Double Droplets Impact an Inclined Superhydrophobic Surface.

The rebound dynamics of double droplets impacting an inclined superhydrophobic surface decorated with macro-ridges are investigated via lattice Boltzmann method (LBM) simulations. Four rebound regions are identified, that is, the no-coalescence-rebound (NCR), the partial-coalescence-rebound of the middle part bounces first (PCR-M), and the side part bounces first (PCR-S), as well as the complete-coalescence-rebound (CCR). The occurrence of the rebound regions strongly depends on the droplet arrangement, the center-to-center distance of the droplets, and the Weber number. Furthermore, the contact time is closely related to the rebound regions. The PCR-M region can significantly reduce the contact time because the energy dissipation in this region may decrease which can promote the rebound dynamic. Intriguingly, the contact time is also affected by the droplet arrangement; i.e., droplets arranged parallel to the ridge dramatically shorten the contact time since this arrangement increases the asymmetry of the liquid film. Therefore, for multidrop impact, the contact time can be effectively manipulated by changing the rebound region and the droplet arrangement. This work focuses on elucidating the wetting behaviors, rebound regions, and contact time of the multiple-droplet impacting an inclined superhydrophobic surface decorated with macro-ridges.

Coalescence-Induced Jumping of Nanodroplets in a Perpendicular Electric Field: A Molecular Dynamics Study.

Coalescence-induced jumping has promised a substantial reduction in the droplet detachment size and consequently shows great potential for heat-transfer enhancement in dropwise condensation. In this work, using molecular dynamics simulations, the evolution dynamics of the liquid bridge and the jumping velocity during coalescence-induced nanodroplet jumping under a perpendicular electric field are studied for the first time to further promote jumping. It is found that using a constant electric field, the jumping performance at the small intensity is weakened owing to the continuously decreased interfacial tension. There is a critical intensity above which the electric field can considerably enhance the stretching effect with a stronger liquid-bridge impact and, hence, improve the jumping performance. For canceling the inhibition effect of the interfacial tension under the condition of the weak electric field, a square-pulsed electric field with a paused electrical effect at the expansion stage of the liquid bridge is proposed and presents an efficient nanodroplet jumping even using the weak electric field.

Bouncing Dynamics of Drops' Successive Off-Center Impact.

Bouncing dynamics of a trailing drop off-center impacting a leading drop with varying time intervals and Weber numbers are investigated experimentally. Whether the trailing drop impacts during the spreading or receding process of the leading drop is determined by the time interval. For a short time interval of 0.15 ≤ Δt* ≤ 0.66, the trailing drop impacts during the spreading of the leading drop, and the drops completely coalesce and rebound; for a large time interval of 0.66 < Δt* ≤ 2.21, the trailing drop impacts during the receding process, and the drops partially coalesce and rebound. Whether the trailing drop directly impacts the surface or the liquid film of the leading drop is determined by the Weber number. The trailing drop impacts the surface directly at moderate Weber numbers of 16.22 ≤ We ≤ 45.42, while it impacts the liquid film at large Weber numbers of 45.42 < We ≤ 64.88. Intriguingly, when the trailing drop impacts the surface directly or the receding liquid film, the contact time increases linearly with the time interval but independent of the Weber number; when the trailing drop impacts the spreading liquid film, the contact time suddenly increases, showing that the force of the liquid film of the leading drop inhibits the receding of the trailing drop. Finally, a theoretical model of the contact time for the drops is established, which is suitable for different impact scenarios of the successive off-center impact. This study provides a quantitative relationship to calculate the contact time of drops successively impacting a superhydrophobic surface, facilitating the design of anti-icing surfaces.

Impact Dynamics of a Droplet on Superhydrophobic Cylinders Structured with a Macro Ridge.

Reducing the contact time of a droplet hitting a solid surface is crucial for many situations. In this work, the dynamic behavior of a low-viscosity droplet on a superhydrophobic surface, which consists of a cylindrical substrate and a macro ridge placed axially on the peak, was numerically investigated via the lattice Boltzmann method. The focus was given to the spreading and the detaching morphology of the droplet at the Weber number We = 0.84-37.8 and the cylinder-to-droplet radius ratio R* = 0.57-5.71. The ridge is found to redistribute the droplet mass and affect the impact outcomes, as well as the contact time. For each R*, a jug rebound, a stretched rebound straddling the ridge, and a split detachment occur sequentially with the increasing We. When R* does not exceed 1.71, the contact time decreases continuously with the increase in We. With R* being taken between 1.71 and 5.14, the contact time initially reduces with We and plateaus after We reaches 10.3. Once R* exceeds 5.14, the split droplets may present as a bestriding shape at We > 30.3 rather than the regular jug shape with a small We. The contact time would be decreased to a second plateau in this case. In most cases, the contact time can be shortened effectively for the droplet on a ridged cylinder compared with that of a smooth cylinder.

