Membrane dehumidification technology has gained significant attention for its efficiency, energy savings, and simplicity. Enhancing the performance of membrane dehumidification is crucial as it directly impacts energy efficiency and indoor comfort, promoting wider adoption of this innovative approach. Significant advances have been made in enhancing membrane dehumidification performance from the perspectives of materials, modules, and systems. This review delves into recent developments, focusing on enhancement methods, dehumidification effects, and limitations. Innovations in membrane materials, such as the use of nanoparticles and hydrophilic functional groups, improve permeability, selectivity, and durability. Moreover, novel module designs, like porous or spiral-wound configurations, increase the surface area and optimize flow dynamics, thereby boosting the dehumidification efficiency. Connecting multiple modules in series or parallel enhances performance but introduces manufacturing complexities, higher flow resistance, and fouling risks. At the system level, integrating membranes with heat recovery or renewable energy systems can reduce energy consumption by over 20 % compared to traditional methods. In this review, the optimization recommendations for membrane materials, modules, and systems were proposed. Combining molecular-scale modeling with experimental testing provides a precise path for upgrading membrane properties. The mass transfer characteristics within modules, along with multi-objective optimization, support a more efficient and rational design of the membrane module. Additionally, the exergy analysis can identify energy-intensive areas, refining the system design strategies for greater efficiency.

In this study, the multiple-factor analysis of dehumidification performance and flow resistance for the cross-flow membrane module was carried out based on the orthogonal test. Three operating and four structural parameters were selected as the independent variables for two test indicators, i.e., dehumidification rate ( γ ) and dehumidification account of per unit pressure drop (Δ φ /Δ p ). The influence of seven factors on the test indicators was ranked by the single factor analysis of range. The results indicated that the inlet velocity of humid air, u in , has the most important influence on γ and Δ φ /Δ p . Among the structural parameters of membrane module, the fiber length has the greatest impact on γ while that is the ratio of fiber pitch to fiber outer radius for Δ φ /Δ p . The empirical correlations of γ and Δ φ /Δ p were obtained by the regression analysis of simulated data, which help to predict the dehumidification performance and flow resistance of membrane systems from known structural parameters and operating conditions. According to plus or minus of the fitted exponents, the influences of seven factors on the two indexes are different. The better dehumidification performance and less flow resistance can be achieved by appropriately increasing w in and l of the membrane module. This study is of guiding significance in the structure optimization of membrane modules.

Hydrophilic nanocomposite membranes have significant advantages in the separation of water vapor which is the core process in air dehumidification. This paper focuses on exploring the micro-mechanism of enhanced separation using graphene oxide-polyvinyl alcohol (GO-PVA) nanocomposite membranes. The sorption and diffusion behaviors of water vapor and nitrogen in GO-PVA membranes were investigated using molecular dynamics (MD) and Monte Carlo (MC) methods. The study showed that embedding GO into a PVA matrix results in a higher glass transition temperature and fractional free volume. The latter is believed to enhance the diffusivity of gas molecules in polymeric membranes. The interaction between the polymer chains and GO nanoparticles notably promotes the adsorption capacity of water vapor and inhibits nitrogen adsorption in the membrane. A water vapor permeance of 8844.07 Barrer and a separation factor of 3.53 could be achieved with the GO-PVA-0.5 membrane. The analysis confirmed that GO has the same effect on single gas and binary gas mixtures, i.e., increasing the water vapor permeability and selectivity. The calculated water vapor permeance of binary gas is 83% lower than that of single gas permeation. It is expected that this research could provide fundamentals for the optimization and synthesis of gas separation membranes.

