Characteristics of Air Bubble Rising in Low Concentration Polymer Solutions

Transcription

1 Characteristics of Air Bule Rising in Low Concentration Polymer Solutions * HASSAN, N. M. S., KHAN, M. M. K. AND RASUL, M. G. College of Engineering an Built Environment Faculty of Sciences, Engineering an Health Central Queenslan University Rockhampton, Ql-4702 AUSTRALIA * n.hassan@cqu.eu.au Astract: - The ule rise phenomena in ifferent low concentration polymer solutions for higher ynols numer are presente in this paper. The main characteristics, namely, the ule velocity, the ule trajectory an the rag relationship are investigate. The experiments were conucte in two ifferent cylinrical columns at various liqui heights y introucing ifferent ule volumes (from 0.1mL to 20.0mL) corresponing to each height. The ule rise velocity, ule size an ule trajectory were measure using a comination of non-intrusive-high spee photographic metho an igital image processing. The parameters that significantly affect the rise of air ule are ientifie. The ule rise velocity of ifferent volumes an the effect of liqui heights on the ule rise velocity are analyse an iscusse. The results show that the average ule rise velocity increases with the increase in ule volume for ifferent low concentration polymer solutions an the ule velocity is not epenant on the size of the test rig. The results of ule trajectory for various ules are compare an iscusse. In trajectory analysis, it is seen that the smaller ules show helical or zigzag motion an larger ules follow spiral motion. A new set of ata of the rag coefficient for air ule for higher ynols numer are reporte an compare with the results of other analytical an experimental stuies availale in the literature. The ule rise characteristics, i.e., ule velocity, trajectory an rag coefficient prouce acceptale an consistent results. Key-wors: - Bule rise velocity, ule trajectory, ule volume, rag co-efficient, ynols numer, polymer solution, non-intrusive metho 1 Introuction Air ules are use in chemical, iochemical, environmental, an foo process for improving the heat an mass transfer. Bules play an important role in many applications such as; in the fermentation process, in the cooking processes, in etermining the rates of heat an mass transfer an coalescence, in the pipeline transport applications, in polymer an sluge processes an others [1]. The ules fin uses in many process inustries such as in vacuum pan operation in sugar inustries which is an important process for the prouction of raw sugar. The most significant ynamic ehaviour of air ules are the ule rise velocity, trajectory an the rag coefficient. The rag coefficient correlates the rag force exerte on a moving air ule to its terminal velocity an projecte surface area. The terminal velocity of an air ule is terme as the velocity attaine at steay state conitions where all applie forces are alance. When the ule rises in a liqui column, uoyancy an rag forces govern the rise velocity of the ule. Drag an uoyancy forces are strongly epenent on flui properties, gravity an the equivalent iameter of the ule. The ule rise velocity an rag coefficient of an air ule are mainly epenent on the properties of the liqui an the ule. For low-ynols numer flows, the viscous forces are large relative to internal terms an the viscous shear stresses transmit the motion of the ule far into the flow. So the viscosity forces ominate the terminal motion an terminal rise velocity increases with iameter of the ule at very low ynols numer. An intermeiate region (>1), ules are no more spherical as their size increases an terminal velocity may increase or remain constant or ecrease with equivalent iameter of the ule. In this region, surface tension an inertia forces etermine the 53

