Effect of Foaming Method on Mechanical Properties of Aqueous

Oct 12, 2012 - Beauty Care Laboratory, Kracie Home Products, Ltd., 13 Goudo, Hodogaya, Yokohama, Kanagawa 240-0005, Japan. Ind. Eng. Chem...
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Effect of Foaming Method on Mechanical Properties of Aqueous Foams Prepared from Surfactant Solution Masayuki Yamaguchi,*,† Chiyo Kanoh,† Jiraporn Seemork,† Shogo Nobukawa,† and Kaori Yanase‡ †

School of Materials Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan Beauty Care Laboratory, Kracie Home Products, Ltd., 13 Goudo, Hodogaya, Yokohama, Kanagawa 240-0005, Japan

‡

ABSTRACT: The effect of foaming methods on the linear and nonlinear rheological properties is studied employing foams prepared from aqueous solutions of sodium laurate. It is found that the liquid-phase fraction of the foam prepared by a foaming net is significantly lower than that by a conventional mixer. Consequently, the foaming net provides a stable foam that hardly shows drainage. Moreover, the foam by the foaming net shows low storage modulus, whereas it exhibits high yield stress. As a result, it behaves as an elastic body in the wide range of the strain. Considering that aqueous foams such as facial cleansing are usually prepared by a foaming net, much attention has to be paid to the foaming method. of MgCl2·6H2O in 1000 mL of deionized water. The foaming solution was obtained by dissolving 0.5 g of the sodium laurate in 50 g of the hardness adjustment water. After the solution was stirred for 4 h at 50 °C, it was foamed by a general-purpose mixer (National, Fiber mixer MX-X107) for 1 min. The volume of the mixer was 1000 cc, and the rotation speed of the blades was 10 200 rpm. Moreover, a foaming net (Towa Industries, Magical Fiber Foaming Net) made from polypropylene fibers was also used for foaming. After about 25 mL of the foaming solution was placed on the foaming net, it was rubbed by both hands 15 times, which took approximately 30 s, to obtain the foam. This is a conventional method to obtain a foam in daily life. The same procedure was carried out several times to collect enough foams for the measurements. 2.2. Measurements. The drainage was evaluated by putting the foam into a cylinder of 100 cc. The water level collected at the bottom was measured as a function of time at room temperature. Moreover, the weight of the foam in the 100 cc cylinder was measured to calculate the liquid-phase fraction at the initial condition. Time variation of the liquid-phase fraction was also evaluated at room temperature using a column without bases. The column was made from poly(tetrafluoroethylene) to accelerate the slippage on the surface. As shown in Figure 1, the lengths beyond/below the water level were measured after putting the foam into the column. The liquid-phase fraction ϕL was calculated by the following relation:

1. INTRODUCTION Aqueous foams prepared from surfactant solutions are widely used in our daily life, such as in facial cleansing and body soap. Because consumers’ interest tends to focus on feeling when they touch foam products, the rheological properties have to be controlled precisely to enhance the value of the products. In particular, the elastic properties have to be considered to a great extent, because people are sensitive to elastic properties rather than viscous ones, as clarified by the pioneering study on psychorheology by Scott Blair.1 It is well-known that a foam behaves like an elastic solid in a small strain region and flows beyond the yield stress.2−7 This was visually demonstrated by Kraynik using transparent tubes.3 Furthermore, it has been generally understood that rearrangement of bubbles occurs beyond the yield point as plastic flow. Moreover, the yield stress is known to increase with decreasing liquid-phase fraction of a foam.8−12 The measurements of rheological properties of a foam, however, are not so easy because of the following two reasons:4 (1) slippage on the surface or wall of a rheometer has to be eliminated or quantitatively comprehended, and (2) bubble size and liquid-phase fraction in a foam change with the storage time after foaming due to Ostwald ripening and gravitational drainage. In this Article, linear and nonlinear rheological properties are investigated with basic characterization of a foam prepared from an aqueous solution of sodium laurate. In particular, it is demonstrated that a flow behavior can be evaluated by a simple method using a transparent cylinder and column. Moreover, the effect of the foaming method on the rheological properties is investigated employing a mixer and a conventional foaming net, which gives important information on the material design of a foam product.

