Electrostatic forces can influence the adsorption of virions to surfaces such as flocs [74] . Researchers utilize various methods to estimate electrostatic forces [1] . The isoelectric point (IP) is the pH at which a particle or surface in an electrolyte solution has a neutral charge. If pH > IP, the surface is negatively charged; the surface is positively charged if pH > IP. Electrophoretic mobility (EM) is a measure of particle motion in the occurrence of an EF and can be employed to deduce the potential close to the particle surface. Electrostatic forces generally control virion adsorption because of the long-range electrostatic effects and the low IP of most enteroviruses, suggesting a strong negative potential close to the particle surface at neutral pH. Nonetheless, EF shielding suppresses electrostatic forces at high ionic strength.

When electrostatic interactions are repulsive or neutral, van der Waals and non-DLVO phenomena (such as the hydrophobic effect and steric hindrance) and interactions with constituents in the water matrix could lead to dissimilarities in virion sorption. In addition, as discussed below, van der Waals and non-DLVO forces are inclined to notably change the impacts of electrostatic forces when electrostatic forces are reduced (e.g., by electrostatic screening or near the IP of the particle) [1] .

Arising from electronic resonance between surfaces, van der Waals interactions form an attractive force proportional to the polarizability of the virion and the abiotic surface [1] . Van der Waals forces could not be measured independently of electrostatic and non-DLVO phenomena [90] . On the other hand, Armanious et al. [94] noticed a minimal effect of surface polarizability on bacteriophage adsorption. Nonetheless, the two surfaces juxtaposed also differed in hydrophobicity.

The hydrophobic effect emerges from hydrogen bonds that preferentially form between water molecules to exclude nonpolar molecules—the hydrophobic effect conducts to the tendency of nonpolar substances to partition out of the aqueous phase [1] [67] . Armanious et al. [94] discovered that the hydrophobic effect moderated electrostatic repulsion to permit the adsorption of bacteriophages fr, GA, MS2, and Qβ to nonpolar surfaces. Likewise, they proposed a manner for quantifying hydrophobicity founded on the size and number of nonpolar patches on the capsid surface. They anticipated a pattern of decreasing hydrophobicity: Qβ >> fr > GA >> MS2. Armanious et al.’s manner was qualified to clarify significant trends in bacteriophage sorption to hydrophobic surfaces, even if isolating the hydrophobic influence from other phenomena remains impossible. Different investigators [1] empirically suggested a relative hydrophobicity of GA > Qβ > MS2.

Investigators [89] noted that surface hydrophobicity could decipher dissimilarities in the sorption of bacteriophages. They juxtaposed the hydrophobicity of bacteriophages MS2, Qβ, and GA with known hydrophobic and hydrophilic surfaces. Hydrophobicity affected virus sorption to surfaces even in low ionic strength solution (1 mM NaNO₃), where electrostatic forces are anticipated to control [89] . Likewise, bacteriophages MS2, PRD1, and ΦX174 were juxtaposed. Despite varying charge densities among the three bacteriophages in low ionic strength electrolytes, Dika et al. [90] established identical EM at high ionic strength (100 mM). However, the bacteriophages diverged in their affinities for membranes of varying hydrophobicity. In addition, hydrophobicity has been established to affect virus sorption to finely powdered activated carbon positively [95] .

On the other hand, the molecular-level structure of virus capsids and the sorbent surface can hinder virion adsorption at close range. Such a steric hindrance happens when interactions between the adsorbent and adsorbate are restricted by the spatial orientation of their molecular structures. Many scientists have established steric hindrance in virus sorption. For example, Penrod et al. [69] discovered that steric interactions (here considering all non-electrostatic repulsion to be steric) might conduct to increased MS2 mobility in porous media when electrostatic forces are screened (i.e., at high ionic strength). Likewise, Armanious et al. [94] proposed that the variable topography of bacteriophage fr and MS2 capsids could have led to poor adsorption to a gold surface compared to bacteriophages Qβ and GA. Despite similar surface hydrophobicity, Dika et al. [89] found that bacteriophages preferentially sorbed to stainless steel over the glass. Such a tendency was more evident at high ionic strength, which conforms with the theory that surface roughness affects electrostatic interactions when the roughness is on a scale comparable to the Debye length (a measure of the effective range of electrostatic forces) [89] . As a rule, steric hindrance seemed to abate sorption in circumstances of identical electrostatic charge and hydrophobicity rather than primarily defining sorption behavior [1] .

