Interfacial Mass Transfer in Trichloroethylene/Surfactants/ Water Systems: Implications for Remediation Strategies

Abstract

The fate of dense non-aqueous phase liquids (DNAPLs) in the environment and the consequential remediation problems have been intensively studied over the last 50 years. However, a scarce literature is present about the mass transfer at the DNAPL/water interface. In this paper, we present a fast method for the evaluation of the mass transfer performance of a surfactant that can easily be employed to support an effective choice for the so-called enhanced remediation strategies. We developed a lab-scale experimental system modelled by means of simple ordinary differential equations to calculate the mass transfer coefficient (K) of trichloroethylene, chosen as representative DNAPL, in the presence and in the absence of two ethoxylated alcohols belonging to the general class of Synperonic surfactants. Our findings revealed that it exists an optimal surfactant concentration range, where K increases up to 40% with respect to pure water.

1. Introduction

Trichloroethylene (TCE) belongs to the dense non-aqueous phase liquids (DNAPLs) and is listed as a carcinogenic contaminant by the International Agency for Research on Cancer (IARC) [1]. Because of its physical-chemical properties, in particular low aqueous solubility and high density, TCE enters the saturated zone of the subsurface as a free phase, leaving behind a tail of discrete ganglia trapped by capillary forces, causing long-term contamination of soils and groundwaters [2,3]. Classical remediation techniques, like pump-and-treat (P&T), are not quite effective for the removal of the stratified contaminant [4,5]; therefore, the surfactant/co-solvent flushing method, where a mixture of chemicals is employed to increase the extraction yield [6,7,8], is becoming more and more popular. Surfactants are being employed also for improving the performances of TCE mineralization techniques, when used in the water phase to oxidate trichloroethylene to unharmful products such as CO₂, H₂O, and HCl, according to the half-reaction

$${\mathrm{C}}_2\mathrm{H}\mathrm{C}{\mathrm{l}}_3+4{\mathrm{H}}_2\mathrm{O}\to 2\mathrm{C}{\mathrm{O}}_2+9{\mathrm{H}}^{+}+3\mathrm{C}{\mathrm{l}}^{-}+6{\mathrm{e}}^{-}.$$

(1)

The most popular oxidants in these processes are ozone, permanganate, persulphate, and the Fenton’s system [9]. Other degradation techniques consist of reduction through zero-valent iron nanoparticles [10] and the catalytic oxidation in gas-phase (either with metal-supported or unsupported catalysts) [11,12,13,14].

Surfactants have essentially a two-fold role in remediation and degradation applications, namely enhancing the solubilisation of the TCE in the water bulk and increasing the kinetics of the process by bringing the oxidant into closer contact with the substrate [15,16,17,18,19]. In fact, surfactants are able to form a great variety of self-assembling structures in solution (micelles, vesicles, coacervates, liquid crystals, etc.), all of which share the characteristic of compartmentalisation between polar and non-polar regions, with defined boundary interfaces [20]. The presence of hydrophobic sites in water solutions is the key factor that promotes a greater dispersion of organic molecules in the bulk, eventually by forming microemulsions [8]. The so-called palisade layer (the most external region of micelles where the polar heads point towards the water) is, instead, the place where the organic molecules in the micellar core come into closer contact with ionic species (permanganate, persulphate, hydroxyl, etc.) responsible for the degradation of the pollutants. Generally, the rational choice of a surfactant for the enhanced degradation of DNAPLs is a trade-off among several factors, including extraction yields, economic costs, and environmental impacts of the surfactant itself. For the in situ remediation, the mass transfer rate between the contaminant pool and the water phase is also of paramount importance. In fact, the oxidation reactions involve the action of many free radical species and the kinetics per se is quite fast; therefore, the slow step in the whole degradation process is generally the transfer rate of the contaminants from the pools to the water phase [17].

