Determining Pathogen Adhesive Parameters on Heterogeneous Surfaces Scott A. Bradford1 and Saeed Torkzaban2 1US Salinity Laboratory, USDA, ARS, Riverside, CA 2CSIRO, Glen Osmond, Australia Funding Sources: USDA NP 214 DLVO or XDLVO Interaction Energies • Uses macroscopic zeta potentials • Neglects microscope heterogeneities Roughness Absorption/desorption of ions, organics, and clays Energy Barrier Sec. min. Primary Min. Microscale Heterogeneities (Taboada-Serrano et al., 2005) Transients in solution chemistry can induce changes in chemical heterogeneity. Surface Integration Techniques Φ ( D) = ∑ ∑ [P(h )(e1 ⋅ ez )(n ⋅ ez )dA] particle wall Duffadar and Davis (2007) Trajectory Analysis dvc ∑ Fi = mc dt i V dωc ∑ Ti = 0.5mc d c i dt FL FD FB FA TApplied TAdhesive FF 1o or 2o min FA • Computationally intensive (small spatial and temporal grid sizes), random heterogeneities, flow field, repeated surface integration, limited to pore-scale and constant solution chemistry. Continuum Scale Models • • • • • Average parameters over the pore-scale (REV) Computationally efficient Large spatial and temporal scales Transients in chemistry How to account for heterogeneities (α, Smax or Sf )? J2 s C2 Sf(IS) α(IS) J1 C1 ∂ (θ w1C1 ) ∂J = − 1 − θ w1αk12 C1 +θ w 2 (1 − α )k 21C 2 ∂t ∂z ∂ (θ w 2 C 2 ) ∂J = − 2 + θ w1αk12 C1 − θ w 2 (1 − α )k 21C 2 − θ w 2ψ 2 s k 2 s C 2 + ρ b k d (s − f c si ) ∂t ∂z ∂ (ρ b s ) = θ w 2ψ 2 s k 2 s C 2 − ρ b k d (s − f csi ) ∂t Surface Integration Az ≅ 4πrc κ (Duffadar and Davis, 2008) • • • • Discretize Az into Nt cells of size Ah and charge ζ1 or ζ2 Total number of cells with ζ2 is N2 Possible charge realization N2 =0, 1, … Nt Mean Φ(h) within Az (Bendersky and Davis, 2011) N2 N2 Φ1 (h ) + Φ (h ) = 1 − Φ 2 (h ) Nt Nt REV Scale • Random distribution, and the fraction of N2 cells at the REV scale is known (Ps) • Prob(N2 ) within Az is given by the binomial distribution: Nt ! N2 Nt − N 2 Prob( N 2 ) = Ps (1 − P s ) N 2 !( N t − N 2 )! • PDF of Φmax is given as plot of Prob(N2 ) and Φ max(N2) • Mean value of Φmax at the REV scale is: Φ max = 〈 Φ max 〉 = * Nt ∑ Prob(N )Φ (N ) N 2 =0 2 max • Variance of Φmax at the REV scale <Φmax2>−<Φmax>2 2 Validation Same approach can be applied to determine: • Φ*(h) • Φmax* • Φ2min* Bendersky and Davis (2011) Φ* 100 0 -100 -200 0 1 2 3 4 5 6 κh 1 simulation 200 surface integrations simulations Colloid Adhesive Parameters • Sf= Sf1 + Sf2 • Sf1 occurs when Φmax=0 (N2>N2crit) • Sf2 is determined from a balance of applied hydrodynamic and resisting adhesive torques. • α=α1+α2 • α1 and α2 is determined using the kinetic energy method Heterogeneous SWI Φ(h, N2) for N2=0, 1…Nt Prob(N2), α(N2), and Sf(N2) Homogeneous porous media Heterogeneous porous media α(N2) and Sf(N2) α* and Sf * Colloid Φ(h, N2) and Prob(N2) Sf2 1 1 ln(Tadhesion ) − µ = + erf 2 2 σ 2 • The CDF of applied hydrodynamic torque determined from pore-scale water flow simulations for different colloid sizes, water velocities, and grain sizes. 100 (b) 80 CDF 60 d50, µm 50 - simulated 50 - predicted 500 - simulated 500 - predicted 5000 - simulated 5000 - predicted 40 20 0 -22 -21 -20 -19 -18 Tapplied (N m) • The resisting adhesive torque (Tadhesion) is derived from information about Φ2min using JKR theory or an empirical value for the friction coefficient. Force Balance - 2o min • KE of diffusing colloids at t=infinity 2 F (E) = k bTk α1 < ∫ ∞ Φ 2 min + Φ bar α2 = ∫ Φ 2 min 0 E πk bTk 0.5 f det = 1 − α 2 − α 1 FA 1.0 F ( E )dE F ( E )dE E exp − k bTk FB 0.8 α2 0.6 0.4 0.2 0.0 -10 -8 -6 Φ 2min -4 Shen et al. (2010) corrected for velocity as αSf -2 0 0.8 Ps Sf1* 0.6 0.1 0.2 0.4 0.4 0.2 0.6 0 0 10 20 30 40 50 ζ2 (mV) Values of Sf1* as a function of ζ2 for a homogeneously charged colloid (-30 mV) on various heterogeneously charged porous media. Simulation properties included the following: ζ1=-70 mV, IS=10 mM, rc=500 nm, Nt=Az/Ah=10, a Hamaker constant of 4.04E-21 J, and Ps=0.1, 0.2, 0.4, and 0.6. 