In this study, robust and defect-free thin film composite (TFC) forward osmosis (FO) membranes have been successfully fabricated using ceramic hollow fibers as the substrate. Polydopamine (PDA) coating under controlled conditions is effective to reduce the surface pores of the substrate and make the substrate smooth enough for the interfacial polymerization. The pure water permeability (A), solute permeability (B) and structural parameter (S) of the resultant FO membrane are 0.854 L·m-2h-1bar-1 (LMH/Bar) 0.186 L·m-2h-1 (LMH) and 1720 µm, respectively. The water flux and reverse draw solute flux are measured using NaCl and proprietary ferric sodium citrate (FeNaCA) draw solutions at low and high osmotic pressure ranges. With increasing the osmotic pressure, higher water flux is obtained but its increase is not directly proportional to the increase in the osmotic pressure. At the membrane surface, the effect of dilutive concentration polarization is much less serious for FeNaCA draw solutions. At an osmotic pressure of 89.6 bar, the developed TFC membrane generates water fluxes of 11.5 and 30.0 LMH using NaCl and synthesized FeNaCA draw solutions. The corresponding reverse draw solute flux is 7.0 g·m-2h-1 (gMH) for NaCl draw solution but it is not detectable for FeNaCA draw solution. This means that the developed TFC FO membranes are defect free and their surface pores are at molecular level. The performance of the developed TFC FO membranes are also demonstrated for the enrichment of BSA protein.

The physical permeation-based membrane dehumidification technology has excellent energy-saving capacity. The nonuniformity of fiber bundles affects largely the flow status in the shell side of pressure-driven membrane modules, and therefore the dehumidification performance and energy efficiency of the membrane system. To explore the effects of fibre bundles nonuniformity, three-dimensional membrane dehumidification models with different fiber arrangements and filling rates were developed. The friction coefficient, dehumidification rate and energy efficiency of the membrane system were discussed for the comprehensive evaluation of module performance. It is found that the dehumidification rate of regular configuration is slightly better than that of random configuration, but the advantage is gradually weakened with the increase in filling rate. The obtained inversely proportional fitting function of f = 58.81/Re can be used to predict the flow resistance in the fiber lumen. Under the same air parameters, operating conditions and fiber size, the fiber distribution has a negligible effect on the dehumidification COP. The dehumidification rate rises significantly with the filling rate, up to 94.88% at a 47% filling rate accompanied by the maximum flow resistance. The dimensionless analysis indicates that the membrane module with a filling rate of 21.5% similar to 23% would achieve optimal performance in terms of system energy efficiency and overall dehumidification capacity.

The membrane dehumidification technology has great energy-saving potential compared to traditional methods. However, the design of composite membrane depends mostly on trial tests. To understand the mechanisms dominating material properties and quantitatively predict the air dehumidification performance of the composite membranes in practical applications, various models combined with different polymeric materials and porous support membranes were developed and investigated by using grand canonical Monte Carlo (GCMC) and Mo-lecular dynamics (MD) simulation methods. The interfacial interactions between the selective layer and the support membrane were analyzed in detail to explore the interface stability and compatibility of various com-posite membranes. The physical characteristics (density, fractional free volume, solubility parameter and cohesive energy density) and transport properties (solubility, diffusivity, permeability and selectivity) of various composite membranes were parametrically evaluated. The polydimethylsiloxane (PDMS) composite membranes exhibited stronger interfacial interaction in comparison to the PVA composite membranes. The hydrophilicity and polarity of polyvinyl alcohol (PVA) polymer resulted in a stronger interaction between the gas molecules and the PVA membrane. According to the solution-diffusion mechanism, the PVA-PVDF membrane presented the optimal H2O permeability of 3121.38 Barrer among all composite membranes. Generally, polyvinylidene fluo-ride (PVDF) or polyacrylonitrile (PAN) as the materials of support membrane had good fiber forming charac-teristics and low gas diffusion resistance, which significantly affects the performance of selective layers. The microscopic mechanisms revealed in this work would lay a solid theoretical foundation for the design of high performance composite membrane for air dehumidification.

In the present work, staggered and inline arranged membrane components are modeled to numerically investigate the flow behavior and mass transfer of humid air across the fiber membrane bundles. For the dehumidification purpose, the humid air flows over the outer surface of the composite membrane fibers, and the lumen side of the membrane maintains a negative pressure where the permeated water vapor is removed from the suction port. The study of flow behavior showed that the velocity contours are denser near the membrane outer wall for both configurations, while a fluid stagnation zone is observed in the staggered arrangement. Through the analysis of the flow and concentration fields in the two configurations, it was found that for the fiber membranes with small radius, the inline arrangement possesses more advantages in terms of dehumidification capacity and energy efficiency. Consequently, the effects of the dimension parameters of inline arrangement on the dehumidification performance of membrane bundles were further explored. The results indicated that the increase of tube pitch has a negative effect on the dehumidification rate. In addition, thickening the thickness of the membrane support layer and decreasing the fiber radius are conducive to the dehumidification performance.