ϕL =

(1)

where H and h are the lengths beyond and below the water level, respectively. Bubble size of foams was measured by an optical microscope (Leica, L2). The bubbles were put on a glass plate, and the

2. MATERIALS AND METHODS 2.1. Materials. Sodium laurate purchased from Wako Pure Chemical Industries was used as a surface-active agent. A hardness adjusted water (CaCO3 equivalent is 54 ppm) was prepared by dissolving 47.6 mg of CaCl2·H2O and 43.9 mg © 2012 American Chemical Society

h h+H

Received: Revised: Accepted: Published: 14408

July 27, 2012 October 3, 2012 October 12, 2012 October 12, 2012 dx.doi.org/10.1021/ie302005d | Ind. Eng. Chem. Res. 2012, 51, 14408−14413

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⎛ ⎞ R F ⎜ 1 − κ2 ⎟ σ= κ− κ⎟ 1 ⎟ 2L πR2 ⎜⎜ 2 ln ⎝ ⎠ κ

()

(3)

where R is the inside diameter of a transparent cylinder, F is the pushing force of a column having the diameter of κR and the height of L, and Q is the volumetric flow rate through the gap between the cylinder and column. The shear rate was obtained by σ/η. In this experiment, the cylinder was made from poly(4methyl-1-pentene), and the radius R was 24.8 mm. Moreover, three types of columns having different radii, 22.3, 23.0, and 23.7 mm, were employed to measure the shear viscosity in the wide range of shear rate. The gap distances (R−κR) were 1.1, 1.8, and 2.5 mm, respectively. The length L of all columns was 20 mm. Before measuring the flow curve of a foam, we confirmed that the shear viscosity can be calculated correctly by this apparatus employing a silicone oil.

Figure 1. Schematic illustration of the measurement method of liquidphase fraction.

average radius of the bubbles was calculated by checking more than 100 bubbles. Dynamic surface tension was measured by the bubble pressure method using an automatic dynamic surface tensiometer (Kyowa Interface Science, BP-D5) at room temperature. The sample liquid was the aqueous solution with 1 wt % of sodium laurate. Frequency dependence of oscillatory shear moduli was measured by a parallel-plate rheometer (TA Instruments, AR 2000ex) at room temperature. To avoid slippage, the surface of the plates was covered with a waterproof sandpaper (roughness #100) to eliminate the slippage, following the method by Khan et al. using grooved plates.13 The gap between two plates was 3 mm, which is almost 10 times as large as the diameter of bubbles for the accurate measurement.4 The oscillatory shear strain applied was 1%, and the radius of the plates was 25 mm. Shear stress at steady state was evaluated by a specific apparatus, illustrated in Figure 2, using the Hagen−Poiseuille

3. RESULTS AND DISCUSSION 3.1. Characterization of Foams. The growth curves of the accumlated liquid volume in the cylinder, that is, the amount of gravitational drainage, are shown in Figure 3. The water level

Figure 3. Growth curves of water level in a cylinder (100 cc) for the foams prepared by (closed symbols) the mixer and (open symbols) the foaming net.

increases with time and seems to be a plateau value in an hour. As is well-known, the water in the films of a foam moves to the plateau border by pressure difference due to the curvature at the adjoining channel, called plateau border suction, and then flows downward by gravitational force through the network pass composed of the plateau border.2−7 Furthermore, the drainage rate is found to be significantly affected by the foaming method, although the foaming solution is the same for both foams. Considering that it takes only a few minutes to prepare enough foams by the foaming net, it can be concluded from the figure that the drainage from the foam prepared by the mixer occurs quickly as compared to that from the foaming net. It is also found that the weight of the foam by the mixer is 5.6 g per 100 cc, whereas that by the foaming net is 1.6 g per 100 cc. Therefore, the initial values of the liquid-phase fraction after foaming are 5.6% for the former foam and 1.6% for the latter one. The results demonstrate that the foam prepared by the foaming net is stable for a long time and dry even at the initial stage. On the contrary, a relatively wet foam is obtained by the mixer and turns into a dry one with time.

