A Colorful Mixing Experiment in a Stirred Tank Using Non

Laboratory Experiment pubs.acs.org/jchemeduc

A Colorful Mixing Experiment in a Stirred Tank Using Non-Newtonian Blue Maize Flour Suspensions Grissel Trujillo-de Santiago, Cecilia Rojas-de Gante, Silverio García-Lara, Adriana Ballescá-Estrada, and Mario Moisés Alvarez* Centro de Biotecnología-FEMSA, Tecnológico de Monterrey at Monterrey, Monterrey, Nuevo León, CP 64849 Mexico S Supporting Information *

ABSTRACT: A simple experiment designed to study mixing of a material of complex rheology in a stirred tank is described. NonNewtonian suspensions of blue maize flour that naturally contain anthocyanins have been chosen as a model fluid. These anthocyanins act as a native, wide spectrum pH indicator exhibiting greenish colors in alkaline environments, blue tones in neutral conditions, and pink− violet colors in acid environments. Students used a continuous injection of a basic solution in an initially acidic environment to reveal mixing patterns and flow structures and to follow their evolution over time in a typical stirred tank configuration. These experiments aim to demonstrate, in a laboratory setting, basic concepts related to mixing: (i) the existence of mixing pathologies in laminar-stirred tanks; (ii) the complex rheology of some real suspensions; (iii) the effect of tank geometry on mixing performance; and (iv) the quantitation of mixedness and mixing evolution using digital color analysis. KEYWORDS: Second-Year Undergraduate, Upper-Division Undergraduate, Chemical Engineering, Hands-On Learning/Manipulatives, Acids/Bases, Applications of Chemistry, pH, Chemometrics

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INTRODUCTION Mixing is one of the most frequently used unit operations in chemical engineering. In particular, the dispersion of a solid in a liquid is a classic example of a mixing operation occurring in diverse applications in the areas of food technology, biotechnology, mining, refining, polymer processing, and wastewater treatment. In many instances, mixing may determine the quality of a product or the efficiency of a process. The recognized importance of mixing by the scientific community is illustrated by the exponential growth in the number of papers related to this subject in the past decade (see Supporting Information; Figure S1). Despite this practical importance, and with some notable exceptions,1,2 mixing has received modest coverage in chemical engineering textbooks. In addition, fluid mixing has been relatively poorly addressed in journals related to science and engineering education. Only two papers referring to mixing experiments have been published in the Journal of Chemical Education. In one of them, the authors3 illustrated the immiscibility of layers of liquids; in a simple experiment, a homogeneous layer in a multiphasic mixture separated into two new layers upon shaking. In the second, an experiment in which students were introduced to the concept of statistical process control (SPC) through a simple inline mixing experiment is presented.4 In this work, a simple experiment conducted in a stirred tank is presented. Stirred tanks may be the most commonly used agitation equipment in the chemical industry. Mixing at low © 2014 American Chemical Society and Division of Chemical Education, Inc.

speeds and high viscosities (in the laminar regime) is examined. While at low fluid viscosities and/or high agitation rates mixing is caused by turbulence2,5 (see Supporting Information), in the laminar regime mixing mechanistically proceeds by triggering chaos,6−8 and stirred tanks are known to exhibit severe mixing pathologies.8−10 Laminar mixing scenarios are frequently found in practical applications related to food technology,11−13 and biotechnology settings.14,15 In many industrial applications and experimental settings, suspensions behave as non-Newtonian fluids;14,15 they do not obey Newton’s law of viscosity (constant viscosity at different shear or agitation rates). In particular, this experiment is intended to illustrate the complexities of laminar mixing in a real non-Newtonian fluid6,16 (its apparent viscosity is a strong function of shear or agitation rate), using as a model a suspension of blue maize flour (a corn variety native to Mexico) in water. This model is convenient and practical for didactic mixing experiments, because the anthocyanins naturally present in blue maize kernels17−19 serve as a natural pH indicator that undergoes drastic changes in color in a wide range of pH values (1.36 to 11.6; see Figure 1a). This experiment can be used to illustrate to students various general concepts relevant to chemical engineering, including mixing, mixing evaluation, rheology of non-Newtonian mixtures, and the importance of the geometry of a system in mixing efficiency in lab courses Published: September 19, 2014 1729

