Supporting Information

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1 Supporting Information Retention and Release of Graphene Oxide in Structured Heterogeneous Porous Media under Saturated and Unsaturated Conditions Shunan Dong 1, Xiaoqing Shi 1, Bin Gao 3, Jianfeng Wu 1, Yuanyuan Sun 1 *, Hongyan Guo 2, Hongxia Xu 1, Jichun Wu 1 * 1 State Key Laboratory of Pollution Control and Resource Reuse, Key Laboratory of Surficial Geochemisty, Ministry of Education, School of Earth Sciences and Engineering, Hydrosciences Department, Nanjing University, Nanjing , China 2 State Key Laboratory of Pollution Control and Resource Reuse, School of Environment, Nanjing University, Nanjing , China, 3 Department of Agricultural and Biological Engineering, University of Florida, Gainesville, FL Contents of this file: 11 pages, 4 figures, and 4 tables. * Corresponding authors. Tel.: ; fax: address: sunyy@nju.edu.cn (Y. Sun), jcwu@nju.edu.cn (J. Wu). S1

2 S1 XDLVO Theory The extended Derjaguin-Landau-Verwey-Overbeek (XDLVO) interactions between GO particles and porous media, GO and GO, and GO and air-water interface can be modeled as the integration of the Lifshitz-van der Waals (LW) attraction, the electrical double layer (EDL) repulsion and the Lewis acid-base (AB) interactions between two parallel plates. 1-3 The Lifshitz-van der Waals attraction per unit area (Φ LW ), the electrostatic double-layer repulsion per unit area (Φ EDL ), the Lewis acid-base (AB) interactions per unit area (Φ AB ), and the total interaction energy per unit area (Φ tot ) can be calculated as follows: 1-3 A Φ LW = - 12πh Φ Φ EDL kt 2 = 32ε0εrκ12 ( ) exp( - κh) (2) ve h0 h AB = ΔG exp( ) (3) - AB h0 λ (1) tot EDL LW AB Φ =Φ +Φ +Φ (4) where A 132 represents the Hamaker constant for substances l and 2 in presence of medium 3, which can be determined from the Hamaker constant of each material, h is the separation distance between the GO particles and sand surface, 0 is the dielectric permittivity of vacuum (8.85*10-12 CV -1 m -1 ), r is the dielectric constant of water (78.5), is the Debye length, k is the Boltzmann s constant, T is the absolute temperature, v is the valence of electrolyte, e is the electron charge ( C), (=0.6 nm).the Hamaker constants of S2

3 between GO and quartz sand and between GO and air-water interface are calculated as and J, respectively. 1, 2 The values of and were calculated using the following equation: 1 0 r kt 2N Ie A 2 (5) 1 2 veξ1 = tanh( ) 4kT veξ 2 = tanh( ) 4kT (6) (7) where 0 and r were previous defined, N A is the Avogadro constant, I is the ionic strength, 1 and 2 were the zeta potential of GO particle and sand respectively. To obtain the values of AB Gh 0, the contact angles (θ) of three probing liquids (water, glycerol and diiodomethane) need to be acquired first. The method was similar to the study of Xu and Ong. 2, 4 According to the followed equations, the LW ( LW GO ), electron-accepting ( + GO ) and electron-donating ( ) interfacial tension values for GO could be determined through the ḠO following equations: L LW LW i ( 1+ cos θ) = 2 i + 2 i + 2 i (8) where i represents water ( L LW + w = 72.8, w = and w = LW , = and = g and + d = - d = 0 mj m -2 ), respectively. 5 The values of g - w 3.92 and = 57.4 mj m -2 ) or diiodomethane ( L ḡ d = 25.5 mj m -2 ), glycerol ( L g = AB Gh 0 were then calculated from the interfacial tension parameters: LW = 50.8, = d =2[ ( - ) ( - ) - - ] (9) G 0 AB h w GO j w w GO j w GO j GO j S3

4 where the subscript j represents sand ( + s = 1.4 mj m -2, - s = 47.8 mj m -2 ), and air ( + a = = 0 mj ā m -2 ). 6, 7 S2 Determination of Pore Water Velocity, Dispersion Coefficient, and Moisture Content S2.1 Saturated columns For all the saturated column experiments, coarse sand area was the fast flow domain () and fine sand area was the slow flow domain (), the pore water velocities (v and v ) corresponding to the two areas were directly calculated as: v = [ ωk uk + (1 - ω) K ][ θ ω + θ (1 - ω)] (10) v = [ ωk uk + (1 - ω) K ][ θ ω + θ (1 - ω)] (11) where the subscripts and refer to the fast flow and slow flow domains in the column, respectively; u was the Darcy velocity total applied in the saturated columns (L T -1 ); ω is the ratio of the volumes of the coarse sand and the total sand system (-); K is the saturated hydraulic conductivity (L T -1 ), which were measured using the constant head method based on the Darcy s Law; θ is the water content (-), which is the porosity of the sand under saturated conditions. The dispersion coefficient (D) of the two areas was determined as: D = δ v (12) S4

