Valéry Salle
email: salle.valery@chu-amiens.fr

Keywords:

1

Introduction

Several studies have highlighted the link between viral infection and the development of autoimmunity [START_REF] Horwitz | Viruses, host responses, and autoimmunity[END_REF][START_REF] Barzilai | Viral infection can induce the production of autoantibodies[END_REF][START_REF] Smatti | Viruses and Autoimmunity: A Review on the Potential Interaction and Molecular Mechanisms[END_REF][START_REF] Hussein | The role of viral infections in the development of autoimmune diseases[END_REF]. Autoimmune diseases (AID) are characterized by the breakdown of immune tolerance and the activation of self-reactive lymphocytes. Many AID are multifactorial, involving both genetic and environmental factors, such as viral infections.

Viruses represent the major environmental factor that triggers the development of autoimmunity in genetically susceptible individuals. There are multiple mechanisms by which viruses can induce an autoimmune reaction, including molecular mimicry, epitope spreading, bystander activation, the presentation of cryptic antigens, B-cell polyclonal activation, and viral superantigens [START_REF] Barzilai | Viral infection can induce the production of autoantibodies[END_REF][START_REF] Hussein | The role of viral infections in the development of autoimmune diseases[END_REF][START_REF] Lardans | Polyclonal B lymphocyte activation induced by mouse hepatitis virus A59 infection[END_REF][START_REF] Fujinami | Molecular mimicry, bystander activation, or viral persistence: infections and autoimmune disease[END_REF][START_REF] Scherer | Superantigens: bacterial and viral proteins that manipulate the immune system[END_REF]. Many viruses have been suspected to trigger or exacerbate AID.

The best examples of viruses inducing the development of AID are coxsackie virus, cytomegalovirus, Epstein Barr virus, and hepatitis B virus [START_REF] Barzilai | Viral infection can induce the production of autoantibodies[END_REF][START_REF] Smatti | Viruses and Autoimmunity: A Review on the Potential Interaction and Molecular Mechanisms[END_REF]. We focus here on findings showing that coronavirus appears to also be associated with autoimmunity.

Animal model systems

Coronaviruses cause diseases in a variety of species of animals, including humans.

The pathogenesis and organ tropism of murine hepatitis coronaviruses (MHV) depends on the viral strain [START_REF] Weiss | Coronavirus pathogenesis[END_REF]. Neurotropic MHV strains (JHM and A59) have been the most frequently studied [START_REF] Weiss | Coronavirus pathogenesis[END_REF]. They induce encephalomyelitis, with demyelination, and serve as one of the few animal models for multiple sclerosis (MS)-like diseases. The role of coronaviruses in the development of autoimmunity has come from experimental studies in animal models. Murine coronavirus infection can induce autoreactive T-cells, B-cell polyclonal activation, and autoantibody production.

Experimental autoimmune encephalomyelitis

Watanabe et al. first reported that infection in Lewis rats with the murine coronavirus JHM can induce an autoimmune response. Lymphocytes from Lewis rats infected with murine coronavirus are sensitized to myelin basic protein and adoptive transfer of these lymphocytes leads to experimental allergic encephalomyelitis (EAE)-like lesions in recipient Lewis rats [START_REF] Watanabe | Adoptive transfer of EAE-like lesions from rats with coronavirus-induced demyelinating encephalomyelitis[END_REF]. Mice infected with MHV 2.2-V-1 develop an immune-mediated demyelinating encephalomyelitis and Pewe et al. showed that the CD8 T cell-mediated demyelination is dependent on Interferon gamma (INF-γ) in MHV-infected mice [START_REF] Pewe | Cutting edge: CD8 T cell-mediated demyelination is IFN-gamma dependent in mice infected with a neurotropic coronavirus[END_REF]. Furthermore, MHV-4-infection can also induce an autoimmune T-cell response in mice [START_REF] Kyuwa | Induction of self-reactive T cells after murine coronavirus infection[END_REF]. Infection with murine coronavirus can also induce the production of autoantibodies.

Experimental coronavirus retinopathy (ECOR)

Experimental coronavirus retinopathy (ECOR) was created in the 1990s [START_REF] Detrick | Immune regulation in the retina[END_REF]. The pathogenesis of this experimental retinal disease is based on three components, a viral component, genetic background, and an immunological component [START_REF] Detrick | Immune regulation in the retina[END_REF]. This degenerative retinal disease is characterized by an early phase, with retinal vasculitis and perivasculitis, and a late phase, with degenerative retinal disease [START_REF] Detrick | Immune regulation in the retina[END_REF]. The pathogenesis of MHV-induced retinal degeneration in BALB/c mice has been shown to be related to autoimmunity, with the presence of antiretinal autoantibodies and anti-retinal pigment epithelial-cell autoantibodies [START_REF] Hooks | Retina and retinal pigment epithelial cell autoantibodies are produced during murine coronavirus retinopathy[END_REF]. Two autoantigens, α fodrin and villin 2, have been identified in ECOR [START_REF] Chin | Identification of α-fodrin as an autoantigen in experimental coronavirus retinopathy (ECOR)[END_REF].