dx.doi.org/10.1021/ed500150z | J. Chem. Educ. 2014, 91, 1729−1735

Journal of Chemical Education

Laboratory Experiment

Figure 2. Evolution of mixing of a blue maize flour suspension in a stirred tank was followed with the addition of a base in an initially acidic condition. (a) Schematic representation of the lid illustrating the location and nomenclature for the addition ports and the suggested position for a pH probe. (b) Body of the system, divided into 16 sections. (c) Frontal photographic images were taken at different time points during the mixing process. Each image was divided into 16 sections (U1 to L4), and the color in the CIE L*a*b* scale was determined by image analysis of each of the center points (indicated by green circles). Figure 1. Blue maize flour suspended in water exhibits (a) different colors and (b) different viscosities in different pH environments. Curves of apparent viscosity (η) versus strain (γ) are presented for blue maize flour suspensions at different pH values.

acid solution (i.e., HCl 3 N) was dispensed to the system (surface addition) and the system was agitated at 1000 rpm until a uniform pink color was achieved; this gave a pH between 3.0 and 4.0. For best results, this addition was performed slowly using small pulses of acid. From the initial homogeneous acidic condition, the students established a new pH set point value of 8.5 and activated the pH control system. A sodium hydroxide solution (NaOH 1 N) was continuously added dropwise using the bioreactor automatic dispensing system until the pH set point was reached. The excursion of pH induced by the continuous injection of a sodium hydroxide solution (NaOH 1 N) allowed for the visualization of the mixing progress and the existence of mixing pathologies. To follow the evolution of the mixing process, frontal photographic images of the entire tank volume were taken at different times using a professional digital camera (Canon Rebel XTi) mounted on a tripod (Figure 2c and Figure 3). Special care was taken to maintain the illumination quality and the camera position for all pictures. During the lab period, students downloaded images and saved them on a cloud file storage site (i.e., Dropbox, from Dropbox Inc., San Francisco, CA). To complete color analysis, the students imported the images into the application Color Companion 4.0 for iPad (Digital Media Interactive LCC, USA). Using this application, the students determined the color (in the CIE L*a*b* color space) for 16 locations in each image (Figure 2). The students processed the data at home, which required approximately 2 h, and generated plots showing the mixing’s evolution over time based on the distance changes between the color at each point and the color at a final mixing state.

related to transport phenomena, mass transfer phenomena, mass transfer unit operations, or rheology. This experiment could also be appropriate to illustrate the existence of and a practical application for natural pH indicators in an analytical chemistry or a food chemistry course.

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MATERIALS AND METHODS

A Complex and Didactic Fluid Model

A suspension of blue maize flour in water was used as a fluid model. Flours of 150 mesh from decorticated blue maize were obtained according to Rojas-de Gante et al.19 To prepare the suspension, 585 g of blue maize flour was dispersed in 1300 mL of distilled water. Stirred Tank System

The basic requirement for conducting the experiment was a transparent, stirred-tank vessel preferably equipped with a variable speed agitation system. It is desirable, but not necessary, to use a system with a pH monitor and control capabilities. In our particular case, a 3 L fully instrumented Applikon model EZ-control reactor (Applikon Biotechnology, Schiedam, The Netherlands) with a working volume of 1.0 to 1.7 L, equipped with a variable speed control, was used (Figure 2). Visualization Experiments

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Visualization experiments were conducted by teams of three students per tank in individual lab sessions lasting 3 h. Students revealed the 3D mixing patterns within the reactor using a continuous injection of a basic solution in an initially acidic environment. To establish a low-pH initial state, a hydrochloric

HAZARDS Special attention should be placed to preparation and dispensing of the hydrochloric acid and the sodium hydroxide 1730



