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Experimental study on the influence of water adsorption effect on water fluidity under different electric field strength
Chemical Physics Letters 735 (2019) 136768
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Research paper
Experimental study on the influence of water adsorption effect on water fluidity under different electric field strength Y.G. Fanga,b, L.F. Guoa, a b
T
⁎
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, Guangdong, China State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou, Guangdong, China
H I GH L IG H T S
viscosity of water is affected by Coulomb interaction caused adsorption. • Dynamic electric field strength can increase the dynamic viscosity of water. • Growing growth of the hydraulic gradient is not conductive to Coulomb adsorption. • The • The influence of ion on Coulomb adsorption differs in different hydraulic gradient.
A R T I C LE I N FO
A B S T R A C T
Keywords: Water adsorption Dynamic viscosity Electric field Ion concentration Seepage
Water adsorption effect on a solid surface can change water fluidity and viscosity to leave an impact on engineering processes. However, the water adsorption effect caused by Coulomb interaction (Coulomb adsorption) has seldom been tested. Therefore, this paper designed a narrow slot seepage experiment to study the water adsorption effect on water fluidity under different external electric field along with different ion concentration and hydraulic gradient. The experiment results showed that the dynamic viscosity of water in the slot would be enhanced by the growing electric field strength; the growth of hydraulic gradient was not conductive to Coulomb adsorption; and there was a threshold hydraulic gradient iT (around 26.67 in this paper) that when i > iT, the growth of ion concentration would be conductive to Coulomb adsorption, while it would be adverse to Coulomb adsorption when i < iT.
1. Introduction Unsaturated charges enriched on a solid surface were reported to have adsorption effect on water [1], which can change the viscosity of water to reduce its fluidity, prolong its migration and redistribution processes, for example, the diffusion of contaminant ions in groundwater [2]. Different charge density on a different material surface can cause different water adsorption effect, which was reported as useful in the industry [3,4]. In addition, the water adsorption effect within many engineering media, such as industrial materials, mineral powders, rivers, and marine sediments can affect their permeability, rheological, plastic and mass transfer characteristics [5–7], and leave an impact on engineering processes. Therefore, tests on water adsorption effect of different solid media can provide reference data for many human activities. However, recent researches focused more on solid media with very small scales, such as media with nanometer-scale pores or nanofluidic channels [7–11], while the adsorption effect in media with ⁎
broader scale channels could be different. In fact, surface adsorption is usually due to van der Waals interaction [12] and Coulomb interaction [13], in other words, the adsorption effect of non-electrostatic particles [14] and electrostatic particles [15]. Van der Waals force pertains to the dipole moment between molecules, and its interaction potential between single molecule is inversely proportional to the 6th power of the distance between the molecules [16]; while Coulomb interaction potential is inversely proportional to the distance between the charges [17]. Therefore, with a smaller decay rate, the adsorption effect caused by Coulomb force (Coulomb adsorption) in some micron-sized channels could be more significant and is necessary to be studied specifically. To study this different effect, in this paper, an artificial-electricfield-narrow-slot (AENS) seepage experiment was designed. In the experiment, two charged plates were used to generate electrostatic effect (similar with the effect manifested in [18]) and adsorb polar water molecules, in order to study the effect of Coulomb adsorption on the viscosity of water within a 500 μm width slot; in which, the effect of ion
Corresponding author. E-mail address: [email protected] (L.F. Guo).
https://doi.org/10.1016/j.cplett.2019.136768 Received 2 June 2019; Received in revised form 21 August 2019; Accepted 12 September 2019 Available online 12 September 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
Chemical Physics Letters 735 (2019) 136768
Y.G. Fang and L.F. Guo
to the dipole moment of water. Eq. (1) showed that the potential of Coulomb adsorption is inversely proportional to the second power of the distance between the charge and the center of the water molecule, and is proportional to the dipole moment of water molecules. Therefore, in consideration of van der Waals potential is inversely proportional to the 6th power of the distance between molecules according to Lennard-Jones potential expression [16], it’s clear that the decay rate of van der Waals adsorption is much faster than Coulomb adsorption. In other words, the influence range of Coulomb adsorption could be much larger than van der Waals adsorption. Especially in some micron-sized channels, the adsorption effect caused by Coulomb force can be more significant than that of van der Waals adsorption. Therefore, the experiment here mainly focused on studying the Coulomb adsorption effect under different external field (electric field and flow field), using the fluidity of the flow field to evaluate the adsorption effect. Higher adsorption potential will manifest stronger hindrance to the flow field, causing lower flowing velocity and greater dynamic viscosity of the fluid. Eq. (1) can be used to analyze the experiment results, while the adsorption of water molecules by all charges on narrow slot surfaces can be obtained by integral calculation of Eq. (1). When there are ions in water, the cations/anions will respectively gather in the vicinity of the cathode/anode surface according to Boltzmann distribution, and the Coulomb adsorption calculation will become complicated. In this paper, the effect of ion concentration on Coulomb adsorption was discussed according to the analysis of experimental results.