In this paper, we present a fast method for the evaluation of the mass transfer performance of a surfactant that can easily be employed to support an effective choice for enhanced remediation strategies. We developed a lab-scale experimental system modeled by means of simple ordinary differential equations. The output fitting parameter is the mass transfer constant measured in mm/s, which accounts for the average velocity at which a molecule of pollutant pass from the organic to the water phase (or the micellar pseudo phase in case surfactants are present). As an example, we compared the efficiency of two ethoxylated alcohols belonging to the general class of Synperonic surfactants that we recently demonstrated to be effective for increasing the solubility of TCE [7,8]. Synperonic compounds have the general formula R(–O–CH₂–CH₂–)n–OH where R is the hydrophobic alkyl chain linked to a variable number of ethylene oxide units. The employed surfactants are the Synperonic 91/5 (SYN91/5, R = 9–11, n = 5) and Synperonic 91/10 (SYN91/10, R = 9–11, n = 10) having a hydrophilic lyophilic balance (HLB) values of 12.54 and 15.28 and a critical micellar concentration (CMC) of 7.94 × 10⁻⁴ M and 5.5 × 10⁻⁴ M, respectively [7,8].

2. Theoretical Approach

Mass transfer at the interface of two miscible and/or slightly miscible liquids is in general a complex mechanism that involves diffusive and advective phenomena [21]. Molecular diffusion, double diffusion [22] and cross-diffusion [23,24,25] can trigger hydrodynamic instabilities (fingers, plumes, waves, etc.) that generally enhance the mixing of the liquids but are difficult to decouple in order to understand the single contributions to the global dynamics. When reactions are present at the interface, complexity increases further [26,27].

When diffusion does not drastically change the density or the surface tension of one of the two liquids, simpler approaches are possible; for example, starting from the seminal Epstein & Plesset equation [28], originally designed for a gas bubble dissolution, several models have been developed to measure the mass transfer in terms of the diffusion coefficient (measured in cm${}^2$ s${}^{-1}$) of a species i in the presence of a concentration gradient (∇C${}_i$). The Epstein & Plesset equation is used to describe the dissolution dynamics of liquid droplets dispersed in a bulk [29,30,31,32]. When a finite concentration difference ($\Delta$C${}_i$) is considered in the place of a gradient, the mass transfer can be described by ordinary differential equations (ODEs). Experimental conditions to meet this requirement can be easily obtained on a lab-scale. Figure 1 sketches the basic features of the batch reactor used in our experiments. A small volume of TCE (∼0.5 $\mathsf{\mu }$L) is poured at the bottom of a spectrophotometric cuvette, pre-filled either with pure water or with surfactant solutions containing SYN91/5 or SYN91/10 at different concentrations. The bulk is continuously stirred at a speed that ensures a homogeneous distribution of the dissolved TCE in the aqueous solution but does not perturb the TCE/water interface. Because of the surface tension at the interface, the volume of TCE tends to assume a spherical shape; the use of quartz cuvette helps to reduce the contact angle between the TCE drop and the bottom of the reactor, thus reducing the deviation from a perfect sphere.

If $A=4\pi r^2$ (with r being the TCE droplet radius) is the interfacial area between the two liquids, the flux per unit area $N_i$ can be described by a first-order mass transfer equation [33]:

$$N_i=\frac{1}{A}\frac{d{n}_i}{dt}=K(C_s-C_i),$$

(2)

where $n_i$ indicates the amount of substance (mol) of the species i, $C_i$ (M) is the molar concentration of the species i in the bulk solution, $C_s$ (M) is the bulk saturation concentration of i, and K is the mass transfer coefficient.

Equation (2) can be rewritten as:

$$\frac{d{C}_i}{dt}{V}_t=AK(C_s-C_i),$$

(3)

where $V_t$ is the bulk total volume. The driving force of mass transfer is obviously the concentration difference $(C_s-C_i)=\Delta C_i$.

Dividing both sides of the Equation (3) by $V_t$ gives the following equation:

$$\frac{d{C}_i}{dt}=aK(C_s-C_i),$$

(4)

with

$$a=\frac{A}{V_t},$$

(5)

where a (mm${}^{-1}$) is the ratio between the droplet surface (mm${}^2$) and the total volume of the solution (mm${}^3$) and r is the droplet radius (mm); in this way, K has the units of mm s${}^{-1}$.