Furthermore, the CD4 T cells from MHV-infected BALB/c mice are specifically activated by α fodrin [START_REF] Chin | Identification of α-fodrin as an autoantigen in experimental coronavirus retinopathy (ECOR)[END_REF]. MHV strain 59 (MHV-59) is a coronavirus that triggers various pathologies in susceptible mice, such as hepatitis, thymus involution, polyclonal B lymphocyte activation, and, after intra-cerebral inoculation, transient demyelination [START_REF] Lardans | Polyclonal B lymphocyte activation induced by mouse hepatitis virus A59 infection[END_REF][START_REF] Godfraind | Morphological analysis of mouse hepatitis virus A59-induced pathology with regard to viral receptor expression[END_REF].

Anti-erythrocyte autoimmunity

Mice infected with MHV-59 and immunized with rat-blood erythrocytes develop high levels of anti-erythrocyte autoantibodies. In contrast, the authors observed only moderate autoantibody production by noninfected mice solely immunized with rat-blood erythrocytes, suggesting that the autoimmune response may be enhanced by MHV-59 infection [START_REF] Lardans | Polyclonal B lymphocyte activation induced by mouse hepatitis virus A59 infection[END_REF].

Mathieu et al. identified two liver proteins, fumarylacetoacetate hydrolase (FAH) and alcohol dehydrogenase (ADH), recognized by autoantibodies in the sera of MHV-A59infected mice [START_REF] Mathieu | Identification of two liver proteins recognized by autoantibodies elicited in mice infected with mouse hepatitis virus A59[END_REF]. The same authors then explored the cross-reaction between FAH and MHV proteins. The autoantibodies recognized cryptic and native FAH epitopes in MHVinfected mice. Two homologous peptides of both FAH and the nucleocapsid were recognized by most antibodies [START_REF] Mathieu | Sequence similarity and structural homologies are involved in the autoimmune response elicited by mouse hepatitis virus A59[END_REF].

Common human coronaviruses and multiple sclerosis

Seven types of coronavirus are known to infect humans (Table 1). The most common human coronaviruses circulating worldwide are OC43, HKU1, NL63, and 229E [START_REF] Liu | Prevalence and genetic diversity analysis of human coronaviruses among cross-border children[END_REF].

Multiple sclerosis is an immune-mediated demyelinating disease in which infectious pathogens could play a role in the pathogenesis of the disease. The possible involvement of human coronaviruses as an environmental trigger of multiple sclerosis (MS) is supported by several studies. Antibodies to coronaviruses OC43 and 229E were found in the cerebrospinal fluid of MS patients more frequently and in higher titers than that of matched controls [19].

Moreover, intrathecal antibody synthesis to OC43 and 229E coronaviruses has been found in 41% and 26% of MS patients, respectively [19]. Human coronavirus HCV-229E can replicate in cultures of various human neuronal and glial cell lines [START_REF] Talbot | Neurotropism of humancoronavirus 229E[END_REF]. Human coronavirus 229E viral RNA has been detected in the brain tissue of MS patients [START_REF] Stewart | Human coronavirus gene expression in the brains of multiple sclerosis patients[END_REF]. Molecular mimicry has been proposed as a putative mechanism in the pathogenesis of MS. T-cell lines isolated from MS patients show cross-reactivity between myelin basic protein and viral antigens from the human respiratory coronavirus 229E [START_REF] Talbot | Myelin basic protein and human coronavirus 229E cross-reactive T cells in multiple sclerosis[END_REF].

SARS-CoV and autoimmunity

In winter 2002-2003, severe acute respiratory syndrome (SARS) emerged in China and subsequently spread throughout the world. SARS is caused by a novel species of coronavirus that has been named SARS-CoV. SARS-CoV infection is characterized by a severe and potentially fatal lung disease. The pathogenic mechanisms of SARS include direct viral cytopathic effects, the dysregulation of cytokines/chemokines, the innate immune response, and the immunogenetics of the host [START_REF] Lo | How the SARS coronavirus causes disease: host or organism?[END_REF][START_REF] Gu | Pathology and pathogenesis of severe acute respiratory syndrome[END_REF]. Several studies have suggested that autoimmunity may also be involved in the pathogenesis of SARS. During the acute phase of the disease, IgM and IgG autoantibodies against cytoplasmic antigens of pneumocytes were detected in the sera of 36 Chinese SARS patients [START_REF] Lo | How the SARS coronavirus causes disease: host or organism?[END_REF]. In another cohort of 22 SARS patients, autoantibodies against human epithelial cells (the A549 human pulmonary epithelial cell-line) and human endothelial cells (human umbilical endothelial cells (HUVEC) and primary human pulmonary endothelial cells (HPEC)) developed approximately one month after the onset of the disease [START_REF] Yang | Autoantibodies against human epithelial cells and endothelial cells after severe acute respiratory syndrome (SARS)-associated coronavirus infection[END_REF]. Sera from SARS patients with high-levels of autoantibodies induced complement-dependent cytotoxicity against A549 cells and HPEC [START_REF] Yang | Autoantibodies against human epithelial cells and endothelial cells after severe acute respiratory syndrome (SARS)-associated coronavirus infection[END_REF]. Lin et al. also showed that antibodies present in the sera of SARS patients reacted with A549 epithelial cells (type-2 pneumocytes) [START_REF] Lin | Antibody to severe acute respiratory syndrome (SARS)-associated coronavirus spike protein domain 2 cross-reacts with lung epithelial cells and causes cytotoxicity[END_REF]. These autoantibodies were primilary of IgG isotype and were detectable 20 days after the onset of fever, the IgG present in the sera of SARS patients had a cytotoxic effect on A549 cells [START_REF] Lin | Antibody to severe acute respiratory syndrome (SARS)-associated coronavirus spike protein domain 2 cross-reacts with lung epithelial cells and causes cytotoxicity[END_REF]. Indeed, there are cross-reactive epitopes on domain 2 of the SARS-CoV spike protein (S2) with human lung epithelial cell proteins. Anti-SARS-CoV spike antibodies enhance the adherence of human peripheral blood mononuclear cells to A549 cells [START_REF] Lin | Antibody to severe acute respiratory syndrome (SARS)-associated coronavirus spike protein domain 2 cross-reacts with lung epithelial cells and causes cytotoxicity[END_REF]. Thus, the autoimmune responses in SARS-CoV infection may contribute to the pathogenesis of the disease.