concentration and hydraulic gradient on Coulomb adsorption were also considered. The experiment results revealed the variation regularity of water fluidity affected by Coulomb adsorption effect generated by different electric field strength, which may benefit in guiding engineering practices. Moreover, the experiment method proposed in this paper can be used to simulate and study the water adsorption effect in many different material formations. 2. Experiment 2.1. Theoretical part Surface adsorption is usually caused by van der Waals adsorption (molecular adsorption) and Coulomb adsorption (electrostatic adsorption). The adsorption potential between molecules of the former decays rapidly with the 6th power of the distance between molecules, while that of the latter decays slowly with the 1st power of the distance between charges, which needs to be studied in a larger scale. The adsorption effects involved in this study was mainly Coulomb adsorption (adsorption caused by Coulomb interaction). Here the Coulomb adsorption was caused by charges induced by the external electric field, the attraction of surface electrostatic charges to polar water molecules. The potential of Coulomb adsorption of single charge j with charge amount q0 on the slot surface to polar water molecule i can be expressed by Eq. (1) (referring to the expression of Coulomb force [17]).
dVij =
1 1 1 2e ·q0 ⎛ ⎞ − · ⎜ ⎟ 4πε0 εr ⎝ rij + re cos θi rij − re cos θi ⎠
2.2. Materials and experiment devices
(1-a)
Eq. (1-a) can be simplified to:
1 2e ·de ·q0 cos θi dVij = · · 2 εr 4πε0 rij − re2cos2 θi
The experiment here was termed as artificial-electric-field-narrowslot (AENS) seepage experiment; it consists of a high voltage DC power supply, narrow slot seepage device, seepage head control panel, precision pressure gauge, etc., which are shown in Fig. 2a. Amidst, the narrow slot seepage device was made of electrical plastic with a 500 μm width micro-permeability slot carved on it, and the electrodes at both ends of the narrow slot seepage device were two parallel electrode plates. Referred to clay pores of flaky clay minerals [19,20], the slot was carved into a narrow plane slot. The sizes and the sketch of the narrow slot seepage device are demonstrated in Fig. 2b and d. The external electric field was set perpendicular to the seepage direction, which was provided by the high voltage DC power supply (adjustable voltage ranges from 0 to 50 kV), so as to generate different charge density on slot surface and different electric field strength in the slot. To comparably simulate the water adsorption effect of different media, the experiment was designed according to the three similarity principals [21]. In the narrow-slot device, positive and negative charges on the left and right side walls of the narrow slot that generated by the artificial electric field would respectively adsorb polar water molecules to form adsorption water films (Fig. 2c). The adsorbed water films formed by negative and positive charges have equivalent properties, thus they can both hinder the water flow in the narrow slot.
(1-b)
In Eq. (1), dVij represents the adsorption potential of surface charge j to the polar water molecule i; re = de /2 and de is the distance between the negative and positive charges of a water molecule expressed by °
de = 0.97A cos(105° /2) , corresponding to Fig. 1; q0 andrij are respectively the charge quantity of charge j and the central distance between the charge j and water molecule i; θi is the angle between de and rij (shown in Fig. 1), and θi = arc cos(z i / rij ) − θ ; however, the direction angle θ has a certain random distribution range which increases with the increase of distance from the surface; ε0 and εr are respectively the vacuum dielectric constant and the relative dielectric constant. In Eq. (1-b), 2e ·de indicates the water molecular dipole moment, which meant that the adsorption potential of charge on polar water molecule is proportional
2.3. Experiment method Since the narrow slot device was equivalent to a parallel plate capacitance, the electric field between the two electrodes can be regarded as a uniform electric field. Therefore, in the AENS seepage model, the relationship between the electric field strength in the narrow slot Ebc was calculated by Eq. (2) [17].
Uad
Ebc = εw
(
2Lab εp
+
2Lbc εw
)
(2)
where Ebc is the electric field strength in the water of the narrow slot, which is depicted in Fig. 2c; Uad is the DC voltage applied to the electrode a and d; εp = 3, which is the relative dielectric constant of the
Fig. 1. Schematic diagram of Coulomb adsorption on two layers of water molecules. 2
Chemical Physics Letters 735 (2019) 136768
Y.G. Fang and L.F. Guo
Fig. 2. Photos of the artificial-electric-field-narrow-slot (AENS) seepage experiment and sketch graphs of the narrow slot seepage device. (a) shows the parts of the experiment; (b) is a photo of the seepage device; (c) and (d) are sketch graphs of the seepage device, while (c) demonstrates the distribution of the electric potential ψ, electric field strength E, and surface charges of the device, and (d) depicts the sizes of the device. In graph (c), the adsorbed water films (thickness δb and δc) formed by the positive and negative charges can both hinder the water flow. In graph (d), H = 45 mm, D = 30 mm, Lab = Lcd = 0.5 mm, Lbc = 0.5 mm. Briefly, AENS seepage experiment is a seepage experiment with an external electric field set perpendicular to the flow direction.