Gas membrane separation technology is widely applied in different industry processes because of its advantages relating to separation performance and economic efficiency. It is usually difficult and time consuming to determine the suitable membrane materials for specific industrial separation processes through traditional experimental research methods. Molecular simulation is widely used to investigate the microscopic morphology and macroscopic properties of materials, and it guides the improvement of membrane materials. This paper comprehensively reviews the molecular-level exploration of the dominant mechanism and influencing factors of gas membrane-based separation. The thermodynamics and kinetics of polymer membrane synthesis, the molecular interactions among the penetrated gases, the relationships between the membrane properties and the transport characteristics of different gases in the composite membrane are summarized and discussed. The limitations and perspectives of the molecular simulation method in the study of the gas membrane separation process are also presented to rationalize its potential and innovative applications. This review provides a more comprehensive reference for promoting the materials' design and engineering application of the gas separation membrane.

A two-dimensional axisymmetric mathematical model was established to describe the pressure-driven water vapor separation in the hollow fiber composite membrane for air dehumidification. The developed transport model considered the permeation in the dense layer and the diffusion in the porous membrane substrate, in which the mass and momentum balance equations were coupled. The predicted results by the simulation model was consistent well with the experimental data. The velocity, pressure and concentration profiles and the mass transfer process in a single hollow fiber membrane were then solved and analyzed in detail, including the effects of feed velocity, feed humidity and transmembrane pressure on the dehumidification performance. The results show that the amount of water vapor separation (outlet humidity) is more sensitive to the medium feed velocity with the separation amount about twice than that of high and low velocities. The separated amount of water vapor by the membrane is less dependent on the feed inlet humidity. And the air dehumidification performance of the membrane could be realized effectively until the transmembrane pressure over a critical value, which is 1.0 bar in this model. The findings deliver an insight into the mass transport in the membrane-based dehumidification process, with the aims to provide a useful reference to the design, process optimization and module development using hollow fiber membrane.

Membrane-based technology for gas separation has great potential in HVAC (Heating, Ventilating, and Air Conditioning) industry. In this research, the nanoparticle filled poly(vinyl alcohol)/poly(vinylidene fluoride) (PVA/PVDF) hollow fiber membrane was fabricated for indoor air dehumidification. The Poly( vinyl alcohol) thin film incorporated with nanoparticles was coated in the cavity of the Poly(vinylidene fluoride) substrate membranes. The enhanced performance of three types of nanoparticles [Zeolite, Titanium Dioxide (TiO2) and Graphene Oxide (GO)] was investigated experimentally for evaluating the water vapor permeability. The effects of nanoparticle types and nanoparticle loading concentration on the permeability enhancement of the nanoparticles filled PVA/PVDF membrane were compared and analyzed. The results indicate that the nanoparticles additives of great benefit to the performance improvement of water vapor permeability. The enhancement performance of three nanoparticles is as follows: Zeolite > GO > TiO2. The addition of 0.05 wt% Zeolite nanoparticles lead to twice enhancement on the water vapor permeance than the original PVA/PVDF membranes. The GO nanoparticle additive enhances the water vapor permeance to around 1500 GPU (gas permeation unit) with the nanoparticle concentration from 0.1 wt% to 0.2 wt%. However, the addition of TiO2 nanoparticle has no obvious enhancement due to its large particle size. This work provides a new perspective for strengthening the air dehumidification performance of composite membrane.

This study focused on the water vapor removal efficiency by the surface-modified poly(vinyl alcohol)/poly(vinylidene difluoride) (PVA/PVDF) hollow fiber composite membranes with poly(dopamine) (PDA) in the dehumidification process. Two different ways of PDA modification were experimentally investigated and examined in terms of the separation performance of water vapor. A laboratory-scale testing device was set up to measure the water vapor permeance and the water vapor/H2 selectivity. Compared with the pristine PVA/PVDF membrane, the membrane modified using PVA/PDA mixture formed a dense and thin layer with high nitrogen solubility, which was not conducive to improve the water vapor removal efficiency. In contrast, the three-layer PDA–PVA/PVDF-modified membrane with PDA significantly enhanced the dehumidification performance. The influences of modification conditions (PDA concentration and PDA modification time) on the water vapor permeance and water vapor/H2 selectivity of PDA–PVA/PVDF-modified membrane were further studied. The highest water vapor permeance of 2898 GPU was obtained at certain conditions (0.1 g L−1 PDA solution and modification time of 30 min). It was demonstrated that the surface modification with PDA could play an important role in enhancing the hydrophilicity and water vapor/H2 separation performance for PVA/PVDF composite membranes.