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THE EXPERIMENT AND THE ANALYSIS OF RESULTS

Rationale of the Experiment

In the related literature, examples of simple experiments to characterize mixing mainly focus on Newtonian systems. Dye injection experiments in transparent or nearly transparent fluids, such as glycerin or water, are typical examples.10,20,21 Frequently, pH indicators are used8 to reveal the transient behavior of a system after the injection of an acidic or basic solution. Here, a model flow consisting of a blue maize suspension that exhibits a complex rheology (i.e., nonNewtonian) allows conducting flow visualization experiments without the need for adding a foreign pH indicator. The anthocyanins naturally present in blue maize flour18 respond to changes in pH by displaying a wide range of colors. At low pH values, blue maize suspensions exhibit a magenta/fuchsia color. Progressively, as pH is increased, transitions to pink, lavender, gray-blue, blue-green, green, and intense green occur (Figure 1a). The presence of this intrinsic and wide-range pH indicator has important practical advantages in the laboratory. In general, available pH indicators exhibit a narrower range of color changes. In a highly viscous system, the adequate dispersion of the indicator might be an issue itself. An additional characteristic makes this system even more interesting from a didactic point of view. Blue maize suspensions not only undergo changes in color as the pH value changes but also show changes in viscosity (see Figure 1b). At basic pH values above 8.0, the viscosity of blue maize suspensions increases dramatically and abruptly, reducing flow and further obstructing mixing.

Figure 3. (a) The CIE L*a*b* scale represents a color in a threecoordinate system in which L is associated with luminosity, ranging from 0 for black to +100 for white. The a and b values define a plane of colors. (b) In the CIE L*a*b* color space, the difference between two colors can be calculated by determining the distance between them in this 3D space.

Visualization of Mixing Pathologies in a Rheological Complex Suspension

solution. In particular, the process of dissolution of NaOH in water is highly exothermic, and NaOH solutions above 0.5 N are corrosive and irritant. Students should wear gloves and protective eyeglasses when preparing or dispensing NaOH solutions. Solution preparation should be done under a safety hood.

In the laminar regime, at low velocities and/or high viscosities, the existence of chaotic motion is mandatory for mixing to occur.6 In conventional stirred tanks, the mechanism for creating chaos and the onset of mixing has been studied in

Figure 4. Mixing evolution in a conventional stirred-tank geometry from an initially homogeneous acidic state (t = 0) toward a final process state (t = 13.0 min) in which segregation still prevails (particularly top−bottom segregation). 1731




Table 1. CIE L*a*b* Scale Color Measurements Taken at Different Times and Positions in the Figure 2 Image Seta Sampling Point, Coordinate j U1

U2

U3

U4

A1

A2

A3

A4

B1

B2

B3

B4

L1

L2

L3

L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b Dij L a b

Time, min; Coordinate i 0

2

3

4

5

6

7

7.5

8

10

11

12

13

52.5 14.8 6.4 22.7 59.3 16.8 5.3 24.8 61.2 19.3 7.0 26.4 60.7 16.1 7.4 23.4 54.0 17.6 5.7 25.2 57.9 18.9 6.3 26.0 60.5 21.3 6.1 28.5 59.2 20.3 8.7 26.4 54.2 15.5 4.8 23.9 57.2 19.0 7.6 25.5 60.6 20.3 6.9 27.3 57.0 18.1 7.7 24.6 31.6 16.9 7.7 34.1 46.2 19.2 9.1 27.0 54.4 18.7 9.9

52.7 17.1 6.1 24.7 59.6 19.3 5.8 26.7 61.6 17.1 6.0 25.1 62.8 18.4 6.6 26.2 53.3 17.0 6.1 24.6 58.4 19.4 5.9 26.7 61.0 20.2 6.8 27.3 61.6 19.1 7.5 26.1 47.5 18.3 6.7 26.7 57.4 18.5 6.1 25.7 59.8 21.5 5.6 28.8 58.4 20.0 8.6 26.1 28.9 16.6 8.3 35.8 52.0 19.4 9.6 25.4 54.8 17.5 8.7

54.3 15.8 6.8 23.1 60.5 18.4 7.2 25.4 61.5 18.8 8.6 25.4 63.7 18.8 8.0 26.2 54.3 17.8 8.2 24.2 58.9 19.6 6.6 26.6 63.8 18.9 9.2 25.8 60.7 18.9 8.6 25.3 52.1 17.5 6.3 25.1 57.7 19.3 8.3 25.5 60.5 19.7 9.0 25.9 58.5 18.0 7.7 24.6 29.0 15.5 8.5 35.0 47.0 22.1 10.4 28.9 54.7 18.1 10.2