electrical plastic; Lab = 30 mm and Lbc = 0.5 mm are respectively the thickness and the width of electrical plastic and narrow slot (can be found in Fig. 2d). During the seepage experiment, the DC voltages on both sides of the seepage device were set respectively as 0, 10, 20, 30 and 40 kV; while, correspondingly, the electric field strength in the slot Ebc was calculated as 6.17, 12.34, 18.51 and 24.68 kV/m. Under the abovementioned set parameters, five different hydraulic gradients (6.67, 11.11, 17.78, 26.67, 66.67) and three ion concentrations (0%, 1% & 5% NaCl aqueous) were considered to compare the different influences on flow velocity and viscosity. Based on the experiment data, gathered with the other two factors, the regularity of the water adsorption effect (Coulomb adsorption) caused fluidity (seepage velocity) and viscosity changes of water were analyzed.
v = i·
2Dh2 ρg ηC
(3)
In Eq. (3), Dh = 4A/S is the hydraulic diameter; A is the slot’s crosssectional area; S is the wet perimeter; η is the dynamic viscosity of water; ρ is the mass density of water; g is the acceleration of gravity; C = 96 is the friction factor of the slot. To better reveal the influence of water adsorption effect on flow fluidity, based on Eq. (3), the relative dynamic viscosity n = η/η0 was used to describe the change of water fluidity, while η0 is the reference dynamic viscosity for comparison, which herein referred to the dynamic viscosity of pure water when i = 6.67 and Ebc = 0. Moreover, to facilitate studying the tangled influences of electric field strength Ebc, ion concentration n0, and hydraulic gradient i on the water adsorption effect that affects the water fluidity, the change ratio of the relative dynamic viscosity γ was calculated, which was defined as the ratio of the viscosity change between Ebc = 0 and Ebc = 24.68 kV/m when Ebc = 0,
3. Results and discussion
n |Ebc = 24.68kV/m −n |Ebc = 0.00kV/m
. Based on the AENS seepage ex-
3.1. Experiment results
i. e., γ =
The experimental results of the artificial-electric-field-narrow-slot (AENS) seepage experiment are given here. First, the average water seepage velocity within the narrow slot under different hydraulic gradient, electric field strength Ebc, and ion concentration of NaCl aqueous solution are shown in Fig. 3. The average seepage velocity under different electric field strength and different ion concentration maintained an approximately linear relationship with the hydraulic gradient (Fig. 3a), while it’s actually nonlinear; with the increase of Ebc, the seepage velocity of the aqueous solution passed through the narrow slot decreased (Fig. 3b); while the seepage velocity correspondingly decreased with the rise of the ion concentration (Fig. 3c). In this paper, the seepage velocity corresponding to the hydraulic gradient i = 6.67–66.7 was tested to be v = 0.015–0.17 m/s, of which the corresponding Reynolds number was Re = 15–167 according to the works of Touloukian et al. [22] and Gravesen et al. [23]. Therefore, the water flow in the slot was distinguished as laminar flow, which its average velocity can be calculated by Eq. (3) [22,24].
periment results, the variation of relative dynamic viscosity n and the change ratio γ are presented in Fig. 4. The results in Fig. 4a demonstrates that the relative dynamic viscosity n of water flow in the slot increased along with the growth of Ebc and n0, and decreased with the growth of hydraulic gradient i, which was essentially consistent with the seepage velocity experiment results in Fig. 3. Furthermore, shown by Fig. 4b, the change ratio of viscosity γ would decrease with the growth of ion concentration n0 when the hydraulic gradient i is small (less than 26.67), while the relationship of γ and n0 would become the opposite and less significant when i is greater than 26.67; shown by Fig. 4c, regardless of the change of ion concentration n0, γ decreased with the growth of hydraulic gradient i. The above descriptions meant that, the increase of electric field strength can enhance the water adsorption effect on the slot sidewalls to increase the water viscosity in the slot, while the enhancement rate would decrease with the growth of ion concentration n0 when the hydraulic gradient i is small, and the enhancement rate would decrease with the growth of hydraulic gradient i. 3
n |Ebc = 0.00kV/m
Chemical Physics Letters 735 (2019) 136768
Y.G. Fang and L.F. Guo
(b)
(a)
(c)
18 6 5
16
4
Flow velocity v (10-2m/s)
14 3 2
12
1 10
15
20
25
Approximate linearity, 10 actually nonlinear
8 Ebc= 0.00kV/m
6
Ebc= 6.17kV/m Ebc= 12.34kV/m
4
Ebc= 18.51kV/m Ebc= 24.68kV/m Ion concentration 0% Ion concentration 5%
2 0
10
20
30
40
50
60
70
Hydraulic gradient i Fig. 3. Results of average seepage velocity in the narrow slot; (a) the relationship between flow velocity and hydraulic gradient; (b) the relationship between flow velocity and electric field strength; (c) the relationship between flow velocity and ion concentration.