Suspended and dissolved matters in the water matrix (e.g., NOM and dissolved salts) could considerably influence virion sorption. Due to the heterogeneous charge distribution and polarity of OM in the aquatic medium, the impact of NOM on virus sorption implicates electrostatic forces, hydrophobicity, and steric interactions. Usually, NOM carries polar and nonpolar moieties and possesses a negative charge at neutral and high pH due to the deprotonation of carboxyl and phenyl groups [70] [94] [96] . In porous media filtration trials, investigators [70] observed that MS2 breakthrough was quicker in sorbed or dissolved OM; however, ΦX174 breakthrough was comparatively unaltered. They concluded that NOM competes for sorption sites on the media and improves the nonpolar virions’ sorption by generating hydrophobic sites. Scientists [94] detected high sorption of bacteriophages GA and Qβ at pH 6 on a NOM-coated surface; however, MS2 and fr sorption was negligible. GA and Qβ sorption diminished considerably from pH 6 to pH 8, probably because of electrostatic repulsion emerging from the deprotonation of carboxyl groups on the NOM and capsid surfaces. When ionic strength was elevated from 10 mM to 100 mM to screen electrostatic forces, Qβ sorption was high even at pH 8; however, MS2 sorption was quantifiable, even so low. Such findings again depict that the hydrophobic effect controls only when electrostatic forces are weak. Investigators [87] noted that MS2 deposition on silica was more significant than on NOM-coated surfaces, even at ionic strengths high enough to screen electrostatic charges efficiently. They concluded that the findings could be related to steric hindrance, by which NOM surface structures avoid binding in contrast to the even surface of silica [1] .

Deposition tests have illustrated that cation bridging may considerably augment virion sorption to like-charged surfaces [86] [97] [98] . In cation bridging, divalent cations (like Ca²⁺ and Mg²⁺) form complexes with negatively-charged moieties on both the capsid and the solid surface [1] . The Ca²⁺ and Mg²⁺ occurrence significantly augments the sorption of viruses to repulsive surfaces in comparison to monovalent ions, beyond the expected increase due to the screening of electrostatic forces [86] [98] . On the other hand, rotavirus adsorption to an oppositely-charged (non-repulsive) surface was independent of Ca²⁺ or Mg²⁺ levels [86] . The influence of cation bridging may be notable at Ca²⁺ and Mg²⁺ levels typical of potable water sources [86] . For the bacterium Pseudomonas aeruginosa, cation bridging considerably improved sorption to repulsive surfaces at levels as low as 10⁻⁵ M Ca²⁺ or Mg²⁺ [1] . Interactions between MS2 virions have been depicted to transition from repulsive to attractive between 10 mM Ca²⁺ and 50 mM Ca²⁺ [97] .

Ca²⁺ ions have been established to possess a more significant positive effect on virus sorption to repulsive surfaces than Mg²⁺ ions [86] [98] . Ca²⁺ ions are large and possess weakly bound hydration spheres, permitting inner-sphere complexation with carboxyl groups on the virus capsid and the solid surface [86] [98] . On the other hand, Mg²⁺ ions have tightly-bound spheres of hydration that could let only outer-sphere complexation. The mechanism for the relatively weak sorption in the occurrence of Mg²⁺ may not be bridging but rather CN by complexation with negatively-charged moieties on either the virion or the surface [98] . The potential to generate bonds with carboxyl groups renders cation bridging very significant in the sorption of negatively charged viruses to NOM [1] . Scientists [98] discovered that Ca²⁺ enhanced the deposition of MS2 on a NOM-coated silica surface to a far greater extent than on a bare silica surface. However, the bare silica was more negatively charged than the NOM-coated surface. For juxtaposition, employing NOM from the same source yet in a monovalent electrolyte, scientists [87] observed poorer adsorption of MS2 on a NOM-coated surface than on a silica surface. Investigators [97] observed that a lower level of Ca²⁺ was needed to destabilize MS2 in the occurrence of NOM (10 mg/L total organic carbon; TOC).

Electrostatic repulsion participates in virion stability; thus, aggregation usually happens at high ionic strength or pH domains near the virion IP [1] . Likewise, Non-DLVO forces could affect virus aggregation. Scientists have pointed out that protein loops extending from the capsid surface could increase virions’ stability by steric hindrance [88] [97] . Virus aggregation is more considerable in the presence of the divalent cation, even if not in the regular Ca²⁺ and Mg²⁺ levels span in potable water [86] [88] [97] . Hydrodynamic forces could as well impact aggregation. Investigators proposed [1] suggested that the low EM of virion aggregates can be because of hydrodynamic drag. Aggregates could display more significant hydrodynamic drag because of permeability. Due to such a drag, aggregates remain aggregated once constituted [1] . On the other hand, the hydrodynamic drag of individual virions due to capsid permeability could counteract the repulsive electrostatic forces of surfaces and neighboring virions, leading to aggregation.