Because of TCE chemical-physical properties (low solubility in water, high vapor pressure, high Henry’s law constant), a little amount of TCE may evaporate and leave the system [34]. For this reason, a volatilization term has been included in the mass balance. The Equation (4) becomes:

$$\frac{d{C}_i}{dt}=aK(C_s-C_i)-K_v{C}_i,$$

(6)

$K_v$ being the volatilization coefficient (s${}^{-1}$) for TCE.

During TCE droplet dissolution, the radius r decreases. Considering this phenomenon, the change of the TCE mass in the droplet is proportional to the flux ($N_i$) of molecules across the interface TCE/H${}_2$O

$$-\frac{d}{dt}\left(\frac{{\rho }_{TCE}}{M{M}_{TCE}}{V}_{TCE}\right)=A{N}_i,$$

(7)

where ${\rho }_{TCE}$ is TCE density, $M{M}_{TCE}$ is the TCE molecular mass, and $V_{TCE}$ is the TCE droplet volume. Considering Equation (3) and assuming that the droplet keeps a spherical shape for the whole dissolution process, the variation of the radius in time can be expressed as [35]

$$-\frac{d}{dt}\left(C_{st}\frac{4}{3}\pi r^3\right)=4\pi r^{2}K(C_s-C_i),$$

(8)

where C${}_{st}$ is the concentration of pure TCE (11.11 M). Rearranging Equation (8), the change of r during TCE dissolution, linearly related to $C_i$, becomes

$$\frac{dr}{dt}=-K\frac{C_s-C_i}{C_{st}}.$$

(9)

Note that, when $C_i\ll C_s$, $C_i$ increases and r decreases linearly with time, respectively.

Coupled Equations (6) and (9) describe the kinetics of the mass transfer across the interface in the system TCE/H${}_2$O (or TCE/SYN91/X/H${}_2$O) when a homogeneous distribution of the dissolved TCE in the aqueous solution is considered and a spherical shape of the droplet is maintained for the whole dissolution process. Their integration and fitting to the experimental data allow one to obtain the parameters K and $K_v$.

3. Materials and Methods

Synperonic 91/5 (SYN91/5, Polyoxyethylene(5) C9-C11 alcohol, density 0.978 g/cm${}^3$) and Synperonic 91/10 (SYN91/10, Polyoxyethylene(10) C9-C11 alcohol, density 0.998 g/cm${}^3$) surfactants were provided by Croda International (UK) and the chemical structures are reported in Figure 2. TCE (analytical grade > 99.5%) was purchased from Sigma-Aldrich (St. Louis, MO, USA). All experiments were performed in ultra-pure water with resistivity >1 M$\mathsf{\Omega }$ cm. The Synperonic solutions at different concentrations were prepared by dilution from stock solutions.

A series of batch experiments were performed using quartz cuvettes with path length 5 cm (1 × 5 × 5 cm) at 23 ${}^{\circ }$C. In order to keep the bulk homogeneous, the system was stirred with a home-made stirring system for the whole duration of the measurements, performed by means of a UV-VIS spectrophotometer (Agilent 8530). The total volume of the solutions for all the experiments was 18 mL. TCE concentration was monitored by measuring the absorbance at $\lambda =$ 230 nm following a calibration procedure. At the beginning of each experiment, 0.5 ± 0.06 $\mathsf{\mu }$L of TCE were placed in the bottom of the cuvette using a 5 $\mathsf{\mu }$L glass syringe.

Images of the dissolving droplet were acquired with a CMOS camera Pixelink PL-D755CU (Pixelink Inc., Ottawa, Canada) at 1 fps and were analyzed by means of the software ImageJ v1.53k [36]. To estimate the parameters K and $K_v$, the experimental data were fitted with the Levenberg–Marquardt algorithm [37,38] by integrating Equations (6) and (9) with CO.PA.SI. software v4.33 [39].