4. Second, according to Eq. (1), the greater the distance between water molecules with the slot surface is, the weaker the Coulomb adsorption will be. We assumed that water flow driven by higher hydraulic gradient i is able to overcome stronger Coulomb adsorption potential, drive more adsorbed water into flowing state and thus weaken its resistance (just like static friction is greater than sliding friction). Then the decrease in the change ratio γ presented in Fig. 4c can be explained as the growth of hydraulic gradient has driven more parts of the adsorbed water layer and reduced its resistance to the flow. Third, ions aggregated on the cathode and anode surface can hinder the induced charge q0 from adsorbing water molecules in the further distance (shielding effect). The growth of ion concentration will enhance the shielding effect and enlarge its affecting range (consistent with Gouy-
3.2. Discussion and analysis With a few proofs and assumptions, the above-described changes of water viscosity were given possible explanations. First, the growth of electric field strength can increase the charge density on the slot surface. Referring to the relationship between induced charge and the potential of Coulomb adsorption given in Eq. (1), it can be learned that the increase of charge density would enhance Coulomb adsorption effect by increasing the water molecular dipole moment (2e ·de ); due to Coulomb adsorption effect, the streaming potential will increase the resistance of water flowing [25–27]; therefore, when the electric field strength was increased, higher resistance to the flow (decreased velocity) and growing dynamic viscosity would be manifested in Figs. 3 and
(b)
1.7
Change ratio of relative dynamic viscosity Ȗ (%)
The relative viscosity of fluid n
70
Ion concentration 0% Ion concentration 1% Ion concentration 5%
1.6
i=11.11 i=26.67 i=66.67
1.5 1.4 1.3 1.2 1.1 1.0 0.9
5
10
15
20
25
Electric field strength Ebc (kV/m)
70
i=6.67 i=11.11 i=17.78 i=26.67 i=66.67
60
50
40
30
20
10
0
0
(c)
Change ratio of relative dynamic vicosity Ȗ (%)
(a)
0
1
2
3
4
Ion concentration n0 (%)
5
n0=0% n0=1%
60
n0=5% 50
40
30
20
10
0
0
10
20
30
40
50
60
70
Hydraulic gradient i
Fig. 4. The relative dynamic viscosity results of the flow in the narrow slot; (a) Variation curve of the relative dynamic viscosity with electric field strength; (b) Variation curve of the change ratio with ion concentration; (c) Variation curve of the change ratio with hydraulic gradient. The change ratio of the relative dynamic viscosity was calculated by γ =
n |E = 24.68kV/m −n |E = 0.00kV/m bc bc . n |E = 0.00kV/m bc
4
Chemical Physics Letters 735 (2019) 136768
Y.G. Fang and L.F. Guo
Technology (Grant No. 2017KB16) and the National Key Scientific Instruments and Equipment Development Projects of China (Grant No. 41827807).
Chapman's theory [28,29]), which will benefit the seepage velocity of water; meanwhile, according to the hydration effect [30], the increase of ion concentration will also increase the number of ionized water molecule, which will decrease the seepage velocity of water and increase water viscosity. Therefore, the regularity presented in Fig. 4b can be reasoned as follows. When the hydraulic gradient is small (less than 26.67), the water flow can only drive a slight part of the adsorbed layer; with the growth of ion concentration, part of the static adsorbed water (not in a flowing state) would be thinned, which would then increase the fluidity of water and reduce its viscosity. On the other hand, when the hydraulic gradient was greater than 26.67, the growth of ion concentration would only reduce the width of flowing-state adsorbed water layer which would slightly increase the water fluidity; and when this increased effect was even weaker than the hydration effect that would increase the viscosity, the change ratio γ of viscosity would then be increased by the growth of ion concentration. In this paper, there was a threshold hydraulic gradient iT (around 26.67) which can divide the two different influences of ion concentration on the change ratio γ. The threshold hydraulic gradient iT indicated a transition state in which the change ratio γ would first decrease and then increase with the growth of ion concentration (Fig. 4b).
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4. Conclusions Unsaturated charges enriched on a solid surface can cause adsorption effect on water, which can leave significant impacts on some engineering processes. However, the adsorption effect caused by Coulomb interaction (the attraction between charges, termed as Coulomb adsorption) hasn’t been widely studied; experimental studies on Coulomb adsorption effect to water are still lacking. Therefore, in this paper, the artificial-electric-field-narrow-slot (AENS) seepage experiment was designed to study the Coulomb adsorption effect induced by different electric field strength; in which, the surface charges on the slot walls were generated by the artificial electric field that was set perpendicular to the flow direction. By means of AENS seepage experiment, the combined influence of electric field strength, ion concentration and hydraulic gradient on water fluidity were studied and analyzed. Based on the experiment results, it’s been found that: (1) the growth of electric field strength would enhance Coulomb adsorption to increase the dynamic viscosity of water in the slot; (2) the growth of hydraulic gradient is not conductive to Coulomb adsorption; (3) there is a threshold hydraulic gradient iT (nearby 26.67 in this paper) that when hydraulic gradient i < iT, the growth of ion concentration would be adverse to Coulomb adsorption, while it would instead be conductive to Coulomb adsorption when i > iT. The experiment in this paper intuitively presented the variation regularity of water fluidity affected by Coulomb adsorption effect generated by different electric field strength. The regularity and mechanism of this experiment could benefit in guiding engineering practices. The experiment method proposed in this paper can also be used to simulate and study the water adsorption effect in many different material formations, for example, clayey soil. Experiments that focus on simulating specific materials under specific conditions will be further studied in the future. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments We would like to acknowledge financial supports from the State Key Lab of Subtropical Building Science, South China University of
5
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Research paper
Experimental study on the influence of water adsorption effect on water fluidity under different electric field strength Y.G. Fanga,b, L.F. Guoa, a b
T
⁎
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, Guangdong, China State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou, Guangdong, China
H I GH L IG H T S
viscosity of water is affected by Coulomb interaction caused adsorption. • Dynamic electric field strength can increase the dynamic viscosity of water. • Growing growth of the hydraulic gradient is not conductive to Coulomb adsorption. • The • The influence of ion on Coulomb adsorption differs in different hydraulic gradient.