Other groups identified sequence homology between four pathogenic regions of the SARS-CoV spike protein and various human proteins [START_REF] Hwa | Peptide mimicrying between SARS coronavirus spike protein and human proteins reacts with SARS patient serum[END_REF]. A proteomic approach showed annexin A2 to be an autoantigen in A459 cell-membrane extracts recognized by the sera of SARS patients and annexin A2 on lung epithelial cells was recognized by antibodies against SARS-CoV S2 [START_REF] Fang | Annexin A2 on lung epithelial cell surface is recognized by severe acute respiratory syndrome-associated coronavirus spike domain 2 antibodies[END_REF]. Furthermore, anti-annexin A2 antibodies recognized purified S2 protein by ELISA. The authors also observed the upregulation of epithelial cell-surface expression of annexin A2 by Il-6 and INF-γ released during the cytokine storm in SARS infection [START_REF] Fang | Annexin A2 on lung epithelial cell surface is recognized by severe acute respiratory syndrome-associated coronavirus spike domain 2 antibodies[END_REF]. The human long interspersed nuclear element 1 (LINE1) endonuclease domain was identified as a putative target of SARS-associated autoantibodies and these antibodies were found in 40.9% of patients with SARS [START_REF] He | Human LINE1 endonuclease domain as a putative target of SARS-associated autoantibodies involved in the pathogenesis of severe acute respiratory syndrome[END_REF].

Can SARS CoV-2 trigger autoimmunity ?

In December 2019, the first cases of patients with severe atypical pneumonia of unknown origin were reported in Wuhan, Hubei province, China. Most of these patients were epidemiologically linked to a seafood market in Wuhan. Pneumonia was caused by a novel coronavirus, severe acute respiratory syndrome coronavirus 2, SARS-CoV-2 (previously known as 2019 novel coronavirus, 2019-nCoV, by the World Health Organization (WHO)). This newly emerged pathogen was isolated and sequenced in China [START_REF] Zhu | China Novel Coronavirus Investigating and Research Team, A Novel Coronavirus from Patients with Pneumonia in China[END_REF][START_REF] Zhou | A pneumonia outbreak associated with a new coronavirus of probable bat origin[END_REF] sequence identity [START_REF] Zhou | A pneumonia outbreak associated with a new coronavirus of probable bat origin[END_REF]. SARS-CoV-2 interacts directly with angiotensin-converting enzyme 2 (ACE2) to enter host cells, particularly alveolar epithelial cells. The cellular entry of SARS-CoV-2 is initiated through an interaction between the transmembrane spike (S) glycoprotein and the ACE2 receptor on human cells [START_REF] Walls | Structure, Function, and Antigenicity of the SARS-CoV-2 Spike Glycoprotein[END_REF]. Furthermore, it has been shown that ACE2 was the same cell entry receptor for SARS-CoV [START_REF] Zhou | A pneumonia outbreak associated with a new coronavirus of probable bat origin[END_REF] and that there is structural and sequence identity between the SARS-CoV-2 and SARS-CoV S glycoproteins [START_REF] Walls | Structure, Function, and Antigenicity of the SARS-CoV-2 Spike Glycoprotein[END_REF]. COVID-19 is typically characterized by fever and respiratory illness, leading to acute respiratory distress syndrome, with admission to the intensive care unit (ICU) for 5% of patients [START_REF] Guan | China Medical Treatment Expert Group for Covid-19, Clinical Characteristics of Coronavirus Disease 2019 in China[END_REF]. However, several observations have shown that COVID-19 also shows a wide clinical spectrum, which includes cardiac injury in 20% of cases [START_REF] Shi | Association of Cardiac Injury With Mortality in Hospitalized Patients With COVID-19 in Wuhan, China[END_REF], venous thromboembolism in 25% of cases [START_REF] Cui | Prevalence of venous thromboembolism in patients with severe novel coronavirus pneumonia[END_REF], disseminated intravascular coagulation, neurological manifestations, or skin involvement. A cytokine storm can be associated with severe forms of the disease [START_REF] Huang | Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China[END_REF][START_REF] Chen | Clinical and immunological features of severe and moderate coronavirus disease 2019[END_REF]. A two-phase immune response is induced by SARS-CoV-2 infection [START_REF] Shi | COVID-19 infection: the perspectives on immune responses. Version 2[END_REF]. First, a specific adaptative immune response leads to viral clearance in most cases. However, immune dysregulation can occur in a subgroup of patients and lead to inflammation-induced lung damage and systemic complications. SARS-CoV-2 infection may therefore be associated with not only an autoinflammatory response but also the development of an autoimmune process. Given the striking similarity between SARS-CoV infection and COVID-19, it is possible that COVID-19 may trigger an autoimmune process through molecular mimicry or the exposure of autoantigens caused by cytokine-induced organ injury.