0.6 Ps 0.1 0.4 Sf1* 0.2 0.4 0.2 0.6 0 0 2 4 6 8 10 Nt=Az/Ah Values of Sf1* as a function of Nt for a homogeneously charged colloid (-30 mV) on various heterogeneously charged porous media. Simulation properties included the following: ζ1=-70 mV, ζ2=0 mV, a Hamaker constant of 4.04E-21 J, and Ps=0.1, 0.2, 0.4, and 0.6. 0.4 IS (mM) 0.3 2 Sf1* 25 0.2 100 0.1 0 0 200 400 600 800 1000 rc (nm) Values of Sf1* as a function of rc for a homogeneously charged colloid (-30 mV) on various heterogeneously charged porous media. Simulation properties including the following: Ah=2500 nm2, ζ1=-70 mV, ζ2=20 mV, Ps=0.1, a Hamaker constant of 4.04E-21 J, and IS=2, 25, and 100 mM. 1 rc (nm) 0.8 5000 α2 ∗ 0.6 2500 0.4 1250 500 0.2 250 0 0 20 40 60 80 100 80 100 IS (mM) 0.1 0.08 sf2* 0.06 0.04 0.02 0 0 20 40 60 IS (mM) Predicted values of α2* and Sf2* as a function of IS and rc. Simulation properties included Ah=500 nm2, ζ1=-70 mV, ζ2=20 mV, Ps=0.1, and a Hamaker constant of 4.04E-21 J. Implications – Larger Pathogens • Bacteria and protozoa parasites have a large value of Az, therefore little primary minima interaction is expected (α1=Sf1 =0). • α2 is large, but Sf2 is close to zero • Grain-grain contacts and large surface roughness locations are expected to play a dominant role in immobilization due their influence on hydrodynamic (lower) and adhesive (increases) forces and torques. E. coli O157:H7 Bradford et al. (2006) Choi et al. (2007) Implications – Virus • Attachment of virus in primary and secondary minima is likely. • Small scale chemical heterogeneity (adsorbed multi-valent cations) can have a strong influence on retention of viruses. • Factors that influence cation exchange will influence release of virus. Sadeghi (2012) Implications - Hysteresis in Retention DI 4 Initial IS (b) 1.1 mm CML 6 mM 0.11 mm CML 1.6 31 mM 2 C/C0 C/C0 3 DI 2 106 mM 56 mM 31 mM 6 mM 56 mM 106 mM 56 mM 31 mM 6 mM 6 mM 1.2 31 mM 0.8 DI after FI Initial IS 56 mM 1 0.4 0 0 400 800 Time (min) 1200 0 0 400 800 Time (min) 1200 Other Modifications Ellipsoidal pathogens Chemical heterogeneity on SWI and colloid Physical heterogeneity (roughness) on SWI *Physical and chemical heterogeneity on SWI Physical heterogeneity on SWI and colloid Physical and chemical heterogeneity on SWI and colloid 60 20 Φ* • • • • • • -20 -60 -100 0 1 2 3 κh 4 5 6 Conclusions • A simple model has been developed to determine pathogen adhesive parameters on heterogeneous surfaces at the REV scale. • Results are consistent with surface integration models. • Values of α* and Sf* were demonstrated to be very complex functions that depend on the charge heterogeneity properties (size, amount, and zeta potential), the colloid size, the solution chemistry, and the system hydrodynamics. • Irreversible colloid immobilization was predicted for smaller colloids and higher IS when Az≤Ah. • Larger colloids and smaller IS tended to yield reversible interactions via a secondary minimum when Az>Ah, and colloid immobilization could only be explained by consideration of other factors (e.g., surface roughness, eddy zones, and grain-grain contacts). • Hysteresis in Sf* with IS can occur because of the different dependence of reversible and irreversible colloid immobilization on solution chemistry.

© Copyright 2022 Paperzz