A R T I C LE I N FO
A B S T R A C T
Keywords: Water adsorption Dynamic viscosity Electric field Ion concentration Seepage
Water adsorption effect on a solid surface can change water fluidity and viscosity to leave an impact on engineering processes. However, the water adsorption effect caused by Coulomb interaction (Coulomb adsorption) has seldom been tested. Therefore, this paper designed a narrow slot seepage experiment to study the water adsorption effect on water fluidity under different external electric field along with different ion concentration and hydraulic gradient. The experiment results showed that the dynamic viscosity of water in the slot would be enhanced by the growing electric field strength; the growth of hydraulic gradient was not conductive to Coulomb adsorption; and there was a threshold hydraulic gradient iT (around 26.67 in this paper) that when i > iT, the growth of ion concentration would be conductive to Coulomb adsorption, while it would be adverse to Coulomb adsorption when i < iT.
1. Introduction Unsaturated charges enriched on a solid surface were reported to have adsorption effect on water [1], which can change the viscosity of water to reduce its fluidity, prolong its migration and redistribution processes, for example, the diffusion of contaminant ions in groundwater [2]. Different charge density on a different material surface can cause different water adsorption effect, which was reported as useful in the industry [3,4]. In addition, the water adsorption effect within many engineering media, such as industrial materials, mineral powders, rivers, and marine sediments can affect their permeability, rheological, plastic and mass transfer characteristics [5–7], and leave an impact on engineering processes. Therefore, tests on water adsorption effect of different solid media can provide reference data for many human activities. However, recent researches focused more on solid media with very small scales, such as media with nanometer-scale pores or nanofluidic channels [7–11], while the adsorption effect in media with ⁎
broader scale channels could be different. In fact, surface adsorption is usually due to van der Waals interaction [12] and Coulomb interaction [13], in other words, the adsorption effect of non-electrostatic particles [14] and electrostatic particles [15]. Van der Waals force pertains to the dipole moment between molecules, and its interaction potential between single molecule is inversely proportional to the 6th power of the distance between the molecules [16]; while Coulomb interaction potential is inversely proportional to the distance between the charges [17]. Therefore, with a smaller decay rate, the adsorption effect caused by Coulomb force (Coulomb adsorption) in some micron-sized channels could be more significant and is necessary to be studied specifically. To study this different effect, in this paper, an artificial-electricfield-narrow-slot (AENS) seepage experiment was designed. In the experiment, two charged plates were used to generate electrostatic effect (similar with the effect manifested in [18]) and adsorb polar water molecules, in order to study the effect of Coulomb adsorption on the viscosity of water within a 500 μm width slot; in which, the effect of ion
Corresponding author. E-mail address: [email protected] (L.F. Guo).
https://doi.org/10.1016/j.cplett.2019.136768 Received 2 June 2019; Received in revised form 21 August 2019; Accepted 12 September 2019 Available online 12 September 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
Chemical Physics Letters 735 (2019) 136768
Y.G. Fang and L.F. Guo
to the dipole moment of water. Eq. (1) showed that the potential of Coulomb adsorption is inversely proportional to the second power of the distance between the charge and the center of the water molecule, and is proportional to the dipole moment of water molecules. Therefore, in consideration of van der Waals potential is inversely proportional to the 6th power of the distance between molecules according to Lennard-Jones potential expression [16], it’s clear that the decay rate of van der Waals adsorption is much faster than Coulomb adsorption. In other words, the influence range of Coulomb adsorption could be much larger than van der Waals adsorption. Especially in some micron-sized channels, the adsorption effect caused by Coulomb force can be more significant than that of van der Waals adsorption. Therefore, the experiment here mainly focused on studying the Coulomb adsorption effect under different external field (electric field and flow field), using the fluidity of the flow field to evaluate the adsorption effect. Higher adsorption potential will manifest stronger hindrance to the flow field, causing lower flowing velocity and greater dynamic viscosity of the fluid. Eq. (1) can be used to analyze the experiment results, while the adsorption of water molecules by all charges on narrow slot surfaces can be obtained by integral calculation of Eq. (1). When there are ions in water, the cations/anions will respectively gather in the vicinity of the cathode/anode surface according to Boltzmann distribution, and the Coulomb adsorption calculation will become complicated. In this paper, the effect of ion concentration on Coulomb adsorption was discussed according to the analysis of experimental results.