52.4 17.4 6.9 24.6 58.6 17.8 8.2 24.2 61.9 20.7 6.4 28.1 62.4 17.0 5.4 25.5 48.9 17.5 7.6 25.2 57.7 17.9 8.3 24.2 62.2 18.6 9.1 25.2 62.7 19.3 8.2 26.3 51.4 16.3 7.7 23.5 56.1 19.2 8.9 25.1 60.7 20.1 9.2 26.2 59.6 19.0 8.7 25.2 27.7 13.9 9.1 35.0 47.7 20.1 10.7 26.8 52.6 17.7 10.7

55.5 15.5 7.8 22.2 63.4 16.1 6.8 24.3 64.2 19.2 8.1 26.6 65.9 18.4 7.2 26.9 55.6 17.3 8.0 23.8 62.7 17.9 7.0 25.5 64.7 19.5 8.3 27.0 64.4 18.2 8.3 25.7 56.4 15.8 8.8 22.1 61.1 17.6 6.9 25.0 64.6 17.8 8.1 25.5 61.8 18.5 9.7 24.8 33.2 14.7 11.9 30.5 51.2 18.4 8.6 25.0 62.0 13.4 10.4

54.6 13.8 5.9 21.8 60.7 15.0 5.2 23.6 61.9 16.6 5.3 25.1 60.6 15.6 7.8 22.7 53.7 8.4 6.2 17.6 58.7 9.9 4.9 19.5 62.4 10.8 7.0 19.7 61.2 9.0 7.5 17.7 50.7 7.7 5.9 18.0 56.5 8.9 5.7 18.1 60.5 9.0 7.5 17.5 57.5 11.1 8.4 18.2 27.8 9.6 7.9 33.3 49.1 13.7 9.7 21.0 53.5 12.0 9.5

55.2 11.5 6.2 19.8 59.9 11.4 5.5 20.4 60.9 15.5 6.6 23.3 59.5 17.5 7.5 24.4 54.4 8.2 5.5 17.9 59.9 6.9 6.1 16.8 61.9 5.7 5.6 17.0 60.9 9.1 8.7 17.0 51.6 3.1 2.3 18.2 55.4 4.1 5.7 15.1 59.4 4.4 5.8 15.4 58.3 11.1 8.4 18.2 27.6 7.3 6.9 32.9 47.9 9.0 8.4 18.4 55.3 8.3 7.9

61.8 11.4 6.7 20.1 65.9 11.0 5.9 21.8 67.5 14.4 7.2 24.3 69.3 15.7 5.4 27.0 60.6 6.5 5.9 16.9 44.7 −5.2 25.9 13.9 69.0 0.2 2.9 20.4 65.3 0.0 7.0 15.0 57.3 −1.5 4.3 14.3 62.2 −0.2 5.3 14.8 66.0 0.0 5.8 16.3 58.0 1.9 5.5 14.2 39.0 6.2 8.1 22.6 59.2 8.5 9.7 15.5 60.6 3.1 7.1

52.5 11.9 10.0 18.4 59.0 12.5 6.5 20.5 61.2 18.1 6.5 25.6 61.0 17.2 6.7 24.7 52.2 7.1 6.3 16.9 58.0 −1.5 5.5 13.2 61.6 −0.6 2.8 16.8 58.9 −1.1 5.6 13.3 50.4 −0.8 5.9 14.1 57.1 −0.4 4.7 14.1 59.2 0.4 4.9 14.4 57.8 −0.7 5.7 13.1 27.0 4.7 7.2 32.5 47.8 8.4 8.8 17.9 54.7 2.4 6.9

61.4 8.0 6.5 17.7 70.9 11.0 9.3 22.9 70.3 16.3 9.1 26.4 71.9 11.1 4.7 25.7 47.2 −3.9 43.2 26.5 52.8 −3.0 31.6 13.8 62.7 −4.5 17.8 6.4 58.2 −5.6 17.1 2.7 48.6 −4.9 16.7 7.9 57.1 −3.7 18.4 0.9 60.5 −4.2 21.5 5.3 58.7 −5.4 16.5 3.3 28.0 −1.7 18.1 28.4 47.0 −3.1 20.5 9.6 52.4 −4.1 20.3