Several reports have highlighted the link between COVID-19 and the development of autoimmunity. Patients with severe SARS-CoV-2 infection show a high risk of thrombosis [START_REF] Helms | Clinical Research in Intensive Care and Sepsis Trial Group for Global Evaluation and Research in Sepsis), High risk of thrombosis in patients with severe SARS-CoV-2 infection: a multicenter prospective cohort study[END_REF]. The presence of antiphospholipid antibodies (APL) (anticardiolipin IgA and anti-β2 glycoprotein I IgA and IgG antibodies) has been reported in three patients with COVID-19 and multiple cerebral infarctions [START_REF] Zhang | Coagulopathy and Antiphospholipid Antibodies in Patients with Covid-19[END_REF]. APL are common during infection. Such APL can be pathogenic but they also transiently arise in the context of viral infection. Harzallah et al. reported the presence of lupus anticoagulant (LA) in almost half of 56 patients with COVID-19 [START_REF] Harzallah | Lupus anticoagulant is frequent in patients with Covid-19[END_REF]. However, in a letter to the editor, Connell at al. suggested that the LA results may be false positives, given the high C-reactive protein levels in patients with COVID-19 [START_REF] Connell | Coagulopathy of COVID-19 and antiphospholipid antibodies[END_REF].

Endothelial cell infection and diffuse endothelial inflammation were observed in a series of patients with COVID-19 and endothelial-cell injury was associated with apoptosis [START_REF] Varga | Endothelial cell infection and endotheliitis in COVID-19[END_REF].

Therefore, it is possible that epitopes of host proteins became abnormally expressed on the plasma membrane surface of apoptotic endothelial cells, leading to the generation of autoantibodies, such as APL.

Several cases of Guillain-Barré syndrome in patients with COVID-19 have been reported [START_REF] Toscano | Syndrome Associated with SARS-CoV-2[END_REF][START_REF] Zhao | Guillain-Barré syndrome associated with SARS-CoV-2 infection: causality or coincidence?[END_REF][START_REF] Scheidl | Guillain-Barré syndrome during SARS-CoV-2 pandemic: A case report and review of recent literature[END_REF][START_REF] Ottaviani | Early Guillain-Barré syndrome in coronavirus disease 2019 (COVID-19): a case report from an Italian COVID-hospital[END_REF][START_REF] El Otmani | Covid-19 and Guillain-Barré syndrome: More than a coincidence![END_REF]. GBS is an acute polyradiculoneuropathy associated with an aberrant autoimmune response and is generally preceded by a viral or bacterial infection. Although the pathogenic mechanisms need to be established, we cannot rule out molecular mimicry between viral epitopes and nerve antigens in the peripheral nerves, as has been suggested as one of the possible mechanisms for Zika virus-associated GBS [START_REF] Muñoz | Neuroviruses Emerging in the Americas Study. Neurological Implications of Zika Virus Infection in Adults[END_REF]. However, no production of antibodies against specific gangliosides has been reported in patients with COVID-19 and GBS. Miller Fisher syndrome (MFS), a variant of GBS, is characterized by a triad of ataxia, areflexia and ophtalmoplegia. Several publications reported cases of MFS associated with COVID-19 infection. Only one patient was positive for anti-ganglioside GD1b IgG antibodies [START_REF] Gutiérrez-Ortiz | Syndrome and polyneuritis cranialis in COVID-19[END_REF].