What Controls the Hole Formation of Nanodroplets: Hydrodynamic or Thermodynamic Instability?

Using molecular dynamics simulations, we investigate the air hole formation of water nanodroplets impacting hydrophilic to hydrophobic surfaces in the range of static contact angles from 30° to 140° with different initial surface temperatures ranging from 300 to 1000 K. We show that the hole dynamics of nanodroplets are different from those observed in millimeter-sized droplets. The hole formation can be observed on smooth surfaces for nanodroplets; however, it only occurs on nonsmooth surfaces for millimeter-sized droplets. We clarify that the hole formation of nanodroplets is triggered by a nucleated vapor bubble due to thermodynamic instability, whereas it is initiated by air bubble entrapment during impact due to hydrodynamic instability for millimeter-sized droplets. The hole formation of nanodroplets relies heavily on the surface temperature and surface wettability, because the nucleated vapor bubble more easily occurs and grows on the surface with high initial temperatures and hydrophobic surfaces. Based on the thermal stability analysis, a criterion is developed to predict the hole formation of nanodroplets, which verifies the dependence of hole formation on the surface temperature and wettability. Furthermore, we show that the ring-bouncing of nanodroplets is triggered by the nucleated vapor bubble. We clarify the reasons for the reduced contact time of nanodroplets caused by the ring-bouncing.

Molecular Insights into Curvature Effects on the Capacitance of Electrical Double Layers in Tricationic Ionic Liquids with Carbon Nanotube Electrodes.

Ionic liquid (IL) electrolytes and carbon nanotube (CNT) electrodes have exhibited promising electrochemical performance in supercapacitors. Nevertheless, the adaptability of tricationic ILs (TILs) in CNT-based supercapacitors remains unknown. Herein, the performance of supercapacitors with (6,6), (8,8), (12,12), and (15,15) CNT electrodes in the TIL [C6(mim)3](Tf2N)3 was assessed via molecular dynamics simulations, paying attention to the electric double-layer (EDL) structures and the relations between the CNT curvature and capacitance. The results disclose that counterion and co-ion number densities near CNT electrodes have a marked reduction, compared with that of the graphene electrode. The capacitance of the EDL in the TIL increases significantly as the CNT curvature increases and the capacitance of the TIL/CNT systems is higher than that of the TIL/graphene system. Moreover, different EDL structures in the TIL and the monocationic IL (MIL) [C6mim][Tf2N] near CNT electrodes were revealed, showing higher-concentration anions [Tf2N]- at the CNT surfaces in the TIL. It is also verified that the TIL has a greater energy-storage ability under high potentials. Furthermore, the almost flat or weakly camel-like capacitance-voltage (C-V) curve of EDLs in the TIL turns into a bell shape in the MIL, because of the ion accumulation at the CNT surfaces and the associations between ions.

Contact Time of Droplet Impact on Superhydrophobic Cylindrical Surfaces with a Ridge.

This study investigates whether adding ridges to a superhydrophobic cylindrical surface can reduce contact times compared to those of ridged flat or cylindrical surfaces, inspired by the shortened contact time achieved by adding ridges to flat surfaces. The study focuses on studying azimuthal ridges on the cylinder through experimentation, emphasizing the impact dynamics and contact time characteristics under varying We (Weber number) and D* (dimensionless droplet diameter). Within the ultralow Weber number range (ULWR), low Weber number range (LWR), and medium Weber number range (MWR), the contact time is longer than on ridged flat surfaces. In the high Weber number range (HWR), the opposite is observed: increased inertial forces lead to the rupture of the liquid film above the ridges due to Rayleigh-Plateau instability. As a result, the primary droplet splits into two sections with curvature effects promoting its recoiling and rebounding. This study introduces a criterion, defined as C = We/D*, and finds that when C exceeds 2.42, not only is the contact time shorter than on ridged flat or cylindrical surfaces, but it also further decreases with an increase in We or a decrease in D*. The contact time characteristics observed in the HWR offer potential applications in areas such as anti-icing.