Figure 2. Schematic illustration of the measurement method of shear viscosity.

law. The system is composed of a transparent cylinder and a column. During the measurement, the force needed to push the column into the foam was collected by a tensile machine (Nidec-Shimpo, FGS-50E) with the volume rate of a foam passing through the gap between the cylinder and column. The shear viscosity η and shear stress σ were provided by the following equations:14 η=

⎛ ⎞ (1 − κ 2)2 ⎟ πσR4 ⎜ 4 (1 ) − κ − ⎟⎟ 1 8LQ ⎜⎜ ln κ ⎝ ⎠

()

(2) 14409

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Figure 4 shows the time variation of the liquid-phase fraction for both foams. The values at t = 0 are almost the same as those

Figure 5. Frequency dependence of the oscillatory shear moduli such as (closed symbols) storage modulus G′ and (open symbols) loss modulus G″ for the foam prepared by the mixer, (circles) 0 min and (diamonds) 10 min after foaming. Figure 4. Liquid-phase fraction as a function of time for the foams prepared by (closed symbols) the mixer and (open symbols) the foaming net.

well without slippage on the surface of plates covered with sandpaper, which is confirmed by changing the gap distance. Moreover, a foam is set in the rheometer and measured again 10 min after foaming to evaluate the time variation of the rheological properties. As seen in the figure, both foams show high level of storage modulus G′ as compared to loss modulus G″. Moreover, the storage modulus hardly depends on the frequency, suggesting that the foam behaves like a solid with low elastic modulus as is well-known.2−7 Furthermore, it is apparent that the modulus decreases with the holding time after foaming, suggesting that a dry foam exhibits low modulus. This is attributed to the increase in the bubble size, leading to the reduction of the surface area of the bubble cell.2−7 The frequency dependence of the oscillatory shear moduli for the foam by the foaming net is shown in Figure 6. As seen

evaluated by the previous experiment. The liquid-phase fraction of the foam by the mixer decreases with time, whereas the foam by the foaming net shows almost a constant value. As a result, both foams show almost the same liquid-phase fraction in an hour. In other words, 1 h is required to be in the quasi-stable state for the foams, at which the liquid-phase fraction is independent of the foaming method. The bubble size is characterized by the optical microscope. The number-average radii of bubbles are shown in Table 1. It is Table 1. Average Radius of Bubbles mixer foaming net

after foaming (μm)

10 min later (μm)

70 160

130 160

found that the size of bubbles prepared by the mixer increases with time because of the gas diffusion from a small bubble to a large one due to the pressure difference between neighbor bubbles having different diameter, which is explained by the Laplace equation.2−7 As seen in the table, on the contrary, the bubble size is almost the same for the foam prepared by the foaming net. The result suggests that plateau border suction is almost balanced with the disjoining pressure occurring in a thin cell wall due to the intermolecular interactions such as van der Waals force and steric interaction for the foam prepared by the foaming net. This result corresponds with Figures 3 and 4. Because of the stability of the foam prepared by the foaming net, the liquid-phase fraction keeps an almost constant value without marked drainage. Although the exact origin of the difference in the stability of the foams is unknown at present, intense shear stress with more chaotic flow in the foaming net may be responsible for the bubbles with thin cell wall. In other words, relentless shear is applied to bubbles in the foaming net. As a result, micelle formation is prohibited in the liquid phase. Furthermore, drainage will be accelerated because mutual dislocation of bubbles excludes excess liquid. Consequently, the drained surfactant solution provides new bubbles by applied force. In the case of the high-speed mixer, however, generated bubbles move upward in which stress level decreases. 3.2. Oscillatory Shear Modulus. The frequency dependence of oscillatory shear modulus for the foam prepared by the mixer is shown in Figure 5. The measurements were performed

Figure 6. Frequency dependence of the oscillatory shear moduli such as (closed symbols) storage modulus G′ and (open symbols) loss modulus G″ for the foam prepared by the foaming net.