concentration and hydraulic gradient on Coulomb adsorption were also considered. The experiment results revealed the variation regularity of water fluidity affected by Coulomb adsorption effect generated by different electric field strength, which may benefit in guiding engineering practices. Moreover, the experiment method proposed in this paper can be used to simulate and study the water adsorption effect in many different material formations. 2. Experiment 2.1. Theoretical part Surface adsorption is usually caused by van der Waals adsorption (molecular adsorption) and Coulomb adsorption (electrostatic adsorption). The adsorption potential between molecules of the former decays rapidly with the 6th power of the distance between molecules, while that of the latter decays slowly with the 1st power of the distance between charges, which needs to be studied in a larger scale. The adsorption effects involved in this study was mainly Coulomb adsorption (adsorption caused by Coulomb interaction). Here the Coulomb adsorption was caused by charges induced by the external electric field, the attraction of surface electrostatic charges to polar water molecules. The potential of Coulomb adsorption of single charge j with charge amount q0 on the slot surface to polar water molecule i can be expressed by Eq. (1) (referring to the expression of Coulomb force [17]).
dVij =
1 1 1 2e ·q0 ⎛ ⎞ − · ⎜ ⎟ 4πε0 εr ⎝ rij + re cos θi rij − re cos θi ⎠
2.2. Materials and experiment devices
(1-a)
Eq. (1-a) can be simplified to:
1 2e ·de ·q0 cos θi dVij = · · 2 εr 4πε0 rij − re2cos2 θi
The experiment here was termed as artificial-electric-field-narrowslot (AENS) seepage experiment; it consists of a high voltage DC power supply, narrow slot seepage device, seepage head control panel, precision pressure gauge, etc., which are shown in Fig. 2a. Amidst, the narrow slot seepage device was made of electrical plastic with a 500 μm width micro-permeability slot carved on it, and the electrodes at both ends of the narrow slot seepage device were two parallel electrode plates. Referred to clay pores of flaky clay minerals [19,20], the slot was carved into a narrow plane slot. The sizes and the sketch of the narrow slot seepage device are demonstrated in Fig. 2b and d. The external electric field was set perpendicular to the seepage direction, which was provided by the high voltage DC power supply (adjustable voltage ranges from 0 to 50 kV), so as to generate different charge density on slot surface and different electric field strength in the slot. To comparably simulate the water adsorption effect of different media, the experiment was designed according to the three similarity principals [21]. In the narrow-slot device, positive and negative charges on the left and right side walls of the narrow slot that generated by the artificial electric field would respectively adsorb polar water molecules to form adsorption water films (Fig. 2c). The adsorbed water films formed by negative and positive charges have equivalent properties, thus they can both hinder the water flow in the narrow slot.
(1-b)
In Eq. (1), dVij represents the adsorption potential of surface charge j to the polar water molecule i; re = de /2 and de is the distance between the negative and positive charges of a water molecule expressed by °
de = 0.97A cos(105° /2) , corresponding to Fig. 1; q0 andrij are respectively the charge quantity of charge j and the central distance between the charge j and water molecule i; θi is the angle between de and rij (shown in Fig. 1), and θi = arc cos(z i / rij ) − θ ; however, the direction angle θ has a certain random distribution range which increases with the increase of distance from the surface; ε0 and εr are respectively the vacuum dielectric constant and the relative dielectric constant. In Eq. (1-b), 2e ·de indicates the water molecular dipole moment, which meant that the adsorption potential of charge on polar water molecule is proportional
2.3. Experiment method Since the narrow slot device was equivalent to a parallel plate capacitance, the electric field between the two electrodes can be regarded as a uniform electric field. Therefore, in the AENS seepage model, the relationship between the electric field strength in the narrow slot Ebc was calculated by Eq. (2) [17].
Uad
Ebc = εw
(
2Lab εp
+
2Lbc εw
)
(2)
where Ebc is the electric field strength in the water of the narrow slot, which is depicted in Fig. 2c; Uad is the DC voltage applied to the electrode a and d; εp = 3, which is the relative dielectric constant of the
Fig. 1. Schematic diagram of Coulomb adsorption on two layers of water molecules. 2
Chemical Physics Letters 735 (2019) 136768
Y.G. Fang and L.F. Guo
Fig. 2. Photos of the artificial-electric-field-narrow-slot (AENS) seepage experiment and sketch graphs of the narrow slot seepage device. (a) shows the parts of the experiment; (b) is a photo of the seepage device; (c) and (d) are sketch graphs of the seepage device, while (c) demonstrates the distribution of the electric potential ψ, electric field strength E, and surface charges of the device, and (d) depicts the sizes of the device. In graph (c), the adsorbed water films (thickness δb and δc) formed by the positive and negative charges can both hinder the water flow. In graph (d), H = 45 mm, D = 30 mm, Lab = Lcd = 0.5 mm, Lbc = 0.5 mm. Briefly, AENS seepage experiment is a seepage experiment with an external electric field set perpendicular to the flow direction.