Although porous media investigations give worthy understandings, not all lessons could be presumed to be relevant to virus coagulation [1] . Unlike sorption to solid surfaces, coagulation could happen by sorption to solid flocs and complexation of the virion surface by dissolved coagulant (CN or inter-particle bridging). Also, metal oxide flocs diverge in structure, charge, and polarity from porous media. Deciding which parameters are necessary and sufficient to describe virion sorption during coagulation/flocculation remains hard.

Hydrophobicity is improbable to highly influence coagulation in several situations since Al(OH)_3(s) and Fe(OH)_3(s) are polar [1] . Nevertheless, in NOM, hydrophobicity could be a crucial partitioning factor for several viruses. Scientists [44] discovered that Al(OH)_3(s) became more hydrophobic following the NOM sorption. Consequently, NOM could improve the sorption of very hydrophobic virions. Because of the irregular, fractal structure of Al(OH)_3(s) and Fe(OH)_3(s) [1] , steric hindrance could likewise contribute to flocs’ sorption.

In 2019, Heffron [1] noted that definite proof of the impact of divalent cations on virus sorption to metal hydroxide flocs (as opposed to electrostatically repulsive and nonpolar surfaces) does not exist. In 1958, investigators [99] concluded that Ca²⁺ and Mg²⁺ could have inhibited virus mitigation. Nonetheless, the juxtaposition was performed between trials utilizing synthetic vs. raw water sources; therefore, the dissimilarity in virus reduction could not be conclusively ascribed to divalent cations, as opposed to, e.g., NOM. Investigators [100] depicted that alum coagulation of bacteriophage T4 was unaffected by Ca²⁺ and Mg²⁺ levels up to 330 mg/L as CaCO₃, even if they employed synthetic water free of NOM. Microbalance tests of virus deposition on Al(OH)_3(s) and Fe(OH)_3(s) surfaces, identical to those performed on silica and NOM-coated surfaces, may better recognize the significance of surface charge, hydrophobicity, and roughness, as well as divalent cations and NOM levels [1] .

Measuring virus demobilization constitutes an empirical defy [1] . Scientists [22] [25] [43] used a cultural plaque assay to express the number of infectious viruses in suspension and those sorbed to solids employing a recovery protocol. Such a procedure could be considered a “plaque-forming unit (PFU) balance.” Viruses are sampled in the supernatant following gravitational separation and recovered from the floc. The total virus recovery is juxtaposed to the untreated control sample to calculate demobilization. A PFU balance differs from a mass balance since it is a discrete count of PFUs, not a continuous measure of mass. Like any plaque assay, the PFU balance may distinguish between infectious and inactive viruses, not between a single virus and an aggregate [1] . Furthermore, juxtaposing recovered PFUs with the initial concentration permits the evaluation of virus demobilization within the expected method recovery efficiency [43] . Nevertheless, the PFU balance’s procedure needs twice the number of plaque assays to analyze the concentrations of viruses in suspension and adsorbed to flocs, augmenting cost, and time inputs.

Other investigators [13] [14] [23] [60] [103] employed qPCR (qRT-PCR for RNA viruses) to contrast copy number decreases with PFU counts. Juxtaposed with plaque assays, qPCR is somewhat fast, and aggregation does not influence qPCR findings. Oppositely to plaque assays, qPCR estimates the total number of intact viral genomes in the sample, in any case, infectivity, permitting a comparison between plaque assay and qPCR findings to evaluate complete demobilization. Nonetheless, there are many worries with juxtaposing molecular and cultural techniques. Because of genome damage, molecular procedures cannot distinguish between physical elimination and demobilization [1] . The copy number of even short amplicons could lessen throughout demobilization [43] . During estimating chemical oxidation using dissolved PACl, researchers [23] likewise noticed a reduction in copy number (around 1 log₁₀ from the initial concentration). However, if the depressed recovery is an artifact of the procedure or indicative of genome destruction remains ambiguous. Such a decrease in copy number during coagulation research would be indiscernible from a lowering because of physical elimination, as depicted in Figure 2. Consequently, qPCR could amplify the physical removal significance and minimize that of demobilization.