Electrically Manipulated Vapor Condensation on the Dimpled Surface: Insights from Molecular Dynamics Simulations.

Random vapor nucleation leads to flooding condensation with degraded heat-transfer efficiency. Since an external electric field has a significant effect on manipulating droplets' motion, it is possible to be one of the effective methods to hinder flooding phenomena and improve the heat-transfer rate by applying the external electric field during condensation. However, the motion of nanodroplets is more sensitive to the electric field owing to the scale effect on the nanoscale. The effect of the electric field on growth has not explicitly been comprehended. This work studied the condensation processes on a nanodimpled surface under an electric field with various strengths and directions. The results showed that condensed droplets' growth under the electric field depends on the competition between the electric field force and solid-liquid interactions. Increased vertical electric field strength, the higher torsion by the electric field hindered the motion of vapor, decreased the collision frequency for water molecules with the cooled surface, and elongated the cluster when the electric field force dominates, thus deteriorating the condensation performance. While applying the horizontal electric field, the greater electric field strength leads to better condensation performance by the larger contacting area for heat exchange. A wetting transition induced by the electric field was observed when the electric field strength increased to a certain extent (E > 5.2 × 108 V/m in this study). When the V-shaped surface replaced the dimpled surface as the condensed substrate, the same wetting transition phenomena occurred under a more significant horizontal electric field strength, showing that this method is universal. Besides, different electric field frequencies influenced both the growth and the nucleation, thus exhibiting various condensation performances.

Theoretical and Three-Dimensional Molecular Dynamics Study of Droplet Wettability and Mobility on Lubricant-Infused Porous Surfaces.

Profiting from their slippery nature, lubricant-infused porous surfaces endow with droplets excellent mobility and consequently promise remarkable heat transfer improvement for dropwise condensation. To be a four-phase wetting system, the droplet wettability configurations and the corresponding dynamic characteristics on lubricant-infused porous surfaces are closely related to many factors, such as multiple interfacial interactions, surface features, and lubricant thickness, which keeps a long-standing challenge to promulgate the underlying physics. In this work, thermodynamically theoretical analysis and three-dimensional molecular dynamics simulations with the coarse-grained water and hexane models are carried out to explore droplet wettability and mobility on lubricant-infused porous surfaces. Combined with accessible theoretical criteria, phase diagrams of droplet configurations are constructed with a comprehensive consideration of interfacial interactions, surface structures, and lubricant thickness. Subsequently, droplet sliding and coalescence dynamics are quantitatively defined under different configurations. Finally, in terms of the promotion of dropwise condensation, a non-cloaking configuration with the encapsulated state underneath the droplet is recommended to achieve high droplet mobility owing to the low viscous drag of the lubricant and the eliminated pinning effect of the contact line. On the basis of the low oil-water and water-solid interactions, a stable lubricant layer with a relatively low thickness is suggested to construct slippery surfaces.

Working Regime Criteria for Microscale Electrohydrodynamic Conduction Pumps.

We investigated the microscale electrohydrodynamic (EHD) conduction pumps in a wide range of working regimes, from the saturation regime to the ohmic regime. We showed that the existing macro- and microscale theoretical models could not accurately predict the electric force of microscale EHD conduction pumps, especially for the cases of a strong diffusion effect. We clarified that the failure is caused by a rough estimate of the heterocharge layer thickness. We revised the expression of heterocharge layer thickness by considering the diffusion effect and developed a new theoretical model for the microscale EHD conduction pumps based on the revised expression of heterocharge layer thickness. The results showed that our model can accurately predict the dimensionless electric force of the microscale EHD conduction pumps even for the cases of a strong diffusion effect. Furthermore, we developed a working regime map of microscale EHD conduction pumps and found that the microscale EHD conduction pumps more easily fall into the saturation regime compared with the macroscale EHD conduction pumps due to the enhanced diffusion effect; in other words, the microscale EHD conduction pumps have a wider saturation regime. We showed that the conduction number C0 could not distinguish the working regime of the microscale EHD conduction pumps because it does not take the diffusion effect into account. By employing the revised expression of heterocharge layer thickness, we proposed a new dimensionless number, C0D to distinguish the working regimes of microscale EHD conduction pumps.

Contact Time of a Droplet Off-Centered Impacting a Superhydrophobic Cylinder.