62.7 10.0 8.5 18.3 67.7 7.3 7.9 19.2 71.0 17.6 7.4 28.4 69.4 15.7 8.3 25.8 45.6 −5.4 37.2 21.8 58.4 −4.8 17.4 2.4 61.5 −4.7 20.1 5.5 58.5 −4.7 23.8 6.0 47.4 −4.8 16.3 9.1 56.1 −4.8 17.5 1.1 60.4 −4.7 20.2 4.6 58.5 −4.5 18.0 2.3 25.1 −0.3 14.9 31.6 45.6 −2.3 19.6 10.9 56.9 −2.9 20.4

61.4 9.6 7.1 18.4 68.8 13.2 9.6 23.0 70.5 14.4 6.6 26.1 66.8 16.0 7.9 24.9 44.4 −1.4 38.4 23.5 56.8 −3.8 24.2 5.9 60.7 −5.1 21.7 5.6 59.7 −4.6 21.4 4.6 44.7 −4.8 20.1 11.8 57.2 −3.6 19.6 1.7 60.3 −3.6 21.1 4.9 56.3 −4.6 25.7 7.4 27.2 −1.3 16.4 29.3 46.5 −3.8 23.8 11.2 54.1 −3.5 23.3

66.6 8.9 8.5 19.3 69.8 11.5 7.8 23.1 67.7 16.7 8.2 25.8 66.4 14.5 8.5 23.3 49.2 −3.3 32.3 15.7 59.7 −4.2 19.8 3.7 64.1 −3.2 17.6 7.9 64.9 −3.9 11.5 11.0 45.8 −4.8 18.2 10.5 56.3 −4.1 18.3 0.0 60.9 −4.0 20.9 5.3 56.3 −4.1 23.5 5.2 28.7 −2.7 17.7 27.6 45.8 −3.1 16.9 10.6 61.2 −1.2 21.9

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Table 1. continued Sampling Point, Coordinate j

L4

STD

Dij L a b Dij

Time, min; Coordinate i 0

2

3

4

5

6

7

7.5

8

10

11

12

13

24.4 52.9 18.9 9.4 24.9 2.57

23.7 53.9 19.8 9.2 25.7 2.64

23.7 54.9 20.3 10.6 25.6 2.64

23.4 53.2 20.0 10.5 25.5 2.63

20.0 57.7 19.1 10.6 24.5 2.30

18.6 56.0 11.2 10.3 17.3 4.03

16.2 56.3 10.9 9.5 17.4 4.31

14.0 53.2 2.9 8.3 12.6 4.21

13.2 56.9 1.8 8.5 11.5 5.58

4.4 52.6 −4.8 19.5 4.0 9.75

2.5 58.4 −2.9 18.6 2.4 10.19

5.5 58.0 −1.5 18.5 3.1 9.28

6.7 57.2 −3.3 18.5 1.2 8.74

a

Readings were taken at the center point of each one of the 16 sections defined by the grid in Figure 2b. The distance in the CIE L*a*b* color space to the mixing end point (Di,j) was calculated, as defined by eq 1, for each of the 16 reading positions (U1 to L4) and 13 time points considered in the experiment. For this particular experiment the final mixing point was considered to be the coordinate t = 13 min at location B2. STD is defined as the standard deviation of the Dij values at the 16 reading positions of each time point.