The membrane-based dehumidification technology is greatly energy-efficient for the humidity control. The poly (vinyl alcohol)/poly (vinylidene fluoride) hollow fiber composite membrane for dehumidification has been developed and evaluated in this study. The Poly (vinylidene fluoride) (PVDF) membrane substrates were prepared by the dry-wet spinning. The Poly (vinyl alcohol) (PVA) selective layer was formed through the dynamic cross-flow coating in the lumen side of the PVDF substrate membranes. The effects of the PVA concentration and the coating time on the water vapor performance and the heat removal ratio of the PVA/PVDF composite membrane were investigated experimentally. The results indicated that the PVA concentration of 5.0 wt% and the coating time of 60 min are the optimal conditions for the fabrication of PVA/PVDF hollow fiber composite membrane. With the composite membrane prepared under optimal conditions, a water vapor permeance of 6084 GPU and a heat removal ratio of 10.94% were obtained at 25 degrees C. This work offers a new sight for the development of a novel high-performance composite membrane for the indoor air dehumidifiers.

This chapter introduces water transport characteristics through different types of polymer membranes in membrane distillation (MD), forward osmosis (FO), and pressure-retarded osmosis (PRO) processes. It starts by briefly explaining the mechanisms of the three membrane processes. It then elaborates the major factors influencing water transport through MD, FO, and PRO membranes as well as the empirical models that describe these factors. Extensive discussion of the driving force, membrane structure, operation conditions, and feed water quality is included to reveal their relationship with water transport. At the end of the chapter, typical applications of MD, FO, and PRO are introduced. Hot topics in the three processes, challenges, and future research prospects are also presented.

Novel tri-bore hollow fiber membranes have been developed from polyvinylidene fluoride (PVDF) for the control the dissolved oxygen (DO) in aquaculture denitrification process. The fabricated hollow fibers are characterized in terms of morphology, porosity, hydrophobicity and mechanical strength. Two membrane modules, each including 200 pieces of hollow fibers, are connected in series or parallel in order to determine the optimum operation mode. The deoxygenation test is firstly conducted for DI water and then for aquaculture water. Various methods including water flushing, air blowing or chemical cleaning have been applied to assure the cleaning efficiency after membrane fouling. A mathematical model has been developed by using the resistance-in-series concept by taking into account boundary layer and membrane characteristics. Overall mass transfer coefficient, radial and axial concentration profiles, and molar flux of oxygen at different water flow rates are calculated. This work has demonstrated that the developed tri-bore hollow fiber membranes are applicable for the control of dissolved oxygen in aquaculture water. The observations have provided solid evidence for the development of membrane-based denitrification system for recirculating aquaculture system (RAS).

This study discloses the critical factors that result in the low osmotic efficiency in forward osmosis (FO). Specifically, dual-layer hollow fiber membranes are prepared with newly-synthesized cellulose acetate propionate (CAP) as the outer active layer and commercial cellulose acetate (CA) as the inner sublayer. By carefully analyzing the hollow fiber cross section images, the porosity of the sublayer is found to be nonuniformly distributed at different locations. Viewing the membrane matrix as three consecutive layers, i.e., the active layer, the sublayer and the interface between them, the draw solute concentration profiles within each layer, the osmotic pressure gradients across each layer, and the transport resistance of each layer are determined. One interesting observation is that the active layer of the CAP-CA hollow fibers creates much larger resistance than the interface and the sublayer, indicating that the low osmotic efficiency (i.e., low water flux) is mainly due to the low water permeability of the active layer while internal concentration polarization (ICP) within the sublayer is less important. For any membranes, the active layer–sublayer interface also creates certain transport resistance. These findings provide a valuable reference for the understanding of FO and the design of advanced FO membranes.

