution is strongly shear thinning with the shear thinning index of 0.2. The polyacrylamide solution behaves as a Boger fluid rheologically. The result shows that the microstructure observed in the wide gap experiment is qualitatively different from the microstructure observed in the monolayer experiments reported in the literature. In glycerin, a random structure is observed. In the shear thinning fluid, particles appear to be weakly chained and aligned along the vorticity direction below 100 s -1 and along the flow direction over 100 s -1. In the Boger fluid, particles align along the vorticity direction and form short strings within the fluid. The alignment appears to be originated from the elastic effect rather than the shear thinning effect. A new flow pattern of the banded structure is occasionally observed for the Newtonian suspension which still shows a random microstructure of suspended particles. This flow pattern is always present in the shear thinning fluid while it is never present in the Boger fluid. Keywords: alignment, string formation, flow pattern, elasticity, shear thinning 1. Introduction The flow of suspension and the formation of a microstructure within the suspension are of great importance both practically and academically. The microstructure of a suspension within the fluid is determined by the balance among interparticle forces such as van der Waals force, Brownian motion and hydrodynamic interactions among particles (Vermant, 2001). Colloidal suspensions of hard spheres show random structures at the rest state or at a low shear rate. At high shear rates, they can form clusters due to strong hydrodynamic interactions (Vermant, 2001; Vermant and Solomon, 2005; Gunes et al., 2008; Pasquino et al., 2010). It has been well established that the rheological properties strongly affect the microstructure in the non- Newtonian fluids through strong hydrodynamic interactions (Michele, 1977; Jefri and Zahed, 1989; Tehrani, 1996; Lyon et al., 2001; Won and Kim, 2004; Scirroco et al., 2004). Alternatively, the microstructure developed during the flow can change the rheological properties of the suspension drastically (Vermant and Solomon, 2005). There have been several reports on the string formation along the flow direction in the monolayer experiments with shear thinning fluids (Michele, 1977, Lyon et al., 2001, Won and Kim, 2004) beginning from the pioneering work of Michel (1977). On the other hand, Scirocco et al. (2004) and Won and Kim (2004) reported *Corresponding author: cykim@grtrkr.korea.ac.kr, Tel.: that particles are evenly distributed with in a Boger fluid without being aligned or chained. Using the video microscopy and the small angle light scattering technique (SALS), Pasquino et al. (2010) recently reported that particle migration toward the wall is of primary importance in the formation of microstructure near the wall and the alignment of particles takes place near the wall, supporting Scirocco et al. s earlier report (2004). Interestingly, Pasquino et al. reported that polystyrene particles of 1.2 µm in a weakly elastic and weakly shear thinning hydroxypropyl cellulose (HPC) solution align along the vorticity direction at a low shear rate, in contrast to the fact that particles of 2.8 µm align along the flow direction in the same fluid. Considering that particles align along the flow direction in the same HPC solution as reported by Scirocco et al. (2004) and the alignment was attributed to the shear thinning effect, the alignment of the 1.2 µm particles along the vorticity direction is somewhat unexpected. Also a question can arise whether the shear thinning effect is also responsible for the orientation along the vorticity direction. In the present study, the formation of microstructure under the torsional flow between two parallel disks is revisited by using the microscopy and the SALS along the velocity gradient direction. In particular, the effect of rheological characteristics of the dispersing medium is studied to confirm whether the string formation is restricted to the case of suspensions in highly shear thinning fluids as reported in the literature. The result shows 2014 The Korean Society of Rheology and Springer 177