detail.6 Briefly, in the laminar regime, conventional concentrically agitated tanks possess a regular flow skeleton.7 When an impeller with blades is used, the repetitive (and normally periodic) passing of the blades disturbs the otherwise completely regular flow structure, thereby triggering chaos.6,8 However, chaos is not widely distributed in concentric laminarstirred tanks, and different mixing pathologies have been identified in Newtonian laminar-stirred tanks.10 Figure 4 presents a sequence of images corresponding to an experiment in which an initially acidic blue maize flour suspension is agitated in a conventional tank after a basic set point has been established. The tank is equipped with a concentrically located radial impeller with an approximate diameter of 0.33D (where D is the tank diameter) rotating clockwise at 1000 rpm. The H/D of the system is 1.15 (where H is the height of the liquid within the tank). The impeller is located at approximately (1/4)H from the bottom of the tank. This experiment visually illustrates the progression of mixing in a concentrically agitated tank, from an initial homogeneous condition to a final state that shows top−bottom segregation. The students noted the development of an area of high pH (see the dark green zone in Figure 4; time from 7.5 to 13 min) resulting from an accumulation of the base around the point of injection. This suggests that the local intensity of mixing at the point of injection is insufficient to effectively and quickly disperse the base. The increase in pH causes also an increase in viscosity (see Figure 1b), further obstructing the dispersion of the base and aggravating the problem, as revealed by the increase in size of the dark green area (see also Supporting Information; Figure S2). The students (a) observed the progress of the mixing process; (b) understood that the rheology of the system imposed conditions that slowed the progress of the acid−base reaction; (c) recognized that in this case, although the reaction was instantaneous, the mixing process became rate limiting and determined the rate of the overall process; and (d) understood that in concentric systems with this geometry (H/D between 1.1 and 1.3 and one agitator), top−bottom segregation persisted even after extended periods of agitation.

(Figure 3). In this system, each color is characterized by three values, L, a, and b. The L value is associated with luminosity, ranging from 0 for black to +100 for white. The a and b values define a plane of colors, shown in Figure 3, where a ranges from negative to positive values (green to red) and b ranges from negative to positive values (blue to yellow). The students estimated the deviation of a particular state of mixing (at a particular location and time) from the final mixing point or the “ideal mixing” state (presumably the final condition of complete mixing) by evaluating differences in colors in the two states (i.e., evaluating the distance between two corresponding points in the CIE L*a*b* coordinate system). For any two L, a, b value points, the distance in the color space, defined by a straight line connecting both points, was calculated by eq 1. Di , j = [(Li , j − Lf )2 + (ai , j − a f )2 + (bi , j − bf )2 ]0.5

(1)

Here, Di,j is defined as the distance, in the CIE L*a*b* space, of the points defined by the L, a, and b coordinates of the sample taken at time i and location j (Li,j, ai,j, bi,j) and a sample representative of the final mixing state (Lf, af, bf). Digital color analysis (DCA), using colors themselves or digital information on colors, has been suggested before as a tool to quantify chromatic changes.22 Students analyzed this sequence of images using the following protocol. A reference grid was used to define 16 sections within every image (Figures 2b and 2c). The center point within each zone was used as a “sample” location where color was determined according to the CIE L*a*b* scale. Consider a sample taken at a time (i) and a location (j) (for example, t = 8 min and location B3 in Figure 4). The color at this sample point in the CIE L*a*b* scale, as determined by analysis using the Color Companion 4.0 application, was Li,j = 59.2, ai,j = 0.4, bi,j = 4.9 (Table 1). By visual inspection, a final state for the mixing process can be approximated. In this experiment students considered the average of the CIE L*a*b* values at the final time point (t = 13 min) in location B2 (i.e., Lf = 56.3, af = −4.1, bf = 18.3) to approximate a desirable, well-mixed condition (mixing end point). Table 1 presents all L, a, and b color values calculated for the series of images in Figure 4, in each one of the sampling locations indicated in Figure 2c. Based on these values, students calculated the set of distances (Di,j) from each time and location to the mixing end point; Di,j values are also reported in Table 1. Therefore, for the case under consideration, the value of D8min,B3 was 14.4. For the set of images in Figure 3, the distance values (Di,j) in the CIE L*a*b* color space corresponding to all times and sampling points are presented in Table 1. The

Following Mixing Dynamics in a Color Space Using External Images

The students were able to follow the mixing process by analyzing the photographic images in Figure 4. A simple, didactic methodology to quantify the state of mixedness and the mixing dynamics through color change analysis was introduced to students. A color scale normally used for image analysis and color applications, namely, CIE L*a*b*, was used 1733