2 terminal rise velocity. On the other han, in very high ynols numer flows the viscous shear stresses only affect the flow close to the wall so a thin ounary layer forms near the ule where the velocity varies from a finite value (relative velocity etween the ule an meium) to approximately zero. The flow outsie of this layer is cause y the pressure graients. The averse pressure graient forme as the flow moves aroun the ack of the ule causes the flow to separate from the ule. The location of this flow separation an the nature of the separation (either steay or unsteay) are calculate y the interaction etween the pressure graients outsie the ounary layer an the viscous flow near the ule so it is etermine y the ynols numer of the flow. At high ynols numer, ules are spherical cap or mushroom shape an the motion of the ule is ominate y the inertia forces. In this region, ule rise velocity increases with the equivalent iameter of the ule [2]. Bule rise characteristic in Newtonian liqui has receive consierale attention an is well stuie. Due to the ominance of non-newtonian liquis use in various process inustries, an unerstaning of ule rise in rheologically complex liquis has grown to e important. The ynamics of the ule characteristics in a gas-liqui system are still not totally unerstoo. From most of the stuy, it was seen that a small ule rises through water in a straight line at its terminal velocity until it finishes its journey. The paths of larger ules were not stale an starte to zigzag an much larger ules followe spiral motion [3-8]. Shew an Pinton [5] presente that the shift of the onset of path instaility to smaller ule size changes remarkaly in the case of polymer solution an it also appeare that the ifurcation to path instaility for increasing ule size was less arupt for the polymer solution in comparison with water. Dewsury et al. [9] have investigate the relationship etween the terminal velocity an volume for larger gas ules in non-newtonian power-law fluis. Tsuge an Hiino [10] reporte that the trajectories of rising spherical an ellipsoial gas ules at higher ynols numers are ientical. Dewsury et al. [11] etermine experimentally that the rag coefficient for a rising soli sphere in non-newtonian pseuo plastic liquis were significantly affecte y its trajectory. A new rag correlation for rising spheres in power-law liquis was presente y Dewsury et al. [12]. It is vali for 0.1<< It escrie the relationship etween C an in creeping, transitional, turulent an even critical flow regimes. Margaritis et al. [13] stuie the rag co-efficient variation for ules over a wie range of in ifferent non-newtonian polysaccharie solutions an propose a correlation which matche very well with experimental ata. For the case of power-law non-newtonian fluis, it has een shown that the rag curve for air ules followe Haamar-Ryczynski moel rather than Stokes moel for < 5 [11, 14]. On the other han, Miyahara an Yamanaka [14] reporte for the case of highly viscous non-newtonian liqui that the rag coefficient eviates from the Haamar Ryczynski type equation if the ynols numer increases. Dhole et al. [15] investigate that the rag coefficient always increases with the increase in power law inex for all values of the ynols numer. There have een limite stuies availale in the literature on ule rise characteristics in low concentration polymer solutions at high ynols numer. More research an in epth analysis on ule rise phenomena in non-newtonian flui is necessary as most of the inustrial fluis are non-newtonian in nature. The aim of this stuy is to measure the ule rise velocity, ule trajectory, an the rag on the ule as it rises through low concentration polymer (shear thinning) fluis an investigate the influence of various parameters namely, the ule sizes, flui properties on the ule rise characteristics (velocity, trajectory, rag etc).the correlation of rag co-efficient of the ule at a higher ynols numer is compare with the results of other analytical an experimental stuies availale in the literature. 2 Experimental Set-up an Proceure 2.1 Experimental test rig The experimental set up selecte in this stuy was similar to that use y Dewsury et al. [9]. The experimental apparatus is shown schematically in Fig. 1. Two-test rigs were use for investigating the ule rise characteristics in xanthan gum an polyacrylamie solution. The first rig consiste of a polycaronate tue approximately 1.8 m in height an 125 mm in iameter. The ule insertion mechanism consiste of a lale or spoon that ha a capaility to control the injection of air. The secon rig was esigne with acrylic tue of 400 mm in iameter an 2.0 m in height. Larger sizes of ule were teste in this rig to eliminate the wall effect. The camera lifting apparatus stans approximately 2.0 m high which allows the movement of the camera mount evice to rise through 1.8 m in height. The variale spee rive of camera lifting apparatus regulates the control of the camera 54