in the figure, the foam shows lower storage modulus than that prepared by the mixer without the holding time. Considering that the foaming net provides a dry foam, it is a reasonable result. As can be seen in Figures 5 and 6, both foams (prepared by the mixer and foaming net) show higher level of storage modulus in the high frequency region. It indicates that there is a weak relaxation mechanism in the high frequency region. This is considered to be the relaxation of individual bubbles,5,15,16 although Durian proposed that collective rather than individual bubble relaxations are responsible for the viscoelastic behavior in the short time region.17 Höhler and Cohen-Addad calculated the relaxation time assuming that it is attributed to a relaxation 14410

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of individual bubbles5 and found it to be 10−5 s. Here, we compare the viscoelastic response with the dynamic surface tension, that is, transient surface tension after applied deformation. It is well-known that the surface tension of an aqueous solution decreases with time after agitation because the distribution of surfactant molecules deviates from that at the equilibrium state. Eventually, the surface tension reaches an equilibrium value, that is measured by, for example, the Wilhelmy plate method and the du Nouy ring method. Figure 7 shows the dynamic surface tension for the foaming solution. It is clarified that the surface tension decreases rapidly

Figure 8. Growth curves of the compression force of the column at various compression rates for the foam prepared by the mixer.

Figure 7. Dynamic surface tension of the foaming liquid at room temperature.

in a short time region and reaches a plateau value. The rapid decrease in the surface tension, that is, redistribution process of surfactant molecules, will be the origin of the relaxation mechanism at high frequencies. 3.3. Shear Viscosity. Shear viscosity at the steady state is measured using the specific equipment illustrated in Figure 2. The column compresses the foam, and then the foam flows through the gap between the column and cylinder. In this experiment, various columns are employed considering the ratio of the gap distance to the radius of bubbles. Furthermore, the whole part of the column is soaked in the foam during the experiment to avoid the effect of the surface tension of the column on the apparent compression force. This method has various advantages. First, the water drained hardly affects the measurement because the liquid phase is collected at the bottom of the cylinder by gravitational force. Second, a wide range of shear rate can be covered by changing the diameter of the column. Third, the flow behavior can be monitored through the transparent cylinder. Last and most importantly, foam products such as facial cleansing and body soap are used in a situation similar to this method. Figure 8 examplifies the growth curves of the force (load) at various compression rates. As seen in the figure, the force increases monotonically with time and eventually reaches a plateau value without any overshooting at each compression rate. The shear stress and viscosity are calculated from the steady values of the force and volumetric flow rate using eqs 2 and 3. The apparent shear stress and viscosity are plotted as a function of the shear rate. As shown in Figure 9, the shear stress is almost independent of the shear rate, although some researchers reported strong shear rate sensitivity using 2D foams.18,19 Moreover, the growth curves of the force (Figure 8) indicate that the shear stress in Figure 9 is close to the yield stress of the foam.

Figure 9. Shear rate dependence of (closed symbols) shear stress and (open symbols) shear viscosity for the foam prepared by the mixer without the holding time after foaming. The measurements are performed by three columns: (circles) κR = 22.3 mm, (diamonds) κR = 23.0 mm, and (triangles) κR = 23.7 mm.

The shear stress is measured again 10 min after foaming by the mixer. As shown in Figure 10, it is found that the shear stress becomes higher than that of the initial foam. The result indicates that the dry foam exhibits high shear stress, that is, high yield stress, which agrees with previous research.8,9,11,12,20 According to Gardiner et al.,12 the yield stress σY of the foams

Figure 10. Shear rate dependence of (closed symbols) shear stress and (open symbols) shear viscosity for the foam prepared by the mixer (the holding time after foaming is 10 min). The measurements are performed by three columns: (circles) κR = 22.3 mm, (diamonds) κR = 23.0 mm, and (triangles) κR = 23.7 mm. 14411

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yield stress. The present experimental results suggest that the second part plays an important role in the apparent shear stress. The rheological properties of the foam are clearly dependent upon the characteristics of a foam even using the same foaming solution. The dry foam after drainage shows high yield stress as shown in Figure 10, whereas it exhibits low modulus in the linear region. Consequently, it can be concluded that the yield strain increases with decreasing liquid-phase fraction. In other words, a dry foam shows elastic behavior in a wide strain range. This will be important information on the material design of a foam product, because consumers prefer elastic foam. The flow curve of the foam prepared by the foaming net is shown in Figure 11. Because the liquid-phase fraction is lower

prepared from various surfactants decreases with increasing liquid-phase fraction as shown below: σY =