Other autoimmune disorders associated with COVID-19 include Immune Thrombocytopenic purpura (ITP) and autoimmune hemolytic anemia (AIHA). COVID-19 has been identified as a causal factor of ITP in a 65-year-old woman with HTA and autoimmune hypothyroidism [START_REF] Zulfiqar | Immune Thrombocytopenic Purpura in a Patient with Covid-19[END_REF]. Other authors described the first case series of 3 patients with ITP associated with COVID-19 [START_REF] Bomhof | COVID-19-associated immune thrombocytopenia[END_REF]. Lazarian et al. reported seven cases of warm and cold AIHA associated with COVID-19 [START_REF] Lazarian | Autoimmune haemolytic anaemia associated with COVID-19 infection[END_REF]. However, an indolent B cell malignancy was present in four of them. Furthermore, another case of AIHA during COVID-19 was reported in a 46-year old female with a medical history of congenital thrombocytopenia [START_REF] Lopez | Simultaneous onset of COVID-19 and autoimmune haemolytic anaemia[END_REF]. Several other hematologic disorders have been associated with COVID-19 such as cold agglutinin syndrome, Evans syndrome or autoimmune thrombotic thrombocytopenic purpura [START_REF] Zagorski | Cold Agglutinin Autoimmune Hemolytic Anemia Associated with Novel Coronavirus (COVID-19)[END_REF][START_REF] Li | Evans syndrome in a patient with COVID-19[END_REF][START_REF] Albiol | Autoimmune thrombotic thrombocytopenic purpura (TTP) associated with COVID-19[END_REF].

The structural similarity between an erythrocyte membrane protein named ANK-1 and the viral protein spike led Angileri et al. to postulate that molecular mimicry could contribute to the pathogenesis of COVID-19-associated AIHA [START_REF] Angileri | Is molecular mimicry the culprit in the autoimmune haemolytic anaemia affecting patients with COVID-19?[END_REF].

In a single-center, retrospective study from an ICU of China'hospital (province of Hubei), the authors described clinical and autoimmune characteristics in 21 severe or critical cases of patients infected with SARS-CoV-2. They detected the presence of anti-52 kD SSA/Ro antibodies, anti-60 kD SSA/Ro antibodies, and antinuclear antibodies in 20%, 25%, and 50% of patients, respectively [START_REF] Zhou | Clinical and Autoimmune Characteristics of Severe and Critical Cases of COVID-19[END_REF]. More recently, a study from the ICU of Evangelismos Hospital, Athens (Greece), showed the presence of several autoantibodies related to systemic autoimmune rheumatic diseases in almost 70% of severely ill patients with COVID-19 [START_REF] Vlachoyiannopoulos | Autoantibodies related to systemic autoimmune rheumatic diseases in severely ill patients with COVID-19[END_REF].

The major autoimmune findings for both SARS-CoV and SARS-CoV-2 are reported in Table 2.

As already described for SARS, the spike surface glycoprotein could play a role in COVID-19-associated immunopathology. Kanduc and Shoenfeld suggested that because the peptide sharing between spike glycoprotein from SARS-CoV-2 and human surfactant-related proteins, the immune response following SARS-CoV-2 infection might contribute to the SARS-CoV-2-associated lung diseases [START_REF] Kanduc | On the molecular determinants of the SARS-CoV-2 attack[END_REF]. However, SARS-CoV-2 includes numerous other proteins that could represent an antigen source for the development of autoimmunity. Lyons-Weiler performed a bioinformatics analysis of the homology between highly immunogenic SARS-CoV-2 epitopes and human proteins. Among the SARS-CoV-2 proteins, those with the largest number of immunogenic peptides were the S protein and the non-structural protein NS3 [START_REF] Lyons-Weiler | Pathogenic Priming Likely Contributes to Serious and Critical Illness and Mortality in COVID-19 via Autoimmunity[END_REF]. Vojdani and Kharrazian reported a potential cross-reactivity between SARS-CoV-2 proteins (spike and nuclear proteins) and human tissue antigens [START_REF] Vojdani | Potential antigenic cross-reactivity between SARS-CoV-2 and human tissue with a possible link to an increase in autoimmune diseases[END_REF]. Lucchese and Flöel reported that the SARS-CoV-2 proteome share three sequences of six aminoacids (GSQASS, LNEVAK, SAAEAS) with three human proteins (DAB1, AIFM, SURF1) related to the respiratory pacemaker in the brainstem. The authors postulated that molecular mimetism between neuronal and viral proteins might contribute to autoimmune mediated respiratory failure [START_REF] Lucchese | Molecular mimicry between SARS-CoV-2 and respiratory pacemaker neurons[END_REF]. Angileri et al. also suggested that some features of COVID-19 such as anosmia, leukopenia and multi-organ damage could be the consequence of similarities between SARS-CoV-2 proteins (ORF7b, ORF1ab, nucleocapsid phosphoprotein) and the following human proteins: OR7D4, PARP9 and SLC12A6, respectively [START_REF] Angileri | Molecular mimicry may explain multi-organ damage in COVID-19[END_REF]. More recently, Megremis et al.

identified three immunogenic linear epitopes with high sequence identity to SARS-CoV-2 protein in patients with autoimmune dermatomyositis [START_REF] Megremis | Antibodies against immunogenic epitopes with high sequence identity to SARS-CoV-2 in patients with autoimmune dermatomyositis[END_REF]. On the basis of these reports, autoimmunity may be, at least partially, involved in the pathogenesis of COVID-19 in genetically predisposed individuals. Further studies will be needed to better characterize the possible link between COVID-19 and the development of autoimmunity, particularly in patients with severe interstitial pneumonia.