Extensive research has shown that a superhydrophobic cylindrical substrate could lead to a noncircumferential symmetry of an impacting droplet, reducing the contact time accordingly. It is of practical significance in applications, such as anti-icing, anticorrosion, and antifogging. However, few accounts have adequately addressed the off-centered impact of the droplet, despite it being more common in practice. This work investigates the dynamic behavior of a droplet off-centered impacting a superhydrophobic cylinder via the lattice Boltzmann method. The effect of the off-centered distance is primarily discussed for droplets taking various Weber numbers and cylinder sizes. The results show that the imposition of an off-center distance can further disrupt the droplet symmetry during the impact. As the off-center distance increases, the droplet movement is gradually tilted toward the offset side until it tangentially passes the cylinder side, resulting in a direct dripping mode. The dynamic features, focusing mainly on maximum spreading in the axial direction and contact time, are specifically explored. A quantitative model of the maximum spreading factor is proposed based on the equivalent transformation from the off-center impact into oblique hitting, considering the full range of off-centered distance. A preliminary contact time model is established for droplet off-centered impacting superhydrophobic cylinders by substituting the maximum spreading and the effective velocity of the liquid moving. This work aims to make an original contribution to the fundamental knowledge of droplet impact and could be of value for related applications.

Effect of Asymmetry on the Contact Time of Droplet Impact on Superhydrophobic Cylindrical Surfaces.

Reducing the contact time during the droplet impact on the surface is crucial for anti-icing, self-cleaning, and heat transfer optimization applications. This study aims to minimize the contact time by modifying the surface curvature to create an asymmetric impact process. Our experiments showed that the increase in Weber numbers (We) and the decrease in the ratio of surface diameter to droplet diameter (D*) intensify the asymmetry of the impact process, yielding four distinct rebound modes. Low asymmetry observes the liquid retract toward the central point (Rebound Modes 1 and 2), whereas high asymmetry yields a wing-like rebound (Rebound Modes 3 and 4). In Rebound Mode 1, increased asymmetry would lead to more extended contact due to the prolonged waiting period. Conversely, the reduction in contact time in Rebound Mode 2 occurs due to increased asymmetry with no waiting period. For Rebound Modes 3 and 4, the retraction time could be divided into three stages, generated by two liquid detachment modes from the surface. Analysis reveals that an increased asymmetry would reduce the retraction time during the first stage but prolong it during the third stage, with no significant effects on the second. Four correlations, each pertaining to a distinct impact mode, are proposed based on these analyses to describe the contact time concerning We and D* for droplets impacting a superhydrophobic cylindrical surface.

Asymmetric Condensation Characteristics during Dropwise Condensation in the Presence of Non-condensable Gas: A Lattice Boltzmann Study.

In this work, the condensation characteristics of droplets considering the non-condensable gas with different interaction effects are numerically studied utilizing a multicomponent multiphase thermal lattice Boltzmann (LB) model, with a special focus on the asymmetric nature induced by the interaction effect. The results demonstrate that for isolated-like growth with negligible interactions, the condensation characteristics, that is, the concentration profile, the temperature distribution, and the flow pattern, are typically symmetric in nature. For the growth regime in a pattern, the droplet has to compete with its neighbors for catching vapor, which leads to an overlapping concentration profile (namely the interaction effect). The distribution of the condensation flux on the droplet surface is consequently modified, which contributes to the asymmetric flow pattern and temperature profile. The condensation characteristics for droplet growth in a pattern present an asymmetric nature. Significantly, the asymmetric condensation flux resulting from the interaction effect can induce droplet motion. The results further demonstrate that the interaction strongly depends on the droplet's spatial and size distribution, including two crucial parameters, namely the inter-distance and relative size of droplets. The asymmetric condensation characteristics are consequently dependent on the difference in the interaction intensities on both sides of the droplet. Finally, we demonstrate numerically and theoretically that the evolution of the droplet radius versus time can be suitably described by a power law; the corresponding exponent is kept at a constant of 0.50 for isolated-like growth and is strongly sensitive to the interaction effect for the growth in a pattern.

Impact Dynamics of a Single Droplet on Hydrophobic Cylinders: A Lattice Boltzmann Study.