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average of the Di,j values (at each time point) is physically related to the global deviation of the system with respect to the final state of mixedness or the mixing end point (Figure 5a). In


ASSOCIATED CONTENT

S Supporting Information *

Additional information related to the experimental system; general educational aims; brief discussion on turbulent and laminar mixing; didactic highlights and recommendations on the experiment; application notes related to equipment, software, and materials; suggestions for additional experiments using a similar experimental setting; student handout for instructional scaffolding during the laboratory session. This material is available via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

C.R.-d.G. is currently a Full-Professor at Tecnológico de Monterrey, Campus Ciudad de México, at the Departamento de Ingenieriá en Biotecnologia,́ CP 14380 Tlalpan, México, Distrito Federal, Mexico. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support of Tecnológico de Monterrey (through the seed fund CAT-122) and CONACYT (through the doctoral scholarship provided to G.T.-d.S.) is gratefully acknowledged. The authors deeply appreciate the donation of the blue maize used in our experiments by Eduardo Lovera (at Federación de Agricultores del Edomex, México). The participation of graduate and undergraduate students from the Tecnológico de Monterrey at Monterrey México in our lab sessions is proudly recognized.

Figure 5. Quantitation of mixing through the concept of distances between mixedness states in the CIE L*a*b* color space. (a) Evolution of the average distance (Di,j) with respect to an ideal mixing state condition. (b) Evolution of the standard deviation (STD) from an initially homogeneous condition to a segregated state.

addition, the standard deviation (STD) of all the Di,j values (corresponding to the same time point) is a direct indicator of the degree of heterogeneity in the mixing conditions within the vessel (Figure 5b). The mixing appears to be near completion (set point) by 9 min as the average Di,j values approach a minimum value. However, the STD also reaches a maximum value at ∼9 min, indicating that the mixing is not uniform. Consistent with a simple visual analysis of the images, the students observed in this particular experiment that the system approached a final state of mixedness in which segregation (indicated by the STD value at each time point) was more prevalent than in the initial condition.

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REFERENCES

(1) Ottino, J. M. The Kinematics of Mixing: Stretching, Chaos and Transport. 1st ed.; Cambridge Texts in Applied Mathematics: New York, 1989. (2) Mixing in the Process Industries, 2nd ed.; Harnby, N., Edwards, M. F., Nienow, A. W., Eds.; Elsevier LTD: USA, 1997. (3) Eckelmann, J.; Lüning, U. Mixing liquidsMission impossible? A colorful demonstration on immiscible systems. J. Chem. Educ. 2013, 90, 224−227. (4) Dickey, M. D.; Stewart, M. D.; Willson, C. G.; Dickey, D. A. An automated statistical process control study of inline mixing using spectrophotometric detection. J. Chem. Educ. 2006, 83, 110−113. (5) Kresta, S. M.; Brodkey, R. S. Turbulence in Mixing Applications. In Handbook of Industrial Mixing: Science and Practice, Paul, E. L., Atiemo-Obeng, V., Kresta, S. M., Eds.; Wiley: Hoboken, NJ, 2004; p 19. (6) Alvarez, M. M.; Zalc, J. M.; Shinbrot, T.; Arratia, P. E.; Muzzio, F. J. Mechanisms of mixing and creation of structure in laminar stirred tanks. AIChE J. 2002, 48, 2135−2148. (7) Alvarez-Hernández, M. M.; Shinbrot, T.; Zalc, J. M.; Muzzio, F. J. Practical chaotic mixing. Chem. Eng. Sci. 2002, 57, 3749−3753. (8) Lamberto, D. J.; Alvarez, M. M.; Muzzio, F. J. Experimental and computational investigation of the laminar flow structure in a stirred tank. Chem. Eng. Sci. 1999, 54, 919. (9) Lamberto, D. J.; Alvarez, M. M.; Muzzio, F. J. Computational analysis of regular and chaotic mixing in a stirred tank reactor. Chem. Eng. Sci. 2001, 56 (16), 4887−4899. (10) Alvarez, M. M.; Guzmán, A.; Elías, M. Experimental visualization of mixing pathologies in laminar stirred tank bioreactors. Chem. Eng. Sci. 2005, 60 (8−9 SPEC. ISS.), 2449−2457.