TCE saturation concentrations ($C_s$) in Synperonic 91/5 and 91/10 solutions were previously measured by Intiso et al. [7] and Garza-Arévalo et al. [8] and are reported in

Table 1. [SYN91/5] and [SYN91/10] tested and the related $C_s$ values.

System	SYN (M)	${\mathit{C}}_{\mathit{s}}$ (M)
H2O	-	(9.74 ± 0.03) × 10−3
SYN91/5 [7,8]	1 × 10−4	(9.74 ± 0.05) × 10−3
	1 × 10−3	0.020 ± 0.001
	0.01	0.022 ± 0.002
	0.05	0.022 ± 0.001
	0.08	0.022 ± 0.003
	0.10	0.022 ± 0.003
	0.20	0.047 ± 0.002
	0.30	0.067 ± 0.002
SYN91/10 [8]	1 × 10−4	(9.74 ± 0.04) × 10−3
	0.01	0.04 ± 0.03
	0.05	0.15 ± 0.01
	0.08	0.26 ± 0.01
	0.10	0.33 ± 0.02
	0.15	0.45 ± 0.01
	0.20	0.64 ± 0.04

. $C_s$ were determined by consecutive additions of TCE to surfactant solutions, followed by vigorous shaking. The last volumetric addition of TCE before macroscopic demixing of the solutions was used to calculate $C_s$. At the thermodynamic equilibrium, for a given temperature, stirring did not affect $C_s$.

4. Results

Figure 3a shows a typical time-series of a TCE droplet dissolution in pure water at T = 23 ${}^{\circ }$C and 2010 rpm. [TCE] ($C_i$) increases in the bulk up to ∼10,000 s where it reaches a maximum at ∼$3\times {10}^{-4}$ M, corresponding to the full dissolution of 0.5 $\mathsf{\mu }$L of TCE in 18 mL of water. After the complete dissolution of the droplet, a certain volatilization from the bulk takes place and [TCE] decreases with time. Fitting of experimental data by means of Equations (6) and (9) (as an example, Figure 3b reports the fitting of the pre-maximum time-series) allowed for estimating the parameters $K\sim$1.7 × 10⁻² mm s${}^{-1}$ and $K_v\sim$6.0 × 10⁻⁵ s${}^{-1}$. Figure 3c reports a series of snapshots of the TCE droplet taken during the dissolution process, as it can be seen that the approximation of the droplet shape to a sphere holds up well to almost the end of the process. This is also confirmed by the time-series of the droplet radius, as extracted from the experimental snapshots, reported in Figure 3d, which shows a linear decrease in time when $C_i\ll C_s$, as predicted by Equation (9).

The dependence of mass transfer coefficient on stirring rate has been evaluated at T = 23 ${}^{\circ }$C in pure water. Figure 4 and

Table A1. K and $K_v$ values at different stirring rates (CI, confidence interval; CC, correlation coefficient).

Stirring	K	95%	${\mathit{K}}_{\mathit{v}}$	95%	$\mathit{K}/{\mathit{K}}_{\mathit{v}}$
(rpm)	(mm s${}^{-1}$)	CI	(s${}^{-1}$)	CI	CC
2010	(1.7 ± 0.2) × 10−2	2.06 × 10−3	(6.0 ± 0.2) × 10−5	2.12 × 10−5	0.956
2750	(2.1 ± 0.2) × 10−2	1.96 × 10−3	(6.0 ± 0.1) × 10−5	1.56 × 10−5	0.767
3840	(2.1 ± 0.2) × 10−2	2.68 × 10−3	(9.3 ± 0.1) × 10−5	1.02 × 10−6	0.888
4820	(2.65 ± 0.03) × 10−2	2.94 × 10−4	(9.7 ± 0.1) × 10−5	1.42 × 10−6	0.922
6034	(4.9 ± 0.1) × 10−2	9.26 × 10−4	(1.1 ± 0.1) × 10−4	1.48 × 10−5	0.899

in Appendix A report the corresponding K and $K_v$.