Conclusion

Coronaviruses represent a large group of virus affecting many species of animals and humans, causing acute and chronic diseases. From animal models to human diseases such as SARS and COVID-19, several studies have highlighted the possible role for autoimmunity through molecular mimicry in coronavirus pathogenesis. The wide spectrum of autoimmunelike manifestations in SARS-CoV-2-infected patients suggests that COVID-19 represents the better example of coronavirus-induced autoimmunity. However, it would be useful to better

Human coronavirus types

  . The disease caused by SARS-CoV-2 infection was later designated Coronavirus disease 2019 (COVID-19) by the WHO. SARS-CoV-2 infection has rapidly spread throughout the world. On March 11, 2020, the WHO declared the COVID-19 coronavirus outbreak a pandemic. SARS-CoV-2 is the seventh type of coronavirus to be identified that infects humans. It belongs to the β coronavirus genus and has been classified under the orthocoronavirinae subfamily. Clinical presentation of COVID-19 mimics that of SARS-CoV infection. SARS-CoV-2 shows phylogenetic similarity to SARS-CoV, with the two genomes sharing 79.6%

2

 2 (the beta coronavirus reponsible for Middle East Respiratory Syndrome, MERS) SARS-CoV (the beta coronavirus reponsible for severe acute respiratory syndrome, SARS) SARS-CoV-2 (the novel beta coronavirus that causes Coronavirus disease 2019, COVID-19)TableMajor autoantibodies reported in SARS-CoV and SARS-CoV-2-infected patientsSARS-CoV SARS-CoV-2Anti-lung epithelial cell Anti-endothelial cell Anti-annexin A2 Anti-endonuclease of the human LINE1 Antiphospholipid antibodies -anti-cardiolipin antibodies -anti-β2 glycoprotein I antibodies -lupus anticoagulant Anti-nuclear antibodies p-ANCA and c-ANCA Anti-CCP antibodies Anti-ganglioside GD1b antibodies CCP, cyclic citrullinated peptide ; ANCA, anti-neutrophil cytoplasmic antibody

Table 1

 1

characterize the role of autoimmunity in pathogenesis COVID-19, particularly in patients with severe forms of disease.

The authors have no conflicts to declare


M Maaroufi

F Bennai

Rafik Belarbi
email: rbelarbi@univ-lr.fr

K Abahri

Experimental and numerical highlighting of water vapor sorption hysteresis in the coupled heat and moisture transfers

Keywords: Sorption hysteresis, Coupled heat and moisture transfers, Hygrothermal modelling, Experimental characterization, Numerical simulations Molar mass (kg/mol)

Highlights

-Experimental and numerical study of water vapor sorption hysteresis.

-Development of a coupled heat and mass transfer model with consideration of sorption hysteresis.

Introduction

Indoor air humidity is as important as indoor air temperature, since moisture can significantly influence the energy performance of households [START_REF] Mendes | Moisture effects on conduction loads[END_REF][START_REF] Zhuang | Adaptive full-range decoupled ventilation strategy and air-conditioning systems for cleanrooms and buildings requiring strict humidity control and their performance evaluation[END_REF], and is one of the main causes of its deterioration [START_REF] Annila | Need to repair moisture-and mould damage in different structures in finnish public buildings[END_REF][START_REF] John | Moisture in buildings[END_REF]. Moisture in porous building materials can also greatly affect the indoor air quality and comfort of occupants, given that excessive low or high humidity can cause multiple respiratory pathologies and allergies [START_REF] Moon | The effect of moisture transportation on energy efficiency and IAQ in residential buildings[END_REF]. To predict those effects, moisture transfer has been studied for a long time, especially in unsaturated porous media based on Darcy and Fick's laws [START_REF] Xu | Study of heat and moisture transfer in internal and external wall insulation configurations[END_REF][START_REF] Zhang | A Fickian model for temperature-dependent sorption hysteresis in hygrothermal modeling of wood materials[END_REF]. To avoid moisture condensation, insulation failure or mold growth in building materials, coupled heat and moisture transfers should be studied together for a better prediction of the hygrothermal behavior of the building, and thus optimize its design [8 -10]. Hygrothermal transfers are often expressed using mainly phenomenological models [START_REF] Bennai | Contribution to the Modelling of Coupled Heat and Mass Transfers on 3D Real Structure of Heterogeneous Building Materials: Application to Hemp Concrete[END_REF][START_REF] Bennai | Periodic homogenization for heat, air, and moisture transfer of porous building materials[END_REF] or models that consider the materials microstructure through porosity or pore size distribution [START_REF] Eitelberger | Prediction of transport properties of wood below the fiber saturation point -a multiscale homogenization approach and its experimental validation: Part i: Thermal conductivity[END_REF][START_REF] Sejnoha | Moisture induced strains in spruce from homogenization and transient moisture transport analysis[END_REF].