3 mount evice. This rive allows the camera to e raise at approximately the same velocity as the ule. A high spee igital vieo camera (Panasonic, NV-GS11, 24X optical Zoom) was mounte on a camera mount evice with a small attachment to the sie of the camera lifting apparatus. A = Stury Base; B = Rotating Spoon; C = Cylinrical test rig (0.125m or 0.40 m iameter), D = Vieo camera; E = Variale spee motor; F = Pulley; an G = Camera lifting apparatus. Fig. 1 Schematic iagram of experimental apparatus 2.2 Bule rise velocity measurement Bule rise velocities were compute y a frame y frame analysis of successive images. The ule images were analyse with the software Winows Movie Maker y which the ule rise time was recore an velocity was measure. It is note that the ule velocity was measure at ifferent liqui heights of 1 m, 1.2 m, 1.4 m an 1.6 for oth xanthan gum an polyacrylamie solutions. 2.3 Bule iameter measurement Bule equivalent iameter was measure from the still frames which were otaine from the vieo image. The still images were then opene using SigmaScan Pro 5.0 commercial software an the ule height ( h ) an the ule with ( w ) were measure in pixels. The pixel measurements were converte to millimetres ase on caliration ata for the camera. The ule equivalent iameter, eq was calculate [16] as ( ) = (1) eq h w where w the long axis length an h is the short axis length of the ule. For this measurement it was assume that the ule was axi-symmetric with respect to its height or short axis irection. 2.4 Bule trajectory measurement Trajectory was etermine from the still images collecte from the igital vieo camera. Bule trajectory was compute from the still frames otaine from the vieo image. The still frames were then opene in SigmaScan Pro commercial software, which was capale of showing pixel location on an image. A ule images that ha een store in the computer were opene in Aoe Photoshop commercial software. The pixel coorinates (X an Y) of the ules centre were note an recore into spreasheet. X coorinate correspons the istance from the left ege an Y coorinate correspons the istance from the top ege respectively. The pixel line running through the centre of the ule release point was known. The eviation of the ule centre from the release point was compute y sutracting the X of the ule centre from the X of the ule release point. 2.4 Calculation of ynols numer an rag coefficient Since the flui viscosity changes as a function of the shear rate so the terminal velocity of the ule also changes with the change in shear rate. The average shear rate over the entire ule surface is equal to U / so the apparent viscosity can e written [13, 17] as n 1 µ = K( U ) (2) In the case of spherical ule, the ynols numer for non-newtonian power law flui was efine as n 2 n ρliqu = (3) K For a non-spherical ule with a vertical axis of symmetry, the ynols numer was efine [3, 13, 17, 18] y n 2 n wu ρliq = (4) K The rag co-efficient for spherical ule was calculate y 4g ρ C = (5) 2 3ρliqU In the case of non-spherical ule, the rag co-efficient was compute y 3 4geq ρ C = (6) 2 2 3ρliqwU The rag co-efficient for non-spherical ule was calculate on the asis of the real ule geometry in 55

4 equation (6), where eq is the equivalent sphere iameter an w is the iameter of the horizontal projection of ule or long axis length of the ule. 2.5 Test fluis The polymer solutions xanthan gum an polyacrylamie use in this stuy were a non-newtonian (shear thinning) flui. The solutions (polyacrylamie an xanthan gum) with concentration of 0.025% (y weight) were use. The fluis were prepare y mixing 0.025% y weight of each material with water in the test rig an stirring it for long hours (5-7 hrs). The temperature of all solutions in this stuy was maintaine at 25 C. For every solution, the measure ensity of the solution was very close to the ensity of water at 25 C since they were low concentration liquis. Rheological properties of the solutions were measure using an ARES (Avance Rheometric Expansion System) rheometer. The rheological properties for ifferent solutions are summarize in Tale 1. The usual range of shear rate to etermine flui rheology was 1-650s -1. Tale 1 Rheological an physical properties of polymer solutions n Density, Flui Type Concentration K, (%) Pa. s n 3 kg / m Polyacrylamie Xanthan Gum Fig. 2 shows that the polymer (xanthan gum an polyacrylamie) solutions exhiit non-newtonian shearthinning pseuoplastic ehaviour which is aequately escrie y Power-Law moel, η n 1 = Kɺ γ (7) The K an n values for the polymer solutions were etermine from this response curve an are shown in the Tale 1. K represents the consistency of the flui ehaviour i.e. the higher the value of K, the more viscous the flui an n enotes power law inex which is a measure of the extent of non-newtonian ehaviour. As seen, the viscous effect of the xanthan gum solution was more than that of polyacrylamie solution ecause the value of K was foun slightly higher. 3 sults an Discussion 3.1 Bule rise velocity The velocity profile of xanthan gum an polyacrylamie solutions for ule volumes of 0.1mL- 5.0mL, carrie out in the smaller rig (125 mm) at ifferent liqui heights are presente in Fig. 3. It is seen that the ule velocity increases with the increase in ule volume for oth solutions. The average ule velocity for these ule sizes was etween 0.22 m/sec an 0.30 m/sec. The velocity profile of xanthan gum an polyacrylamie solutions for ule volumes of 0.1mL- 20mL measure at ifferent liqui heights in the larger test rig (400 mm) are shown in Fig. 4. It shows the same phenomena as oserve in Fig. 3. The average ule velocity for these ule sizes was etween 0.22 m/sec an 0.41 m/sec at 1.0 m height. As seen, the velocities for corresponing ule sizes are nearly same for oth solutions. However, for the ule volume of 20mL at a height of 1 m, the ule velocity of xanthan gum is foun slightly lower than that of polyacrylamie solution. This is ue to the higher viscosity of xanthan gum as higher viscosity restrains the ule to rise faster. Viscosity, Pa.s % Xanthan gum 0.025% Polyacrylamie Bule velocity (m/sec) Vel. of xanthan sol n at 1.0 m Vel. of poly sol n at 1.0 m Vel. of xanthan sol n at 1.2 m Vel. of poly sol n at 1.2 m Vel. of xanthan sol n at 1.4 m Vel. of poly sol n at 1.4 m Vel. of Xanthan sol n at 1.6 m Vel. of poly sol n at 1.6 m Shear Rate, 1/s Fig. 2 Viscosity vs. shear rate of xanthan gum solutions emonstrating the pseuoplastic ehaviour Bule volume (ml) Fig. 3 Velocity profile for polyacrylamie an xanthan gum solutions at ifferent heights (125mm rig) 56