For a stirring rate greater than 4800 rpm, the mass transfer rate increases significantly probably because of the development of turbulent flows at the droplet/bulk interface. As reported in Table A1, the value of $K_v$ also rises with the stirring, as expected. In order to simulate a stagnant pool of contaminants stratified under groundwater, a stirring rate of 2010 rpm (corresponding to 4.2 m/s for the stirrer having a radius of 0.2 cm) has been chosen for all the experiments with surfactants. To prove that TCE quickly reaches a homogeneous distribution in the water phase during the dissolution process, we performed an experiment by dissolving a drop (5 $\mathsf{\mu }$L) of a water-soluble dye (ferroin 25 mM), having a diffusivity similar to TCE ($D_{\mathrm{TCE}}=8.16\times {10}^{-6}$ cm${}^2$ s${}^{-1}$ [5], $D_{\mathrm{Fe}}=7\times {10}^{-6}$ cm${}^2$ s${}^{-1}$ [40]), into the stirred reactor (2010 rpm) filled with 18 mL of water; we then measured the time employed to reach the equilibrium concentration in the bulk (0.007 mM). We found that the system concentration reached the theoretical plateau value in 150 s (see Figure A1 in Appendix B), which is a very short time if compared with that taken for the complete dissolution of the TCE pool (11,000 s for a volume 10 times smaller) and with our sampling time (600 s). Therefore, we can consider that TCE reaches a homogeneous distribution in the bulk fast enough to model the process by ODEs.

As showed in Figure 5a and reported in

Table A2. Mass transfer coefficients K and volatilization coefficients $K_v$ at different concentrations of SYN/X (CI, confidence interval; CC, correlation coefficient).

System	SYN	K	$95\%$	${\mathit{K}}_{\mathit{v}}$	$95\%$	$\mathit{K}/{\mathit{K}}_{\mathit{v}}$
	(M)	(mm s${}^{-1}$)	CI	(s${}^{-1}$)	CI	CC
H2O	-	(1.7 ± 0.2) × 10−2	2.06 × 10−3	(6.0 ± 0.2) × 10−5	2.12 × 10−5	0.956
SYN91/5	1 × 10−4	(1.84 ± 0.03) × 10−2	2.99 × 10−4	-	-	-
	1 × 10−3	(6.4 ± 0.8) × 10−3	8.42 × 10−4	(2.3 ± 0.1) × 10−4	9.8 × 10−5	0.886
	0.01	(1.06 ± 0.01) × 10−2	8.83 × 10−5	(2.9 ± 0.2) × 10−5	2.02 × 10−6	0.802
	0.05	(2.1 ± 0.1) × 10−2	1.98 × 10−3	(7.1 ± 0.8) × 10−5	1.37 × 10−5	0.758
	0.08	(1.85 ± 0.02) × 10−2	2 × 10−4	(3.4 ± 0.5) × 10−5	8.54 × 10−6	0.952
	0.10	(1.86 ± 0.01) × 10−2	1.01 × 10−4	(2.8 ± 0.2) × 10−4	1.96 × 10−5	0.793
	0.20	(5.9 ± 0.1) × 10−3	1.15 × 10−3	(4.2 ± 0.1) × 10−5	1.26 × 10−5	0.897
	0.30	(7.9 ± 0.6) × 10−3	1.09 × 10−3	(2.4 ± 0.2) × 10−4	1.96 × 10−4	0.945
SYN91/10	1 × 10−4	(1.83 ± 0.01) × 10−2	1.15 × 10−5	(4.2 ± 0.1) × 10−5	1.25 × 10−6	0.930
	0.01	(1.44 ± 0.08) × 10−2	8.00 × 10−4	-	-	-
	0.05	(9.59 ± 0.02) × 10−3	2.00 × 10−5	-	-	-
	0.08	(2.0 ± 0.1) × 10−2	1.25 × 10−3	(5.0 ± 0.5) × 10−5	5.59 × 10−6	0.717
	0.10	(1.8 ± 0.1) × 10−2	1.21 × 10−3	-	-	-
	0.15	(1.20 ± 0.01) × 10−2	1.15 × 10−3	(2.5 ± 0.1) × 10−5	1.68 × 10−6	0.861
	0.20	(7.1 ± 0.2) × 10−4	1.75 × 10−5	(9.5 ± 0.5) × 10−5	3.48 × 10−6	0.916