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CONCLUSION Mixing is an important unit operation in chemical engineering processes, yet it is covered relatively poorly in chemical education. A mixing experiment using blue maize flour suspensions as fluid model is presented to demonstrate several important mixing concepts to students. In order to produce an educational and interesting experiment for students, we selected a fluid model with an instrinsically wide range of pH indicators and a highly complex non-Newtonian rheology. Students indicated that the experiment was useful in showing the existence of top−bottom segregation in stirred tanks, illustrating the slower rate of convective mixing in laminar systems compared to their turbulent counterparts, and providing an understanding of the added complexity of agitating a non-Newtonian suspension. Additional recommendations and other mixing experiments based on this blue maize suspension system are provided as Supporting Information. 1734




(11) Maingonnat, J. F.; Doublier, J. L.; Lefebvre, J.; Delaplace, G. Power consumption of a double ribbon impeller with Newtonian and shear thinning fluids and during the gelation of an iota-carrageenan solution. J. Food Eng. 2008, 87, 82−90. (12) Bouvier, L.; Moreau, A.; Line, A.; Faqtah, N.; Delaplace, G. Damage in agitated vessels of large visco-elastic particles dispersed in a highly viscous fluid. J. Food Sci. 2010, 76, E384−E391. (13) Migliori, M.; Correra, S. Modelling of dough formation process and structure evolution during farinograph test. Int. J. Food Sci. Technol. 2013, 48 (1), 121−127. (14) Craig, K. J.; Nieuwoudt, M. N.; Niemand, L. J. CFD simulation of anaerobic digester with variable sewage sludge rheology. Water Res. 2013, 47, 4485−4497. (15) Zhang, H. L.; Baeyens, J.; Tan, T. W. Mixing phenomena in a large-scale fermenter of starch to bio-etanol. Energy 2012, 48, 380− 391. (16) Arratia, P. E.; Shinbrot, T.; Alvarez, M. M.; Muzzio, F. J. Mixing of non-Newtonian fluids in steadily forced systems. Phys. Rev. Lett. 2005, 94, 084501. (17) Ryu, S. H.; Werth, L.; Nelson, S.; Scheerens, J. C.; Pratt, R. C. Variation of kernel anthocyanin and carotenoid pigment content in USA/Mexico borderland land races of Maize. Econ. Bot. 2013, 67, 98− 109. (18) Urias-Peraldí, M.; Gutiérrez-Uribe, J. A.; Preciado-Ortiz, R. E.; Cruz-Morales, A. S.; Serna-Saldívar, S. O.; García-Lara, S. Nutraceutical profiles of improved BM (Zea mays) hybrids for subtropical regions. Field Crops Res. 2013, 141, 69−76. (19) Rojas-de Gante, C.; Ríos-Licea, J. M.; Tinoco-Pérez, B. Method for producing biofilms from cereal grains, biofilms obtained said method and use thereof for producing receptacles for containing and preserving foods. Instituto Tecnológico y de Estudios Superiores de Monterrey. Published on March 2010; WO 2010/024657. (20) Sánchez-Cervantes, M. I.; Lacombe, J.; Muzzio, F. J.; Alvarez, M. M. Novel bioreactor design for the culture of suspended mammalian cells. Part 1: Mixing characterization. Chem. Eng. Sci. 2006, 61, 8075− 8084. (21) Bulnes-Abundis, D.; Carrillo-Cocom, L. M.; Aráiz-Hernández, D.; García-Ulloa, A.; Granados-Pastor, M.; Sánchez-Arreola, P. B.; Murugappan, G.; Alvarez, M. M. A simple eccentric stirred tank minibioreactor: Mixing characterization and mammalian cell culture experiments. Biotechnol. Bioeng. 2013, 110, 1106−1118. (22) Suzuki, K.; Hirayama, E.; Sugiyama, T.; Yasuda, K.; Okabe, H.; Citterio, D. Ionophore-based lithium ion film optode realizing multiple color variations utilizing digital color analysis. Anal. Chem. 2002, 74, 5766−5773.

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A Colorful Mixing Experiment in a Stirred Tank Using Non

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