Adsorption and desorption isotherms are among the most important hydric properties of porous building materials, since they describe the equilibrium water content as a function of the ambient relative humidity, at a certain temperature. Cement based materials often exhibit a hysteresis loop, meaning the moisture content at the same relative humidity is different whether the material experiences wetting or drying. Therefore, the moisture content also depends on the hydric history of the material [START_REF] Pedersen | Combined Heat and Moisture Transfer in Building Constructions[END_REF], and the water content follows the intermediate scanning curves (fig. 1, curves B and D) located between the two main adsorption and desorption curves (fig. 1, curves A and C) [START_REF] Maaroufi | Moisture transfer modelling in polystyrene mortar with consideration of sorption hysteresis[END_REF].

Fig. 1 Sorption hysteresis curves [START_REF] Pedersen | Transient calculation on moisture migration using a simplified description of hysteresis in sorption isotherms[END_REF] Sorption hysteresis should then be taken into consideration in any hygrothermal transfers research, since it illustrates the fact that it is easier for water to get in than to get out of a porous medium [START_REF] Samri | Analyse physique et caractérisation hygrothermique des matériaux de construction: approche expérimentale et modélisation numérique[END_REF] and is highly correlated to capillary forces [START_REF] Schiller | Capillary Forces and Sorption Hysteresis of Cement Pastes with Small Slit Pores[END_REF]. In the past few decades, the interest about this phenomenon has highly increased, and researchers began developing hygrothermal models considering the effect of sorption hysteresis. However, it remains unknown and less studied in the literature, unlike other conventional phenomena such as hydration or carbonation. Some researches exhibited sorption hysteresis experimentally and considered it in the heat and mass transfers modelling. In his work, Zhang [START_REF] Zhang | Modelling of sorption hysteresis and its effect on moisture transport within cementitious materials[END_REF] studied cement pastes initially saturated, then subjected to hydric cycles varying from 33% to 80% and finally 53,5% of relative humidity. He then validated his hygrothermal model using experimental saturation profiles. However, he only subjected the samples to only one cycle of wetting and drying, which is not representative of buildings. Ait Oumeziane [START_REF] Oumeziane | Evaluation des performances hygrothermiques d'une paroi par simulation numérique : application aux parois en béton de chanvre[END_REF] also studied sorption hysteresis phenomenon in a hemp concrete, a very hygroscopic material. Samples were subjected to many cycles of 75% of relative humidity during 8h, then 33% during 16h, corresponding to the NORDTEST protocol for the determination of Moisture Buffer Value [START_REF] Rode | Moisture Buffering of Building Materials[END_REF]. However, some input parameters were only taken from literature and not measured for the studied material, and thermal conductivity dependency was modeled based on its values at the dry and saturated state only. The evolution of the water content in the material was compared to numerical simulations. In line with this work, Lelièvre [START_REF] Lelièvre | Simulation numérique des transferts de chaleur et d'humidité dans une paroi multicouche de bâtiment en matériaux biosourcés[END_REF] also studied hysteresis in hemp concrete through three different experimentations. The difference lies in the duration of the relative humidity levels, which varies from few hours to few days. Nevertheless, thermal properties of the material were considered constant regardless of its water content, and most of the input parameters were taken from previous works in literature.

Other researches designed sorption hysteresis modelling using a physical approach, based on the microstructure of the materials. Schiller et al. [START_REF] Schiller | A model for sorption hysteresis in hardened cement paste[END_REF] recently proposed a hysteresis model in hardened cement pastes with consideration of the sorption in the interlayer space between the C-S-H sheets, which is supposed to be responsible for low-pressure hysteresis of water sorption isotherms. Their work is based on a macroscopic approach using a simple mathematical model coupled to volume change diagrams. Only computed hysteresis loops were compared to those observed experimentally. Jiang et al. [START_REF] Jiang | Modelling of water vapour sorption hysteresis of cement-based materials based on pore size distribution[END_REF] developed a model to predict water vapor sorption hysteresis of cement-based materials based on pore size distribution obtained from adsorption isotherms. No suited experimental campaign was led to validate the model, which was verified using water vapor sorption isotherms from literature.

However, sorption isotherms are determined at equilibrium, while materials in buildings undergo dynamic humidity variations. Fig. 2 Main and average sorption curves for hemp concrete [START_REF] Bennai | Experimental characterization of thermal and hygric properties of hemp concrete with consideration of the material age evolution[END_REF] In most of the numerical studies of hygrothermal transfers, sorption hysteresis is often neglected. Some works prefer to overestimate the water content and consider that it varies according to the evolution of the main desorption curve for each variation of the daily relative humidity, whether it is a wetting or a drying [27 -29]. Some researchers assume that the water content rather follows the path of the main adsorption curve and do not consider sorption hysteresis [START_REF] Samri | Analyse physique et caractérisation hygrothermique des matériaux de construction: approche expérimentale et modélisation numérique[END_REF], and others even consider a mean curve between the main sorption isotherms, introducing some weighting coefficients [START_REF] Zhang | Modelling of sorption hysteresis and its effect on moisture transport within cementitious materials[END_REF]. These choices are difficult to justify, given that water content in a porous material follows different paths whether it is subjected to a wetting or drying. In fact, at the same relative humidity, water content has two different values, and the relative gap between them is very high. In the case of very hygroscopic materials such as hemp concrete [START_REF] Bennai | Experimental characterization of thermal and hygric properties of hemp concrete with consideration of the material age evolution[END_REF], the difference can go from 50% to 100%, as shown in figure 2.