5 D = δ v (13) where δ is the saturated longitudinal dispersivity (L), which were determined from the tracer experiments of the corresponding saturated homogeneous columns. S2.1 Unsaturated columns For unsaturated columns, fine sand area was the fast flow domain () and coarse sand area was the slow flow domain (). Flow calculations of and were carried out using the TOUGH2 EOS9 module based on the dual-permeability conceptual model (implemented using Multiple Interacting Continua method in TOUGH2), 8 which simulated the whole draining process (during the preparation of the unsaturated columns) and the unsaturated flow according to Richards equation. 9 Capillary pressure and relative permeability functions of saturation for the dual domains are based on the van Genuchten formulation. 10 The material properties that were used for the dual domains were referred to the van Genuchten formulation 10 and modified based on the corresponding saturated permeability values obtained from experimental measurements. The equivalent pore water velocities (v) and moisture contents (θ) of and were calculated from the numerical simulator TOUGH2 and used in the GO retention and transport model (equation 1 and 2 in the manuscript). S5

6 The unsaturated longitudinal dispersivity for was also obtained from the tracer experiments of unsaturated homogeneous columns (with corresponding sand and moisture content), which was then used to calculate the dispersion coefficient (D). Table S1. Surface Properties of the GO and Sands and XDLVO Results Sand ( mm) Sand ( mm) Sand ( mm) Sand ( mm) Sand ( mm) Sand ( mm) GO IS (mm) Zeta-potential (mv) (kt μm -2 ) Table S2. Summary of the β, Peclet and Damkohler Number for All the Experiments Peclet number β Damkohler number Damkohler Damkohler number Column (cm -1 ) for mass transfer number for 1 mm for 20 mm S S S S S S U U U Where and represent fast flow domain and slow flow domain respectively. β represent geometry coefficient S ( β =, where S is the contact area between coarse and fine grains packed in the column, V is the volume of each Vθ S6

7 vh domain, and θ is the moisture content). Peclet number ( Pe =, where v is the velocity of pore water, H is the height of D the column, D is the dispersion coefficient) compares the advection and dispersion processes. Damkohler number βαh (Damkohler number for mass transfer: Da MT =, where α is the mass transfer coefficient; Damkohler numbers for v kh GO deposition: Da CD =, where k is the retention rate constant) compares the time scale of the two processes; when v its value is >>1 or <<1, one of the process dominants. Table S3. Summary of Recovery Rate for All Columns According to GO Transport Experiment and Model IS 1 mm IS 20 mm Column MR ** MR ** MR Total ** MR Total MR ** MR ** MR Total ** MR Total S S S S S S U U U Where MR represent mass recovery rate from effluent according to GO transport process; and represent fast flow domain and slow flow domain; superscript ** represent parameters determined from the GO transport model. Table S4. Summary of Recovery Rate for All Columns According to GO Release Process Where MRR represent mass recovery rate from effluent according to GO release process; and represent fast flow domain and slow flow domain. Column MRR MRR MRR Total S S S S S S U S7

8 U U S8

9 (a) (b) (c) (d) (e) (f) Figure S1. XDLVO energy between GO and sand grain of different size (a: mm; b: mm; c: mm; d: mm; e: mm; f: mm) under different NaCl solution (1 mm and 20 mm NaCl). Figure S2. XDLVO energy between GO and GO under different NaCl solution (1 mm and 20 mm NaCl). S9

10 Figure S3. XDLVO energy between GO and air-water interface under different NaCl solution (1 mm and 20 mm NaCl). (a) (b) (c) (d) Figure S4. SEM micrographs of cleaned quartz sand (a) and the quartz sand excavated from the inlet of the packed column (b), and the corresponding EDX spectrum of cleaned quartz sand (c) and the quartz sand excavated from the inlet of the packed column (d). S10

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12 (9) Richards, L. A. Capillary conduction of liquids through porous mediums. J. Appl. Phys. 1931, 1 (5), (10) van Genuchten, M. T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 1980, 44 (5), S12