This study numerically investigates the effects of the Weber number (We) and cylinder-to-droplet radius ratio (R*) on the impact dynamics of a low-viscosity droplet on a hydrophobic cylinder by the lattice Boltzmann method. The intrinsic contact angle of the surface is chosen as θ0 = 122°± 2°, which ensures a representative hydrophobicity. The regime diagram of the impact dynamics in the parameter space of We versus R* is established with categories of split and nonsplit regimes. The droplet would split during impact as α = We/R* exceeds a critical value. In the nonsplit regime, the droplet bounces off the cylinder at most Weber numbers unless the impact velocity is minuscule (We < 2). The contact time of the droplet on the cylinder surface decreases with increasing R* or decreasing We, indicating bouncing is facilitated under such conditions. This can be explained by the suppressed adhesion dissipation between the droplet and surface due to a reduction in the contact area. In the split regime, sufficient kinetic energy inside the impacting droplet determines whether the whole droplet could detach from the surface. With a small cylinder (R* < 0.83) and large We (>25), the adhesion effect is weakened for the side fragments because of the small contact area, and it facilitates the dripping of fragments. For other conditions, the detachment, especially for the tiny droplet on the cylinder top, only occurs if the deformation is prominent at We > 35. Moreover, the spreading dynamics of the impacting droplet are also highlighted in this work.

Effects of Nanodroplet Sizes on Wettability, Electrowetting Transition, and Spontaneous Dewetting Transition on Nanopillar-Arrayed Surfaces.

In this study, the wetting and dewetting behaviors of water nanodroplets containing various molecule numbers on nanopillar-arrayed surfaces in the presence or absence of an external electric field are investigated via molecular dynamics (MD) simulations, aiming to examine whether there is a scale effect. The results show that, in the absence of an electric field, nanodroplets on coexisting Cassie/Wenzel surfaces may be in the Cassie or the Wenzel state depending on their initial states, and apparent contact angles of the Cassie or Wenzel nanodroplets increase monotonously with increasing the droplet size. Energy analysis shows that on the same coexisting Cassie/Wenzel surface, when an electric field is imposed, a small nanodroplet possesses a lower energy barrier separating the Cassie state from the Wenzel state. Therefore, the small nanodroplet is easier to collapse into the Wenzel state. Moreover, the spontaneous Wenzel-to-Cassie dewetting transition is not observed for the nanodroplets after the removal of the electric field because the Wenzel state is a globally stable energetic state. With the same pillar geometry, both the wetting transition and the dewetting transition are significantly modified for liquids with higher intrinsic contact angles. The energy barrier of the wetting transition increases for both the large and small nanodroplets, meaning that the Cassie state becomes more robust. The energy curve shows that the Wenzel state of the large nanodroplet has higher energy so that the droplet can return to the Cassie state when removing the electric field. Intriguingly, although the small Wenzel nanodroplet has lower energy in the presence of the electric field, the dewetting transition still occurs. The increased solid-liquid interfacial tension when removing the electric field is responsible for this abnormal result. The wetting and dewetting transitions follow different energy pathways, leading to a hysteresis energy loop. There exists a critical water molecule number separating the unstable/stable Wenzel configurations, above which the Cassie state is energetically favorable and the dewetting transition can occur spontaneously after removing the electric field.

Rebound Behaviors of Multiple Droplets Simultaneously Impacting a Superhydrophobic Surface.

The rebound behaviors of multiple droplets simultaneously impacting a superhydrophobic surface were investigated via lattice Boltzmann method (LBM) simulations. Three rebound regions were identified, i.e., an edge-dominating region, a center-dominating region, and an independent rebound region. The occurrence of the rebound regions strongly depends on the droplet spacing and the associated Weber and Reynolds numbers. Three new rebound morphologies, i.e., a pin-shaped morphology, a downward comb-shaped morphology, and an upward comb-shaped morphology, were presented. Intriguingly, in the edge-dominating region, the central droplets experience a secondary wetting process to significantly prolong the contact time. However, in the center-dominating region, the contact time is dramatically shortened because of the strong interactions generated by the central droplets and the central ridges. These findings provide useful information for practical applications such as self-cleaning, anticorrosion, anti-icing, and so forth.

Harnessing Reversible Wetting Transition to Sweep Contaminated Superhydrophobic Surfaces.