2 Jungmi Yoo and Chongyoup Kim that the microstructure observed in the wide gap experiment is qualitatively different from the microstructure observed in the monolayer experiments, especially for the case of negligibly shear thinning elastic fluid, i.e., a Boger fluid. In the Boger fluid, particles align along the vorticity direction and form short strings within the fluid, and hence the alignment within the fluid appears to be originated from the elastic effect rather than the shear thinning effect. This result is somewhat different from the alignment in the monolayer experiment in which alignment occurs only in the shear thinning fluids. Also a new flow pattern of the banded structure is occasionally observed for the Newtonian suspension which still shows a random microstructure of suspended particles. This banded structure is always present in the shear thinning fluid while it is never present in the Boger fluid. 2. Experimental 2.1. Materials Three different kinds of suspensions were prepared by suspending spherical polystyrene particles (PS particles) in Newtonian, shear thinning and non-shear thinning elastic fluids. PS particles were synthesized by the dispersion polymerization method (Lok and Ober, 1985; Shin and Kim, 2013) and dispersed in the fluids described below. Particle volume fraction was fixed at 1%. This volume fraction is in the same range of volume fractions in earlier studies (Scirocco et al., 2004, Pasquino et al., 2010). The average diameter of the PS particles was 2.2 µm, and they were practically mono-disperse in size as shown in Fig. 1. Two kinds of non-newtonian dispersing media were prepared in addition to glycerin (Sigma Aldrich Co.), a Newtonian fluid. A shear thinning fluid was prepared by dissolving xanthan gum (XG: Sigma Aldrich Co.) in water; an elastic fluid with a negligible shear thinning effect was prepared by dissolving a small amount of polyacrylamide (PAAm: Sigma Aldrich Co.) in glycerin. The 8% master Fig. 1. Scanning electron microscopic image of the particles. solution of XG was prepared by dissolving XG by using the Thinky mixer (Model AR-100, Thinky Co.). The 0.3% master solution of PAAm was prepared by dissolving PAAm in glycerin by using a magnetic stirrer at an elevated temperature of 45 o C. Suspensions were prepared by dispersing the PS particles in dispersing media by using the Thinky mixer first and the mixture was mixed further using a magnetic stirrer for 24 hours. The homogeneity of the dispersion was verified by the optical microscopy (x20 objective lens, Olympus IX-50) before each experiment. Particles were well dispersed in the fluids without dispersing agents Apparatus The rheological properties were measured by using rotational rheometers (MCR302, Anton Paar; AR2000 and DHR-3, TA Instruments). The small angle light scattering experiments were performed by using the MCR302 rheometer with the standard SALS accessory with a parallelplate fixture and a He-Ne laser (wave length 658 nm, power 10 mw). In this set-up, the laser passes through the fluid sample in the velocity gradient direction. The quartz parallel-plates have the diameter of 42.9 mm. The observations were made at a distance of 17.8 mm from the center of the plate. The SALS images were captured by using a CCD camera (Model LU075C, Lumenera Co.). The number of pixels of each image was , but only a portion of the pixels contained the SALS image because the distance between the screen and the lens of the CCD camera could not be adjusted to obtain a larger image due to the geometrical restriction under the rheometer. The gap distance between the two parallel plates was fixed at 100 mm for strong scattering signals. This optimum gap distance was determined by examining the brightness levels for differing gap distances. After loading a sample a preshear of 0.5 s -1 was imposed for 15 mins before imposing the main shear flow. The preshear was necessary to eliminate the microstructure developed during the sample loading which is a high shear rate process and the direction of shear is perpendicular to the torsional flow between the parallel plates. The shear rate was varied from 0.5 and 1000 s -1. Shear rate was hold at a value for 5 mins before changing to the next value. Images were obtained at every 10 s. All the experiments were performed at 24±1 o C. The rheological properties of the suspension were not monitored because the particle loading is small and hence the change from the value for the dispersing medium is small. The microstructure of the suspension under flow conditions were directly observed by using a microscopy accessory of MCR302. The magnification of the objective lens was 20. The microscopic images were captured by using a CCD camera (EoSens/MC1362, Microtron). The exposure time was set at 200 µs to avoid blurring caused by the fast movement of particles. The microscopic obser- 178 Korea-Australia Rheology J., Vol. 26, No. 2 (2014)