5 It can e oserve from Fig. 3 an Fig. 4 that the average ule velocity slightly ecreases with the increase in liqui height ut not to a significant extent, although the pressure changes with the increase in height is very small. Bule velocity (m/sec) Vel. of xanthan sol n at 1.0 m Vel. of poly sol n at 1.0 m Vel. of xanthan sol n at 1.2 m Vel. of poly sol n at 1.2 m Vel. of xanthan sol n at 1.4 m Vel. of poly sol n at 1.4 m Vel. of xanthan sol n at 1.6 m Vel. of poly sol n at 1.6 m Fig. 6 presents the ata otaine from oth test rigs for a liqui column of 1.0 m height. It is seen that the ule velocity ata fall on the same straight line for corresponing ule volume an liqui height. A similar tren was also foun for all liqui heights. Hence the ule velocity was foun to e rig inepenent. Bule velocity (m/sec) Bule vel. of xanthan sol n at small rig Bule vel. of xanthan sol n at large rig Bule vel. of poly sol n at small rig Bule vel. of poly sol n at large rig Bule volume (ml) Fig. 4 Velocity profile for polyacrylamie an xanthan gum solutions at ifferent heights (400mm rig). Davies an Taylor [19] propose in their stuy a correlation for the calculation of the ule rise velocity which is shown in equation (8). The same (8) was also use y Talaia [20] for larger ules. U = g (8) eq The current results of ule rise velocity as a function of the ule equivalent iameter is compare with the result of Davies an Taylor in Fig. 5. As seen, the current experimental ata agrees well with this correlation for larger ules at higher ynols numer with some variations for lower ule size in low ynols numer. This is consistent since the equation (8) is vali for larger ules. Bule rise velocity, m/sec Davies an Taylor (1950) Current experiment: 0.025% xanthan gum Current experiment: 0.025% polyacrylamie Bule equivalent iameter, m Fig. 5 Bule rise velocity vs. ule equivalent iameter Bule volume (ml) Fig. 6 Velocity profile at ifferent rig size correspons to the same ule volume. 3.2 Bule trajectory The trajectory results of xanthan gum solution are shown in Fig. 7 for ifferent ule sizes when measure over a height of 1.0 m from the point of air injection. The figure shows the eviation of ule from its release point as it rises through a liqui column. The general tren was for the ule to remain close to the release centre, when the ule was release an as it rose through the liqui, it sprea out as the height increases. For the xanthan gum solution, the smaller ules (0.1mL an 2mL) eviate more horizontally with respect to the ule release centre an the ule travele with a helical motion. The larger ule of 5.0mL initially eviate horizontally an finally, they followe a spiral path. In the eginning, the 10mL ule followe the straight path, then eviate horizontally an finally followe spiral path. Smaller ules less than 2 mm in iameter rise in straight or linear path [21, 22] ut the linear trajectory was not oserve as the ule equivalent iameter of this stuy was more than 5 mm. At low for smaller ule, the rising ule showe a zigzag trajectory. At high, the larger ules isplaye a spiral trajectory ecause the effect of wake sheing influence the ule to inuce a spiraling rising motion. The horizontal movement is oserve less in polymer solution in the case of smaller ules than that of water where the small ules eviate more than the larger ules [6, 7, 23, 24]. 57