Sweeping deposited particles is absolutely essential in order to maintain the excellent functionality of superhydrophobic surfaces. Many methods have been proposed to sweep microparticles deposited on tips of micro/nanostructures. However, how to sweep nanoparticles trapped in cavities of superhydrophobic surfaces has remained an outstanding issue. Here, we show that harnessing the reversible wetting transition provides a feasible way to sweep such nanoparticles. Using molecular dynamics simulations, we demonstrate that the electrically induced CB-W wetting transition makes liquid intrude into a groove and wet a trapped hydrophilic nanoparticle; however, once the electric field is removed, a spontaneous W-CB dewetting transition happens, and the extruded liquid transports the hydrophilic nanoparticle to the groove top, successfully picking up the trapped hydrophilic nanoparticle. We further find that the adhesion between the nanoparticle and groove bottom wall hinders the successful pickup, and picking up such a nanoparticle requires a stronger particle hydrophilicity. With the introduction of amphiphilic Janus particles into a liquid, we exhibit that the electrically induced reversible wetting transition can also successfully pick up a trapped hydrophobic nanoparticle. By means of calculations of the potential of mean force (PMF), we reveal pathways of both the CB-W wetting transition and the W-CB dewetting transition and hence answer why and how a hydrophilic or a hydrophobic nanoparticle is picked up successfully.

Universal Model for the Maximum Spreading Factor of Impacting Nanodroplets: From Hydrophilic to Hydrophobic Surfaces.

Using molecular dynamics (MD) simulations, we investigate impact behaviors of water nanodroplets on hydrophilic to hydrophobic surfaces with static contact angles ranging from 21 to 148° in a wide Weber number range of 15-90, aiming to understand how the surface wettability influences the maximum spreading factor of nanodroplets. We show that the existing macroscale and nanoscale models cannot capture the influence of surface wettability on the maximum spreading factor. We demonstrate that the failure is attributed to the rough estimation of the spreading velocity during the spreading stage, which is assumed to be a constant value in these models. We show that the spreading velocity strongly depends on both the surface wettability and the Weber number. After scaling with the impact velocity, we obtain a universal function of the spreading velocity with respect to the static contact angle and the Weber number. We employ this function to modify the expression of viscous dissipation and develop a new model of the maximum spreading factor. We verify that the model is in excellent agreement with the MD simulations regardless of hydrophilic and hydrophobic surfaces, with the mean relative deviation ranging from 0.88 to 4.75%. We also provide evidence to support the fact that incorporating the influence of surface wettability by modifying viscous dissipation is more reasonable than by modifying surface energy for nanodroplet impact.

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Potassium (K) is the second most abundant nutrient in plant leaves after nitrogen (N) and the most abundant cation in plant cells. It plays an important role in plant growth regulation, homeostasis maintenance, and stress response. Previous studies on the effects of N input on plant nutrient status mainly focus on N and phosphorus (P), but less on K and its stoichiometry. We examined the effects of N input and mowing on K content and N:K at both plant functional group and community levels. We analyzed the relative contribution of changes in functional groups and community composition to changes of community level nutrition status. The results showed that N input increased N content of each plant functional group and increased K content of rhizomatous grasses and legumes. Mowing reduced N content of rhizomatous grasses and bunchgrass, but did not affect K content and N:K of all functional groups. Nitrogen input significantly increased plant N and K contents at the community level, while mowing significantly increased plant N content. Both N input and mowing did not affect plant N:K at functional group and community levels. The contribution of nutritional changes in plant functional groups to the variation at the community level was greater than that of changes in community composition. For all the three examined nutritional traits, the contribution of nutrients at functional group level and that of community composition showed negative covariation. Our results indicated that plant N:K had high homeostasis in meadow steppe and that plants could regulate N and K balance, which was of great significance for maintaining N:K stoichiometry under the background of increasing N deposition.

Homogeneously and heterogeneously structured biofilm models for wastewater treatment.

Biofilm, a layer comprising extracellular polymeric substances, is the platform where the embedded living cells degrade the substances in the wastewaters. Biofilm models have been developed as part of the comprehensive models for the wastewater treatment process. This review summarizes the biofilm models applied in contemporary literature based on the spatial dimensions adopted for model build-up. The most commonly applied biofilm models are null-dimensional, considering the biofilm active biomass for the substrate sink's biological reaction. The one-dimensional, multi-species models are the second standard models for contemporary studies, providing transport and reaction resistances of substrates in the biofilm matrix and the interactions of competing or collaborating strains in the biofilm. The structural homogeneity of the biofilm challenges the validity of the uniformly structured models, highlighting the need to re-examine the validity of the uniformly structured models. The challenges and prospects of biofilm model developments and applications are outlined.