A new cellulose acetate propionate (CAP) polymer has been synthesized and used to prepare high-performance forward osmosis (FO) membranes. With an almost equal degree of substitution of acetyl and propionyl groups, the CAP-based dense membranes show more balanced physicochemical properties than conventional cellulose acetate (CA)-based membranes for FO applications. The former have a lower equilibrium water content (6.6 wt. %), a lower salt diffusivity (1.6×10 14 m 2 s −1 ) and a much lower salt partition coefficient (0.013) compared with the latter. The as-prepared and annealed CAP-based hollow fibers have a rough surface with an average pore radius of 0.31 nm and a molecular weight cut off of 226 Da. At a transmembrane pressure of 1 bar, the dual-layer CAP-CA hollow fibers show a pure water permeability of 0.80 L m −2 h −1 bar −1 (LMH/bar) and a rejection of 75.5% to NaCl. The CAP-CA hollow fibers were first tested for their FO performance using 2.0 M NaCl draw solution and deionized water feed. An impressive water flux of 17.5 L m −2 h −1 (LMH) and a reverse salt flux of 2.5 g m −2 h −1 (gMH) were achieved with the draw solution running against the active CAP layer in the FO tests. The very low reverse salt flux is mainly resulting from the low salt diffusivity and salt partition coefficient of the CAP material. In a hybrid system combining FO and membrane distillation for wastewater reclamation, the newly developed hollow fibers show very encouraging results, that is, water production rate being 13–13.7 LMH, with a MgCl 2 draw solution of only 0.5 M and an operating temperature of 343 K due to the incorporation of bulky propionyl groups with balanced physiochemical properties. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1245–1254, 2013

We have examined the gypsum (CaSO4·2H2O) scaling phenomena on membranes with different physicochemical properties in forward osmosis (FO) processes. Three hollow fiber membranes made of (1) cellulose acetate (CA), (2) polybenzimidazole (PBI)/polyethersulfone (PES) and (3) PBI-polyhedral oligomeric silsesquioxane (POSS)/polyacrylonitrile (PAN) were studied. For the first time in FO processes, we have found that surface ionic interactions dominate gypsum scaling on the membrane surface. A 70% flux reduction was observed on negatively charged CA and PBI membrane surfaces, due to strong attractive forces. The PBI membrane surface also showed a slightly positive charge at a low pH value of 3 and exhibited a 30% flux reduction. The atomic force microscopy (AFM) force measurements confirmed a strong repulsive force between gypsum and PBI at a pH value of 3. The newly developed PBI-POSS/PAN membrane had ridge morphology and a contact angle of 51.42° ± 14.85° after the addition of hydrophilic POSS nanoparticles and 3 min thermal treatment at 95 °C. Minimal scaling and an only 1.3% flux reduction were observed at a pH value of 3. Such a ridge structure may reduce scaling by not providing a locally flat surface to the crystallite at a pH value of 3; thus, gypsum would be easily washed away from the surface.

Internal concentration polarization (ICP) that occurs in the membrane sublayer is considered a serious problem restricting the performance of forward osmosis (FO) processes. Aiming at reducing ICP and fouling propensity, novel nanofiltration (NF) hollow fiber membranes with two apparently dense skins have been designed from cellulose acetate (CA) for FO applications by manipulating different phase inversion rates and degrees of annealing at the inner and outer layers. For the CA hollow fibers precipitated rapidly and then annealed at the lumen side, the surface pores within the inner skin layer show a very narrow size distribution with a mean radius of 0.34nm. Being also relatively dense, the outer skin layer may keep the feed solutes from entering the sublayer and avoid their accumulation within the sublayer if the feed solutes are macromolecules or multi-valence ions with relatively larger sizes. Thus, the double-skinned FO membrane would have improved performance by suppressing ICP at a cost of additional external concentration polarization (ECP) at the outer surface. In the FO process, the CA hollow fiber membrane with inner selective layer generates a water flux of 17.1LMH (Lm−2h−1) with 2.0M MgCl2 draw solution running at the lumen side of the fibers and DI water feed at the shell side. When using 1.0M Sucrose (26.7bar osmotic pressure) as the draw solution at the shell side and DI water feed at the lumen side, a water flux of 12.9LMH is obtained with a negligible reverse Sucrose flux. This FO performance is comparable to that created by 1.0M MgCl2 draw solution although 1.0M MgCl2 has a much higher osmotic pressure of 93.7bar. With wastewater feed containing 200–2000mgL−1 mixed metal ions at the lumen side and 0.5M Sucrose draw solution at the shell side, water fluxes in the range of 9.9–6.5LMH with minimal reverse Sucrose fluxes are observed. These results have revealed great potential of the newly developed double-skinned CA hollow fiber membranes as well as using Sucrose as the draw solute for wastewater reclamation and macromolecule recycle.