3 Alignment of spherical particles in rheologically complex fluid under torsional flow vations were made at a distance of 10 mm from the center of the plate. This position is not the same as the SALS pattern is observed. This is because the objective lens has to be placed at a different position due to the short working distance of the objective lens and the geometrical restriction. The macroscopic flow patterns were also observed by using a transparent parallel-plate fixture of the optical analysis module of ARES (Rheometrics Co.). The images of macroscopic flow patterns were obtained by using a digital camera (Nikon D7100) with a macrolens (AF-S Micro NIKKOR 60 mm F2.8g ED). 3. Results 3.1. Rheological characteristics of dispersing medium Fig. 2 shows the rheological properties of the dispersing media used in the present study. Glycerin shows a constant viscosity and is a Newtonian fluid. The xanthan gum solution is shear thinning in the whole range of viscosity measurements and the power law index is 0.2 approximately. The xanthan gum solution shows similar G and G values for a wide range of ω, which are typical characteristics of suspensions of rodlike polymers. The polyacrylamide solution in glycerin has a constant viscosity between 0.1 and 10s -1 of shear rate and is slightly shear thinning over 10 s -1. But the shear thinning is not as strong as the xanthan gum solution. It is noted that the viscosity of polyacrylamide solution in glycerin is smaller than the viscosity of the pure solvent. It appears that water was absorbed by the hydroscopic glycerin during the solution preparation and storage. G is larger than G for the whole range of measurements and the slope of G approaches 1 as ω tends to zero while the slope of G approaches 2 as ω tends to zero. The constant viscosity and the patterns of G and G are typical characteristics of Boger fluids (Larson, 1999; Shaqfeh, 1996). The rheological measurements show that both the xanthan gum solutions and the Boger fluid are elastic Flow patterns of suspensions: Stripe formation Fig. 3 shows the observed flow patterns by using transparent parallel-plates for three different kinds of suspensions 14 mins after shearing together with the initial image which is practically the same for all the fluids. An irregulary banded structure of alternatingly dark and bright regions is occasionally developed in the Newtonian suspension. Bright and dark bands of a few millimeters width are formed but the number varies with time. Considering that the gap distance is 100 µm, the band is very wide. The white band should be rich in particles while the dark band should be depleted of particles. This means that particles become demixed in the torsional flow. The locations and the width of the particle rich bands varied with time. In the case of suspensions in shear thinning fluids, similar patterns are present, but the banded structure appears more regular than the Newtonian case. In the Boger fluid the banded structure does not appear and the suspension remains homogeneous under the shear stress. Hence the banded structure Fig. 2. (Color online) Rheological properties of the dispersing media (a) Viscosity (b) G and G of polymer solutions. Fig. 3. Comparison of macroscopic flow patterns for three different fluids after 14mins shearing at 500 s -1 (a) Initial state (b) Suspension in the Newtonian fluid (c) Suspension in the shear thinning fluid (d) Suspension in the Boger fluid. Korea-Australia Rheology J., Vol. 26, No. 2 (2014) 179

4 Jungmi Yoo and Chongyoup Kim that is present in the Newtonian fluid and the shear thinning fluid should not be caused by either elasticity or shear thinning characteristics of non-newtonian fluid. The presence of the banded structure is in contrast to the pattern observed by Kim et al. (2008) for the suspensions of 100 µm polymethylmethacrylate (PMMA) particles. The difference between two studies is in the sizes of particle and gap distance: in the present case, the particles are much smaller (2 µm) and the gap distance between the two disks is also much smaller. The ratio between the gap distance and particle diameter is 50 approximately. In the case of Kim et al., the ratio is 10 approximately and the particle size is 165±15 µm. It is not certain whether the different ratio is the reason for such a difference. One may consider the effect of the secondary flow within the torsional flow. But the secondary flow caused by the inertial effect spans the whole region by a single vortex of the torus shape (Savins and Metzner, 1970). Therefore the secondary flow cannot explain the presence of multiple rings. The migration of particles can affect the particle distribution. From the scaling law of the diffusivity of migration, D γ a 2 (Leighton and Acrivos, 1987), the migration length scale, l 2Dt has an order of 0.2 mm when the radius of the particle (a) is 1mm, and the shear rate ( γ ) is 100 s -1 and the time t is 200s. Therefore the migration cannot be the reason for the stripe formation. Another reason why the migration can be