6 In the xanthan gum solutions, the horizontal motion of the smaller ule is reuce than that of water ue to increase in viscosity an less friction acting upon their surface compare to the larger ules an so the smaller ules experience less resistance to vertical movement. The larger ules however experience more resistance on top an eform as their size increases that result in spiral motion. Fig. 8 shows the trajectory results of polyacrylamie solution. It can e seen that the polyacrylamie solution shows the similar phenomena as is oserve for xanthan gum solution in Fig. 7. However, the horizontal movement of smaller ules is oserve a little it less in comparison with xanthan gum solution ue to less viscosity of polyacrylamie solution. Distance, mm lease point 0.1mL ule 2mL ule 5mL ule 10mL ule Deviation, mm Fig. 7 Rise trajectories of ifferent sizes of ules in 0.025% xanthan gum solution. Distance, mm lease point 0.1mL ule 2mL ule 5mL ule 10mL ule Deviation, mm Fig. 8 Rise trajectories of ifferent sizes of ules in 0.025% polyacrylamie solution. 3.3 Drag co-efficient Bule rag coefficients as a function of ynols numer for xanthan gum an polyacrylamie solutions are presente in Fig. 9 an Fig. 10 respectively. For 0.1, the creeping flow regime, the governing equation for rag force can e given y [25], F = 3πµ U (9) which is a form of Stokes Law. This Stokes moel is given y 24 C = (10) The equation (10) is only vali for soli ule or particle at very low ynols numer ut not suitale for gas ules rising in power-law liquis. It is note that no universal rag curve for the case of rising air ules in non-newtonian Power-Law fluis has een evelope yet in the availale literature. The gas ules oey the Haamar-Ryczynski moel at very low ynols numer which is given [14] y 16 C = (11) The rag coefficient for soli particles can also e etermine [26] y, C = ( ) + (12) ,300 The aove correlation converges to Stokes moel at low numer. A moifie correlation was propose for gas ules in non-newtonian power-law fluis [3], given y C = ( ) + (13) ,300 The equation (13) converges to the Haamar - Ryczynski equation, at low ynols numer. The following two equations (14) an (15) have een suggeste for spherical ules [21], 6 21 C = (14) 0.5 C 0.5 ( ) 2 = (15) The aove equations are vali for (0.1< < 4000) an ( < 6000) respectively. Again, the equation (14) was also use y other researcher for spherical ule [27]. It can e seen from Fig. 9 that the eviation of the experimental C was initially higher in comparison with the equations (12), (13), (14) an (15) ut this eviation appeare to e less with the increase in. For = 3200 an higher, it is seen that the values of the experimental C an the preicte C from these equations are nearly same an constant. This phenomenon is also oserve in Fig.10 for polyacrylamie solution at = 4000 an higher. 58

7 C Experimental C By equation 12 By equation 13 By equation 14 By equation Fig. 9 Drag coefficients vs. ynols numer for rising air ule in xanthan gum solution.. C Experimental C By equation 12 By equation 13 By equation 14 By equation Fig. 10 Drag coefficients vs. ynols numer for rising air ule in polyacrylamie solution The reporte experimental ata of rag coefficient constitute a new set of ata for air ule at higher ynols numer eyon ynols numer of As seen, these new ata are escrie well with the pulishe equations mentione aove. 5 Conclusions The following conclusions can e reache from this stuy: The average ule rise velocity increases with the increase in ule volume for oth xanthan gum an polyacrylamie solutions. The average ule velocity slightly ecreases with the increase in liqui height for corresponing ule volume. The ule velocity of xanthan gum is foun slightly lower than the velocity in polyacrylamie solution for corresponing ule sizes. The ule velocity is not epenant on the size of the test rig. In the trajectory analysis, it is seen that small ules followe a helical motion while larger ules followe a spiral motion. As the ule size increases, initially, the ule follows straight path, attains its terminal velocity an shape, then it switches to spiral path.this is ue to the increase in viscosity an less resistance on rising of ules. A new set of ata of rag co-efficient are reporte for higher ynols numer eyon the = The relationship etween C - for low concentration polymer solution showe acceptale results with the availale analytical an experimental stuies of the literature ut it eserves further stuy for a wie range of ynols numer. Nomenclature: [m] ule iameter [m] ule height h [m] projecte iameter onto horizontal plane w [m] equivalent sphere iameter eq µ [Pa.s] apparent viscosity [-] ynols numer C [-] rag coefficient F [N] rag force g [m/s 2 ] acceleration ue to gravity U [m/s] ule rise velocity n [-] power law inex K [Pa.s n ] consistency inex g [m/s 2 ] gravitational acceleration γɺ [s -1 ] shear rate Greek letters ρ [kg/m 3 ] ensity ifference etween liqui an air ule [kg/m 3 ] liqui ensity ρ liq ferences: [1] Shosho, C. an Ryan, Micheal, E., An experimental stuy of the motion of long ules in incline tues, Chemical engineering science, 56, 2001, [2] Kulkarni, A. A. an Joshi, J. B., Bule Formation an Bule Rise Velocity in Gas-Liqui Systems: A 59

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