electrical plastic; Lab = 30 mm and Lbc = 0.5 mm are respectively the thickness and the width of electrical plastic and narrow slot (can be found in Fig. 2d). During the seepage experiment, the DC voltages on both sides of the seepage device were set respectively as 0, 10, 20, 30 and 40 kV; while, correspondingly, the electric field strength in the slot Ebc was calculated as 6.17, 12.34, 18.51 and 24.68 kV/m. Under the abovementioned set parameters, five different hydraulic gradients (6.67, 11.11, 17.78, 26.67, 66.67) and three ion concentrations (0%, 1% & 5% NaCl aqueous) were considered to compare the different influences on flow velocity and viscosity. Based on the experiment data, gathered with the other two factors, the regularity of the water adsorption effect (Coulomb adsorption) caused fluidity (seepage velocity) and viscosity changes of water were analyzed.
v = i·
2Dh2 ρg ηC
(3)
In Eq. (3), Dh = 4A/S is the hydraulic diameter; A is the slot’s crosssectional area; S is the wet perimeter; η is the dynamic viscosity of water; ρ is the mass density of water; g is the acceleration of gravity; C = 96 is the friction factor of the slot. To better reveal the influence of water adsorption effect on flow fluidity, based on Eq. (3), the relative dynamic viscosity n = η/η0 was used to describe the change of water fluidity, while η0 is the reference dynamic viscosity for comparison, which herein referred to the dynamic viscosity of pure water when i = 6.67 and Ebc = 0. Moreover, to facilitate studying the tangled influences of electric field strength Ebc, ion concentration n0, and hydraulic gradient i on the water adsorption effect that affects the water fluidity, the change ratio of the relative dynamic viscosity γ was calculated, which was defined as the ratio of the viscosity change between Ebc = 0 and Ebc = 24.68 kV/m when Ebc = 0,
3. Results and discussion
n |Ebc = 24.68kV/m −n |Ebc = 0.00kV/m
. Based on the AENS seepage ex-
3.1. Experiment results
i. e., γ =
The experimental results of the artificial-electric-field-narrow-slot (AENS) seepage experiment are given here. First, the average water seepage velocity within the narrow slot under different hydraulic gradient, electric field strength Ebc, and ion concentration of NaCl aqueous solution are shown in Fig. 3. The average seepage velocity under different electric field strength and different ion concentration maintained an approximately linear relationship with the hydraulic gradient (Fig. 3a), while it’s actually nonlinear; with the increase of Ebc, the seepage velocity of the aqueous solution passed through the narrow slot decreased (Fig. 3b); while the seepage velocity correspondingly decreased with the rise of the ion concentration (Fig. 3c). In this paper, the seepage velocity corresponding to the hydraulic gradient i = 6.67–66.7 was tested to be v = 0.015–0.17 m/s, of which the corresponding Reynolds number was Re = 15–167 according to the works of Touloukian et al. [22] and Gravesen et al. [23]. Therefore, the water flow in the slot was distinguished as laminar flow, which its average velocity can be calculated by Eq. (3) [22,24].
periment results, the variation of relative dynamic viscosity n and the change ratio γ are presented in Fig. 4. The results in Fig. 4a demonstrates that the relative dynamic viscosity n of water flow in the slot increased along with the growth of Ebc and n0, and decreased with the growth of hydraulic gradient i, which was essentially consistent with the seepage velocity experiment results in Fig. 3. Furthermore, shown by Fig. 4b, the change ratio of viscosity γ would decrease with the growth of ion concentration n0 when the hydraulic gradient i is small (less than 26.67), while the relationship of γ and n0 would become the opposite and less significant when i is greater than 26.67; shown by Fig. 4c, regardless of the change of ion concentration n0, γ decreased with the growth of hydraulic gradient i. The above descriptions meant that, the increase of electric field strength can enhance the water adsorption effect on the slot sidewalls to increase the water viscosity in the slot, while the enhancement rate would decrease with the growth of ion concentration n0 when the hydraulic gradient i is small, and the enhancement rate would decrease with the growth of hydraulic gradient i. 3
n |Ebc = 0.00kV/m
Chemical Physics Letters 735 (2019) 136768
Y.G. Fang and L.F. Guo
(b)
(a)
(c)
18 6 5
16
4
Flow velocity v (10-2m/s)
14 3 2
12
1 10
15
20
25
Approximate linearity, 10 actually nonlinear
8 Ebc= 0.00kV/m
6
Ebc= 6.17kV/m Ebc= 12.34kV/m
4
Ebc= 18.51kV/m Ebc= 24.68kV/m Ion concentration 0% Ion concentration 5%
2 0
10
20
30
40
50
60
70
Hydraulic gradient i Fig. 3. Results of average seepage velocity in the narrow slot; (a) the relationship between flow velocity and hydraulic gradient; (b) the relationship between flow velocity and electric field strength; (c) the relationship between flow velocity and ion concentration.