Nowadays, inadequate access to clean water has become one of the most pervasive problems due to the rapidly expanding global population and thus the exponentially growing demand in water and food supply, industry and social life (Shannon et al. 2008). Problems with water have called out for a large number of researchers to pay more attention to water sustainability and put forth effort to explore more robust technologies for wastewater treatment and desalination in addition to improving the efficiency of the current water production and distribution systems (Sikdar 2011). Among many potential solutions, membrane processes such as reverse osmosis (RO), nanofiltration (NF), ultrafiltration (UF), and microfiltration (MF) have found their overwhelming applications in water industry. However, these technologies are either chemically or energetically intensive, thus are castigated for high cost due to substantial chemical and energy consumptions as well as high fouling propensity which requires frequent backwash or cleaning. Forward osmosis (FO), utilizing the natural phenomenon of osmosis, is an emerging membrane process driven by the osmotic pressure gradient created across a semipermeable membrane by two flowing streams of varying concentration (i.e., the draw solution and the feed). Hence, the energy required to transport water across the membrane is almost negligible. Far from being so, FO creates much less problem of fouling and cleaning (Mi and Elimelech 2010). By virtue of these unique features, FO distinguishes itself from other membrane processes for sustainable supply of clean water. An example of the FO unit for wastewater treatment is shown in Fig. 1. In the FO process as illustrated, the draw solution (an aqueous solution of magnetic nanoparticles covered with thermosensitive polymer) (Ling et al. 2011) and the feed (wastewater) partitioned by the membrane flow co-currently through corresponding channels. The draw solution, having a higher osmotic pressure than the feed, draws water from the feed and flows back to the reservoir. As it continuously takes clean water from the feed, the draw solution in the reservoir becomes diluted. A regeneration process is connected to the reservoir to re-concentrate the draw solution as well as to produce clean water. A portion of the diluted draw solution is pre-heated with the aid of solar panel or waste heat and traverses a magnetic field. Upon heating, the magnetic nanoparticles covered with thermosensitive polymers change their surface property from hydrophilic to hydrophobic and are easily seized by the magnetic field or other filtration processes. As a result, clean water freely passes through and is collected as the product. The trapped magnetic nanoparticles are then sent back to the reservoir to replenish the draw solution. The 1st key component of the FO unit is the membrane material which should be semipermeable, i.e., allowing water to permeate through while blocking all the solutes in the draw and feed solutions. A tremendous amount of research has been conducted on the molecular design of new membrane materials with superior FO performance and great progress has been achieved in the past 5 years. To date, several types of FO membranes have been reported such as (1) flat sheet membranes made of cellulose esters (Wang et al. 2010a; Zhang et al. 2010); (2) J. Su M. M. Ling T.-S. Chung (&) Department of Chemical & Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore e-mail: chencts@nus.edu.sg

The development of the forward osmosis (FO) process has been constrained by the slow development of appropriate draw solutions. Two significant concerns related to draw solutions are the draw solute leakage and intensive energy requirement in recycling draw solutes after the FO process. FO would be much attractive if there is no draw solute leakage and the recycle of draw solutes is easy and economic. In this study, polyelectrolytes of a series of polyacrylic acid sodium salts (PAA-Na), were explored as draw solutes in the FO process. The characteristics of high solubility in water and flexibility in structural configuration ensure the suitability of PAA-Na as draw solutes and their relative ease in recycle through pressure-driven membrane processes. The high water flux with insignificant salt leakage in the FO process and the high salt rejection in recycle processes reveal the superiority of PAA-Na to conventional ionic salts, such as NaCl, when comparing their FO performance via the same membranes. The repeatable performance of PAA-Na after recycle indicates the absence of any aggregation problems. The overall performance demonstrates that polyelectrolytes of PAA-Na series are promising as draw solutes, and the new concept of using polyelectrolytes as draw solutes in FO processes is applicable.