in Appendix A, the two surfactants have a similar effect on TCE mass transfer rate across the interface, with a minimal deviation of the maximum rate peak. In detail, SYN91/5 is more efficient in the concentration range 0.05–0.1 M, whereas SYN91/10 in the range 0.08–0.1 M, with 30–40% increase in mass transfer rate compared to water. Under the CMC, the mass transfer is comparable with pure water for both the surfactants. In contrast, the kinetics of dissolution is strongly inhibited at high tested concentrations of surfactants, becoming a rate slower than in water. This result might appear in contrast with the enhanced solubility of TCE measured at high surfactant concentrations (Table 1); however, it is worth noting that K measures the speed at which a molecule of TCE crosses the interface and moves freely in the bulk. The net TCE flux across the interface ($dn/dt$), measured in terms of mass (number of TCE molecules) per time, and driven by $\Delta$C${}_i$, is always greater in the presence of surfactants with respect to pure water, as reported in Figure 5b,c. In other words, when the surfactants are present at high concentrations, the aggregates they form in solution are larger and can dissolve more TCE molecules, but, as a drawback, move slower into the bulk. Such a limitation was pointed out by several authors that found the aqueous micellar diffusion to be potential rate-limiting steps in interphase mass transfer [41,42,43,44]. In the case of SYN91/5, we could confirm a slowing effect of the micelles by comparing the TCE diffusion coefficients in pure water at 25 ${}^{\circ }$C (D = 8.16 × 10⁻⁶ cm${}^2$ s${}^{-1}$ [5]) with the diffusivity of SYN91/5 found to be in the range of ∼$5\times {10}^{-7}$–∼$2\times {10}^{-6}$ cm${}^2$ s${}^{-1}$ at 25 ${}^{\circ }$C (0.01 < [SYN91/5] < 0.1 M) [45].

5. Conclusions

The fate of DNAPLs in the environment and the consequential remediation problems have been intensively studied over the last 50 years. However, a scarce amount of literature is present about the mass transfer at the DNAPL/water interface. In the case of TCE, to the best of our knowledge, only one study exists where a value of mass transfer coefficient K for the system TCE/H₂O can be found. Urynowicz and Siegrist [46] have found $K=6.98 \times {10}^{-3}$ mm s${}^{-1}$ at T = 20 ${}^{\circ }$C at a stirring rate of 350 rpm, which, considering the different experimental conditions, is in line with our findings ($K=1.66 \times {10}^{-2}$ mm s${}^{-1}$ at T = 23 ${}^{\circ }$C and stirring rate 2010 rpm).

In this paper, we presented a fast and reliable method that allows for estimating the mass transfer coefficients in a system of two slightly miscible fluids. The analysis of K trends permits, for example, to assess the efficiency of surfactants in transferring TCE from stagnant pools to the water bulk. In the specific case, we compared two ethoxylated alcohols belonging to the general class of Synperonic, to find that an optimal range exists where the presence of the surfactant effectively increases the mass transfer kinetics. The presence of a maximum in the K trends of Figure 5 is related to the aggregation state of the surfactant in solution (micelles, liquid crystals, etc.), which, in turn, influences the mobility and diffusivity of the TCE in the bulk phase. The obtained results lead to the conclusion that the SYN91/5 would be a better choice for groundwater remediation because it is more efficient than SYN91/10 at lower concentrations. The knowledge of K in specific environmental conditions would also help the optimization of in situ remediation strategies based on oxidation reactions (Reaction (1)).

Another interesting effect of surfactant presence is the significant decrease of the volatilization coefficient. This phenomenon is related to the lower air/bulk partition coefficient in the presence of micellar systems [47]. In environmental terms, this would help to prevent the dispersion of TCE into the atmosphere during remediation activity.