excluded from the reason for stripe formation is that the migration can induce only monotonic variation since it is a diffusion-like process and hence the demixing of particles cannot be explained by the migration only. It has been known that the secondary flow by the purely elastic instability caused by the first normal stress difference can show such a pattern (Larson, 1992). In the present study, the first normal stress difference of the suspension in the Newtonian fluid could not be measured because of the limit in the rheometer resolution. However, it is conceivable that the normal stress difference is the largest for the most elastic Boger fluid among the test fluids. This means that the normal stress difference cannot be the major reason for the stripe formation even though it could affect the motion. It appears that the mechanism of the stripe formation in the Newtonian and the shear thinning fluid requires a separate investigation SALS pattern of suspensions and microscopic observations Next we consider the microstructure of particles developed in the suspension under the shear stress examined by using the SALS technique. In the following the shear rate value is the nominal shear rate which is the shear rate at the rim of the plate. Since the position of the laser beam is 17.8 mm from the plate center, the shear rate at the laser beam position is 83% of the nominal shear rate. Since the microstructure obtained here can be unique characteristics of the torsional flow, the nominal shear rate is used throughout this article rather than the shear rate at the laser beam position. Fig. 4a shows the SALS pattern changes of Newtonian suspension with shear rate. At first the SALS patterns of the Newtonian suspension are isotropic at all shear rates up to 1000 s -1 of nominal shear rate. However the speckling patterns are different and almost no speckling is observed at high shear rates. The diminishing of the speckling at high shear rates appears to be the result of the spatial averaging of the speckling by the motion of the fluid during the exposure time of the CCD camera. From the SALS patterns, the suspension in the Newtonian fluid is expected to have an isotropic microstructure. With the SALS image only, it may not be possible whether particles form chains or not because the SALS pattern should be isotropic when the chains are tumbling without being aligned along a specific direction even if particles are chained in the Newtonian fluid. To resolve the problem we may refer to the rheological data or direct observations. The detailed microstructure will be discussed in the next section when we consider the microscopic images of flowing suspensions. Fig. 4b shows the SALS patterns of the aqueous xanthan gum solution. When a low shear stress is imposed as a preshear, the SALS pattern has an isotropic image with speckling. At this low shear rate, the pattern is almost the same as the SALS pattern of the Newtonian fluid as expected. As shear rate increases to 10 s -1, the SALS image appears to be extended along the flow direction slightly and then returns to the isotropic pattern when shear rate is 60 s -1. When shear rate reaches 300 s -1, the SALS pattern becomes elongated slightly along the vorticity direction. When shear rate reaches 100 s -1, the SALS pattern becomes radially symmetric. The result of the SALS experiments on the shear thinning fluid implies that particles are chained or aligned and the chained particles are oriented along the vorticity or the flow direction depending on shear rate. Fig. 4c shows the SALS patterns of the polyacrylamide solution in glycerin, which is a nonshear thinning, elastic fluid. When a low shear stress is imposed as a preshear, the SALS pattern has an isotropic image with speckling as before. As shear rate increases to 10 s -1, the SALS image is extended in the flow direction and the degree of extension becomes larger as shear rate increases until 60 or 100 s -1 and the degree of extension becomes smaller again to have a nearly isotropic pattern when shear rate is 1000 s -1. The extension of the SALS pattern along the flow direction means that the particles are chained and the chained particles are oriented along the vorticity direction. Also the extension of the SALS pattern along the vorticity direction means that the chained particles are oriented along the flow direction. Therefore, in the xanthan gum solution, a shear thinning fluid, the 180 Korea-Australia Rheology J., Vol. 26, No. 2 (2014)