Identically, a few parts of demobilized viruses are possibly retained with the flocs and thus considered as physical removal. Demobilized viruses can unexpectedly be disproportionately eliminated. Destruction of viral proteins could considerably modify virion structure and genome packing [111] . The influence of morphological alterations on sorption could not be minor. If infectious viruses are more easily retained in flocs, then qPCR analysis of treated water would be suitable for assessing total viruses (infectious + inactive). If inactive viruses are easily included in the floc phase, qPCR analysis would once more systematically underreport demobilization [1] .

Researchers [60] examined the liquid phase and dissolved floc of treated water using qPCR and plaque assay (essentially performing both a PFU balance and a copy number balance). Despite significant decreases in amplicons in the liquid phase, they recovered roughly all MS2 and Qβ amplicons from the floc. The elevated recovery designates that MS2 and Qβ demobilization by genome destruction was below detection [60] . Such absence of genome demobilization may mirror

the demobilization pathway of PACl. Nonetheless, Qβ demobilization was evident in the floc and liquid phases, showing the retention of demobilized viruses in flocs. For both bacteriophages, a more considerable disparity between molecular and cultural quantification was noticed in the liquid phase than in the floc phase. The more noticeable difference in the liquid phase may be related to aggregation, mainly considering that the liquid phase was only centrifuged (2000 × g, 10 min), not dissolved and agitated for resuspension like the floc phase [1] . Nonetheless, such findings [60] propose that genome demobilization could not considerably affect qPCR findings for several bacteriophages and treatment techniques. On the other hand, employing qPCR without recovery from flocs could under-represent demobilization related to the sorption of demobilized viruses in the floc, like in the situation of Qβ. Following the appointed study remains needed to determine a firm methodological basis before utilizing qPCR and plaque assays without recovery from flocs.

The scope of data that could be acquired utilizing the quantification procedures examined above is recapitulated in Figure 2. Integrating plaque assay with recovery from flocs furnishes the most detailed account of virus fate; nonetheless, one or more of such fates are possibly to be undetectable in practice. A plaque assay with recovery likewise gives more pertinent data (i.e., the level of infectious viruses in the sludge) than qPCR and plaque assay without recovery [1] . If several fates could be seen as inessential for a specific usage (esp., demobilization related to genome damage), integrating qPCR and plaque assay without recovery would be comparable to plaque assay with recovery.

Dealing with increased degrees of virus lowering (i.e., logarithmic representations are usual) likewise constitutes a problematic question. Whether quantified by molecular or cultural methods, demobilization is assessed by subtracting a concentration of recovered PFUs or amplicons from an initial higher concentration of several orders of magnitude. As the error of each quantity is relative to the concentration, demobilization can only be assessed to a statistical degree of certainty when inactivation is a primary reduction mechanism, as illustrated in Figure 3 [1] .

Also, demobilization is commonly seen as independent from physical removal rather than additive. If demobilization works as a polishing step, small numbers of demobilized viruses could have a considerable influence. For instance, if an additional 0.09% of the initial virus concentration is demobilized beyond the 99.9% that can be retained in flocs, that minimal reduction signifies the difference between satisfying the EPA’s SWTR requirements and not [59] . The restricted data obtainable advocates demobilization might have such a polishing impact [1] . As debated in Section 3.1, scientists [60] noticed more significant demobilization of MS2 and Qβ in the liquid phase than in the floc phase, which significates that demobilization may participate in virus removal beyond the potential of physical removal alone (i.e., demobilized viruses would not necessarily have been physically retained were they not demobilized). After physical retention, demobilization’s “polishing” impact would greatly diminish the level of viruses remaining in the treated water. Nevertheless, such a modest virus removal would be lost on the scale of the original spiked concentration. Consequently, even if crucial for disinfection, the degree of demobilization would be hard to recognize practically. If the demobilization cannot be precisely determined, demobilization parameters cannot be adjusted.

As illustrated in Figure 2, aggregation stays quantitatively indiscernible in all methods from at least some demobilization—aggregation guides to artificially low plaque counts since each originates from numerous viruses instead of one [1] . Founded on aggregate size, researchers [112] observed that aggregation could be responsible for more than 4 log₁₀ lowering in PFUs (from an initial concentration of around 10¹¹ PFU/mL). Nevertheless, extra control could furnish some “insurance” against aggregation for the plaque assay with the recovery method. The efficiency of the recovery method could be examined below parameters of minimal demobilization (like adsorbing viruses on pre-formed flocs or quenching oxidants with sodium thiosulfate). The recovery efficiency depicts those viruses can be recovered from the flocs and that the viruses in the treated water are no more aggregated than in the initial virus suspension. Scientists [60] [78] have likewise relied on electron micrographs to illustrate the occurrence or absence of aggregates qualitatively.