4. Second, according to Eq. (1), the greater the distance between water molecules with the slot surface is, the weaker the Coulomb adsorption will be. We assumed that water flow driven by higher hydraulic gradient i is able to overcome stronger Coulomb adsorption potential, drive more adsorbed water into flowing state and thus weaken its resistance (just like static friction is greater than sliding friction). Then the decrease in the change ratio γ presented in Fig. 4c can be explained as the growth of hydraulic gradient has driven more parts of the adsorbed water layer and reduced its resistance to the flow. Third, ions aggregated on the cathode and anode surface can hinder the induced charge q0 from adsorbing water molecules in the further distance (shielding effect). The growth of ion concentration will enhance the shielding effect and enlarge its affecting range (consistent with Gouy-
3.2. Discussion and analysis With a few proofs and assumptions, the above-described changes of water viscosity were given possible explanations. First, the growth of electric field strength can increase the charge density on the slot surface. Referring to the relationship between induced charge and the potential of Coulomb adsorption given in Eq. (1), it can be learned that the increase of charge density would enhance Coulomb adsorption effect by increasing the water molecular dipole moment (2e ·de ); due to Coulomb adsorption effect, the streaming potential will increase the resistance of water flowing [25–27]; therefore, when the electric field strength was increased, higher resistance to the flow (decreased velocity) and growing dynamic viscosity would be manifested in Figs. 3 and
(b)
1.7
Change ratio of relative dynamic viscosity Ȗ (%)
The relative viscosity of fluid n
70
Ion concentration 0% Ion concentration 1% Ion concentration 5%
1.6
i=11.11 i=26.67 i=66.67
1.5 1.4 1.3 1.2 1.1 1.0 0.9
5
10
15
20
25
Electric field strength Ebc (kV/m)
70
i=6.67 i=11.11 i=17.78 i=26.67 i=66.67
60
50
40
30
20
10
0
0
(c)
Change ratio of relative dynamic vicosity Ȗ (%)
(a)
0
1
2
3
4
Ion concentration n0 (%)
5
n0=0% n0=1%
60
n0=5% 50
40
30
20
10
0
0
10
20
30
40
50
60
70
Hydraulic gradient i
Fig. 4. The relative dynamic viscosity results of the flow in the narrow slot; (a) Variation curve of the relative dynamic viscosity with electric field strength; (b) Variation curve of the change ratio with ion concentration; (c) Variation curve of the change ratio with hydraulic gradient. The change ratio of the relative dynamic viscosity was calculated by γ =
n |E = 24.68kV/m −n |E = 0.00kV/m bc bc . n |E = 0.00kV/m bc
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Chemical Physics Letters 735 (2019) 136768
Y.G. Fang and L.F. Guo
Technology (Grant No. 2017KB16) and the National Key Scientific Instruments and Equipment Development Projects of China (Grant No. 41827807).
Chapman's theory [28,29]), which will benefit the seepage velocity of water; meanwhile, according to the hydration effect [30], the increase of ion concentration will also increase the number of ionized water molecule, which will decrease the seepage velocity of water and increase water viscosity. Therefore, the regularity presented in Fig. 4b can be reasoned as follows. When the hydraulic gradient is small (less than 26.67), the water flow can only drive a slight part of the adsorbed layer; with the growth of ion concentration, part of the static adsorbed water (not in a flowing state) would be thinned, which would then increase the fluidity of water and reduce its viscosity. On the other hand, when the hydraulic gradient was greater than 26.67, the growth of ion concentration would only reduce the width of flowing-state adsorbed water layer which would slightly increase the water fluidity; and when this increased effect was even weaker than the hydration effect that would increase the viscosity, the change ratio γ of viscosity would then be increased by the growth of ion concentration. In this paper, there was a threshold hydraulic gradient iT (around 26.67) which can divide the two different influences of ion concentration on the change ratio γ. The threshold hydraulic gradient iT indicated a transition state in which the change ratio γ would first decrease and then increase with the growth of ion concentration (Fig. 4b).
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4. Conclusions Unsaturated charges enriched on a solid surface can cause adsorption effect on water, which can leave significant impacts on some engineering processes. However, the adsorption effect caused by Coulomb interaction (the attraction between charges, termed as Coulomb adsorption) hasn’t been widely studied; experimental studies on Coulomb adsorption effect to water are still lacking. Therefore, in this paper, the artificial-electric-field-narrow-slot (AENS) seepage experiment was designed to study the Coulomb adsorption effect induced by different electric field strength; in which, the surface charges on the slot walls were generated by the artificial electric field that was set perpendicular to the flow direction. By means of AENS seepage experiment, the combined influence of electric field strength, ion concentration and hydraulic gradient on water fluidity were studied and analyzed. Based on the experiment results, it’s been found that: (1) the growth of electric field strength would enhance Coulomb adsorption to increase the dynamic viscosity of water in the slot; (2) the growth of hydraulic gradient is not conductive to Coulomb adsorption; (3) there is a threshold hydraulic gradient iT (nearby 26.67 in this paper) that when hydraulic gradient i < iT, the growth of ion concentration would be adverse to Coulomb adsorption, while it would instead be conductive to Coulomb adsorption when i > iT. The experiment in this paper intuitively presented the variation regularity of water fluidity affected by Coulomb adsorption effect generated by different electric field strength. The regularity and mechanism of this experiment could benefit in guiding engineering practices. The experiment method proposed in this paper can also be used to simulate and study the water adsorption effect in many different material formations, for example, clayey soil. Experiments that focus on simulating specific materials under specific conditions will be further studied in the future. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments We would like to acknowledge financial supports from the State Key Lab of Subtropical Building Science, South China University of
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