5 Alignment of spherical particles in rheologically complex fluid under torsional flow Fig. 4. (Color online) Small angle light scattering pattern for differing fluids with the change in shear rate. (a) Suspension in glycerin (b) Suspension in the 4% aqueous solution of xanthan gum (c) Suspension in the 1500 ppm polyacrylamide solution in glycerin. All the images were obtained after reaching the steady state at each shear rate. chained particles are aligned along the vorticity direction at low shear rates (smaller than 60 s -1 ) while they are aligned along the flow direction at high shear rates (larger than 60 s -1 ). In the Boger fluid, an elastic solution with negligible shear thinning, the chained particles are aligned along the vorticity direction but they tend to lose the orientation as shear rate increases after reaching the maximum orientation when shear rate is approximately 100 s Discussion To quantitatively analyze the SALS images, an alignment factor can be used as defined below (Scirocco et al., 2004): 2π Iqφ (, ) cos( 2φ) dφ A f ( q) = , (1) 2π Iqφ (, ) dφ 0 where q is scattering vector and I is the intensity and φ is the angle from the flow direction. But this relation requires the computation of the angles from the discrete image data. Also A f (q) is a function of q and is not a single number for a given image. This means that a measure has to be defined to represent A f (q). One may consider IAF= A f ( q)2πqdq as a measure, but it has been found that the integral cannot represent the extension along x- or y-direction properly due to the sensitivity problem. This problem occurs because the denominator in Eqn (1) is a function of q and is very small at a large q (a large radial position from the center). Hence a small deviation from the radial symmetry of the image is amplified by the small intensity value at large q values. Considering that the images are elongated only in the x- or y-direction, in the present study we used the ratio of the second moments along the flow (x) and the vorticity (y) directions to investigate the extension of the SALS image along either of the directions as follows: M AF = xx (2) M xx M yy = x 2 Iq ( ) dq M yy = y 2 Iq ( ) dq. (4) The second moments are readily obtained by using the SALS software provided by the manufacturer. If this value is larger than 1, the chained particles are oriented along the flow direction and if it is smaller than 1, the chained particles are oriented along the vorticity direction. When this ratio is 1, we cannot decide even whether the particles are chained or not because both the randomly oriented rods and randomly distributed spherical particles can show the same isotropic image. To resolve this, the optical microscopy was used as supplementary evidence. Fig. 5 shows that the change of AF with time when the Boger fluid is subjected to an abrupt change in shear rate. Both of the cases of increasing shear rate from 0.5 to 10 and from 100 to 300 s -1 show that the time constant of particle chain orientation is approximately 100 s. It is noted that at 100 s -1, the initial AF is not 1 reflecting that the microstructure is not random at this shear rate. Other fluids show the similar value. Because the SALS patterns were obtained after 5 mins, they can be considered the steady state orientations. Fig. 6 shows the change in AF with shear rate for Newtonian, shear thinning and Boger fluids. As already (3) Korea-Australia Rheology J., Vol. 26, No. 2 (2014) 181

6 Jungmi Yoo and Chongyoup Kim Fig. 5. (Color online) Change in alignment factor (AF) with time while increasing shear rates. The dispersing fluid is 1500ppm polyacrylamide solution in glycerin. Fig. 7. (Color online) Microstructural images at the middle of the gap. The fluid is the 1500 ppm PAAm solution. The arrow indicates the flow direction. (a) Rest state (b) Enhanced image for the square in (a) showing a random structure. (c) Shear rate of 200 s -1 (d) Enhanced image for the square in (c) showing the particle chaining and the alignment along the vorticity direction. The boxes in (d) represent the slits formed by chained particles along the vorticity direction. The arrows represent the flow direction. Fig. 6. (Color online) Alignment factor (AF) change with shear rate for polystyrene particle suspensions in differing fluids. When AF = M xx /M yy = 1 (solid line) there is no alignment. When AF is smaller than 1, the chained particles are oriented along the vorticity direction. When AF is larger than 1, the chained particles are oriented along the flow direction. described, the Newtonian suspension shows no shear rate dependence and the AF value remains at slightly below 1. AF of the shear thinning fluids shows that particles are chained and the chained particles are oriented along the vorticity direction when shear rate is below 100 s -1 while they are aligned along the flow direction when shear rate is over 100 s -1. The reorientation of the chained particles in the shear