Dynamic Light Scattering (DLS) is a procedure for estimating the electrokinetic response of colloids and the size distribution of particles in suspension. Several investigations [23] [60] [90] [103] [112] employed DLS analysis to regulate circumstances where virions aggregate. Nevertheless, DLS analysis needs very high virus concentrations (>10⁹ PFU/mL) [43] —higher than even the usual spiking concentrations utilized for testing (commonly 10⁷ - 10⁸ PFU/mL). Consequently, scientists cannot directly evaluate aggregation in the same samples to be tried by plaque assay and/or qPCR. As an alternative, investigators should attempt to establish whether or not aggregation happens in circumstances identical to those tried [1] .

An important volume of virus stock suspension is requisite for DLS to reach the needed concentrations. Such stock suspensions could possess higher ionic strengths and diverge considerably in composition from natural waters. Electrolyte composition may greatly influence electrokinetic responses such as aggregation [83] . Aggregation is more considerable in phosphate-buffered saline (PBS), which is usually utilized for virus stocks, than in deionized water or bicarbonate solution [87] . Ideally, virus stocks must be purified and spiked into the identical water matrix employed for coagulation tests. Nonetheless, the procedure of virus purification could likewise considerably impact virion characteristics. As discussed above, scientists [89] juxtaposed three approaches of MS2 purification: PEG precipitation, successively dialyze in deionized water and 1 mM NaNO₃, and ultracentrifugation in a CsCl gradient. PEG precipitation led to a larger hydrodynamic radius of unaggregated viruses, with aggregation detected at pH 6. Dialysis led to aggregation at pH 4; however, viruses separated in a CsCl gradient did not aggregate at any pH. Each procedure possesses disadvantages: PEG seems to adhere to the capsid surface, dialysis retains viral and non-viral particles based only on membrane exclusion, and cesium ions may permanently deform protein structures [89] . Nevertheless, the test does not define which purification best approximates virus behavior in the environment [1] .

Coagulation techniques implying zero-valent or ferrous iron possess the gathered complexity of redox reactions. Different from Al, Fe has several stable valence states. The products generated by mixed-valent iron precipitation change from ferrous minerals (e.g., green rust and magnetite) to ferric minerals (e.g., ferrihydrite, lepidocrocite, and goethite) [113] [114] [115] [116] . The unique precipitation products generated are a function of the degree of the ions in suspension; however, the oxidative circumstances finally control the valence state of iron [114] [115] [116] . Fe oxidation via dissolved oxygen (DO) can catalyze the oxidation of other metals and organic compounds [1] [117] [118] [119] . Ferrous oxidation has also been examined for disinfection implementations [120] [121] . Therefore, one possible pathway of virus reduction via ferrous chloride coagulation/iron EC is demobilization due to ferrous iron oxidation.

Researchers [120] [122] established virus demobilization using iron oxidation due to Fenton’s reagent and ferrous/zero-valent iron alone. Disinfection was more significant at pH 5.5 - 6), possibly related to an augmented residence period with ferrous ions and more excellent radical oxygen species formation. They observed greater MS2 abatements employing zero-valent iron nanoparticles than ferrous ions, and the nanoparticles were less dependent on DO. They supposed that viruses might have been demobilized by surface interactions without oxygen to form hydrogen peroxide, leading to Fenton-like reactions [1] [120] [123] .

Employing enzyme-linked immunosorbent assay (ELISA) to reveal a reduction in antigenicity and qRT-PCR to reveal chromosomal destruction, researchers [120] discovered that capsid deterioration (lower antigenicity) was a route of MS2 disinfection for ferrous ions. At the same time, qRT-PCR did not detect genomic harm. Zero-valent nanoparticles were observed to demobilize viruses by both capsid and genome destruction. Even if the investigation utilized ELISA and qRT-PCR besides cultural procedures to emphasize virus demobilization, the participation of virus aggregation in log lowering in PFUs could not be completely ruled out since the MS2 phages were not eluted following treatment. Also, regardless of being adopted mainly as a surrogate virus for filtration treatment units, MS2 could be more vulnerable to some forms of disinfection than other likely bacteriophage surrogates for human viruses of interest [1] [124] .