1/3 0.0165Γ (1 − ϕL) R ϕL1/4

(4)

where Γ is the surface tension, and R is the radius of bubbles. The equation predicts that the yield stress at the initial foam is 130 Pa, using the data of Γ = 28 mN/m, ϕL = 0.05, and R = 70 μm. Although the predicted value is close to the present experimental data, the equation does not express the present results correctly because of the strong effect of the bubble size on the yield stress. When measuring the flow behavior of a foam, the slippage and yield stress have to be taken into consideration.3,21,22 Bretherton first insisted that a foam moves by plug flow on a thin lubricating liquid layer with a thickness of δW, based on the experimental results of a capillary flow.23 He proposed the following equation, which was confirmed by several researchers:2,24−26 (10−5 < Ca < 10−2)

δ W = 1.337rCa 2/3

(5)

where r is the radius of the capillary, and Ca is the capillary number defined by the following relation: Ca =

μL Vb (6)

Γ

where μL is the viscosity of a foaming liquid, and Vb is the bubble velocity. Teletzke et al. considered the effect of intermolecular forces in thin films and modified his relation:27 δ W = 2.12rCa 2/3

(10−5 > Ca)

Figure 11. Shear rate dependence of (closed symbols) shear stress and (open symbols) shear viscosity for the foam prepared by the foaming net without the holding time after foaming. The measurements are performed by three columns: (circles) κR = 22.3 mm, (diamonds) κR = 23.0 mm, and (triangles) κR = 23.7 mm.

(7)

Meanwhile, Heller and Kuntamukkula proposed the following relation focusing on the liquid-phase fraction and the radius of bubbles:2 ⎛ 3μ γ ̇ ⎞2/3 ϕL1/2 δ W = 3.576⎜ L ⎟ R ⎝ Γ ⎠ (1 − ϕ )1/3 L

Finally, Calvert found the following relation: δW =

than the initial foam by the mixer, the stress is higher than that for the foam by the mixer. Similar to the foam left for a long time, the foam prepared by the foaming net shows elastic response in a wide strain region. Furthermore, the results indicate that the preparation method has to be seriously considered to evaluate the rheological properties, especially to correlate with the feeling of consumers.

(8) 20

4. CONCLUSION It is found that the preparation method greatly affects the rheological properties of the foams obtained from aqueous solution with 1 wt % of sodium laurate. The foam prepared by a foaming net has low modulus and high yield stress because of the low value of the liquid-phase fraction, whereas that by a conventional mixer has high modulus and low shear stress. Consequently, elastic response is dominated in a wide strain range for the foam prepared by the foaming net as compared to that prepared by the mixer.

4RϕL 3(1 − ϕL)1/3

(9)

All equations (eqs 5, 7, 8, and 9) predict that the thickness of the liquid layer is in the range from 4 to 15 μm for the present experiments. Assuming that all deformation takes place only in the liquid layer, the shear rate is calculated to be 170−490 s−1. Because the viscosity of the foaming liquid is close to 1 mPa s, the expected shear stress at the layer, that is, local stress, is 0.15−0.45 Pa. This value is too low to provide the measured shear stress in the figure. The result suggests that the stress ascribed to the deformation of bubbles, such as rearrangement of bubbles and interfacial tension due to the enlarged surface area, contributes to the apparent shear stress. According to Prud’homme and Khan,4 there are three parts of a foam at the pressure flow beyond the yield stress. The first one is a thin fluid layer attached to the wall, that is, surface region. The second part located between surface and center regions exhibits the viscous flow by rearrangement of bubbles. The final and center part shows plug flow in which shear stress is below the

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +81-761-51-1621. Fax: +81-761-51-1625. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Scott Blair, G. W. Food Stuffs; North Holland Publisher: Amsterdam, 1853. 14412

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