thinning fluid appears similar to the reorientation of spheroidal particles in the parallel plate geometry when shear rate increases (Gunes, 2008). In the Boger fluid particles are chained and the chained particles are aligned along the vorticity direction. Two neighboring chains form a slit-like region along the vorticity direction. The alignment is strongest when shear rate is 100 s -1. The reason why the alignment becomes weak cannot be determined from the present experiment only. It is surmised that the chaining becomes weak when shear rate becomes larger as each particle within a chain is subjected to a largely different shear stress because the shear rate increases with radial position. Fig. 7 shows the microscopic images for the Boger fluid. At the rest state, particles are randomly distributed. When the shear rate is 200 s -1, some particles are chained and the chained particles are aligned perpendicular to the flow direction. In other words, they are aligned along the vorticity direction. The alignment of particles and the formation of slit-like regions by the aligned particles can be easily seen from the enhanced image in (d). Since the radial position at which the microscopic image is obtained is not the same as the SALS pattern is obtained, the nominal shear rate of 200 s -1 corresponds to the nominal shear rate of 100 s -1 for the SALS image. The microscopic image confirms that the microstructure predicted by the SALS pattern indeed represents the true microstructure of the suspension. If particles are aligned along the flow direction and form a chain, a particle contained in the chain cannot rotate in the same direction individually because the interstitial region between two adjacent spheres should be subjected 182 Korea-Australia Rheology J., Vol. 26, No. 2 (2014)

7 Alignment of spherical particles in rheologically complex fluid under torsional flow to very large shear stress. Rather the particle chain rotates as a single rod. Hence it is worth considering the motion of rodlike particles in shear flows. Rodlike particles can develop preferred orientations when subjected to flow. There are many reports that rodlike particles tend to align along the vorticity direction in non-newtonian fluids. (Leal, 1975; Brunn, 1977; Harlen and Koch, 1993). This is called a log-rolling motion. When the shear rate is small, the fluid behaves as a Newtonian fluid and hence the rod particles (chained particles), if formed, show the kayaking motion following the Jefferey orbit. When the shear rate increases, the kayaking motion dissipates too much energy and hence the chain tends to align along the vorticity direction. The orientation along the vorticity direction appears to be caused by elasticity. In the shear thinning fluid, a flip-over occurs to the flow direction as shear rate increases while no such flip-over occurs in the Boger fluid. The reason for this flip-over requires a systematic study on the hydrodynamic interaction among particles in viscoelastic and shear thinning fluids. This is far beyond the scope of the present study. 5. Conclusions The effects of rheological properties on the flowinduced alignment of spherical particles in suspensions have been investigated by using the Rheo-SALS technique and optical microscopy. In the Newtonian fluid, particles do not form chains and have a random structure. In the shear thinning fluid particles form chains and aligned along the vorticity direction at low shear rates and they are reoriented to the flow direction as shear rate increases. The reorientation process is not abrupt with the increase in shear rate meaning that the chained particles show the kayaking motion during the transition. In the Boger fluid, it is first found that particles form chains and the chained particles are oriented along the vorticity direction up to shear rate of 1000 s -1. This is in contrast to the previous reports. To understand the mechanism of chaining and alignment of particles in the bulk phase, the hydrodynamic interaction of particles in non-newtonian fluid under the torsional flow should be studied more. A new flow pattern is reported here for the Newtonian and shear-thinning suspensions. The suspensions show a stripe pattern of concentric circles. From the fact that no alignment is found in the Newtonian suspension, the stripe pattern appears to be a result of flow instability. Acknowledgment This work was supported by Mid-career Researcher Program through NRF grant funded by the MEST (Ministry of Education, Science and Technology), Korea (No ) References Brunn, P.O., 1977, The slow motion of a rigid particle in a second-order fluid, J. Fluid Mech. 82, Gunes, D.Z., R. Scirocco, J. 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