The water content depends then on the relative humidity of the environment in addition to the previous hydric states of the material. Therefore, sorption hysteresis must be taken into account in the modelling of coupled heat and mass transfers in building materials, because it allows determining a more precise value of water content at any given time.

In this context, we propose a hygrothermal transfer model considering the sorption hysteresis phenomenon using the sorption isotherms. The heat and mass transfer model is based on Luikov's equations [START_REF] Luikov | Heat and Mass Transfer in Capillary-porous Bodies[END_REF], including some improvements in the hypotheses. Indeed, input parameters were not supposed constant, and their temperature and water content dependency were considered. Sorption hysteresis phenomenon is also considered, and an adequate experimental campaign was carried on in order to validate the computed results. Moreover, in order to reduce the environmental footprint of building sector, a recycled expanded polystyrene mortar will be the material of interest. It is an eco-friendly material that helps reuse the expanded polystyrene waste and has improved thermal insulation properties. It is a highly heterogeneous material with a complex microstructure, and is composed of two materials whose hygrothermal behavior highly varies.

In what follows, the hygrothermal model will be presented, along with its implementation on Matlab and Comsol multiphysics. The experimental setup allowing the highlight of hysteresis will be presented, and the obtained results will be compared to the ones from the numerical calculations using the hysteresis model. A non-hysteresis model will also be used in order to enhance the influence of the sorption hysteresis phenomenon. It is implemented using the main adsorption isotherm only, and it aims to show the importance of sorption hysteresis consideration in hygrothermal transfers modelling.

Modelling

Heat and mass transfers modelling

In this study, the implemented model is a coupled heat and mass transfers model using respectively temperature and water content as driving potentials. Afterwards, it will be coupled to a physical model that allows calculating the water content inside the pores from the ambient relative humidity with the consideration of sorption hysteresis.

The mass balance equations for the water vapor and liquid water phases respectively are written below:

+ div j = -m (1)
+ div j = m (2)
By adding the two equations, we obtain the equation (3) that simplifies into equation [START_REF] John | Moisture in buildings[END_REF].

+ + div j + div j = 0 (3)
+ div j + j = 0 (4)
Given that the volume water content is function of the mass water content and the materials density (equation ( 5)), the mass balance equation becomes equation [START_REF] Xu | Study of heat and moisture transfer in internal and external wall insulation configurations[END_REF].

U = ρ × ω (5) ρ + div j + j = 0 (6)
Flux densities of water vapor and liquid water can be expressed using adequate diffusion coefficients, which depend on the hydric state of the material as:

j = -. ∇P (7) j = -. ∇P (8)
In order to simplify the boundary conditions, water vapor content is considered the only driving force of the mass transfers. Moreover, both the water vapor pressure and the capillary pressure are related to relative humidity through the saturated vapor pressure and Kelvin law.

P = RH × P # (9)
P = $%& ' ln RH (10)
Given the dependency of relative humidity on the temperature, the derivative of equation ( 10) is expressed as follows [START_REF] Ferroukhi | Hygrothermal behavior modeling of the hygroscopic envelopes of buildings: A dynamic co-simulation approach[END_REF]:

∇P = + $%& ' , $-∇RH. + + $%& ' / 0 $- % 1 + $& ' ln RH . ∇T (11)
The thermal diffusion is negligibly small, and considered of no importance in building science applications [START_REF] Janssen | Thermal diffusion of water vapour in porous materials: Fact or fiction?[END_REF][START_REF] Trabelsi | Assessment of temperature gradient effects on moisture transfer through thermogradient coefficient[END_REF]. Therefore, the total mass flux can be expressed in the equation [START_REF] Bennai | Periodic homogenization for heat, air, and moisture transfer of porous building materials[END_REF].

j 3 = -+ P # + $%& ' , 45 . ∇RH (12)
The moisture storage capacity 6 7 is defined as the slope of the sorption isotherm curves [START_REF] Koronthalyova | Moisture storage capacity and microstructure of ceramic brick and autoclaved aerated concrete[END_REF].

It is then a function of relative humidity and water content. It is an important property of the material as it represents the water accumulation in the pores due to sorption hysteresis.

6 7 = $- (13)
The final expression of the mass balance equation is then explicated in equation ( 14).

ρ -div + ∇ω + @ ∇ω . = 0

The moisture diffusion coefficient that appeared in the mass balance equation is defined as below [START_REF] Lelièvre | Simulation numérique des transferts de chaleur et d'humidité dans une paroi multicouche de bâtiment en matériaux biosourcés[END_REF][START_REF] Kunzel | Simultaneous heat and moisture transport in building components: one-and two-dimensional calculation using simple parameters[END_REF][START_REF] Colinart | Influence de l'hystérésis sur le comportement hygrothermique d'un enduit de finition intérieure biosourcé[END_REF]:

@ 7 ω = A B C P # = δ ω P # (16)
The heat balance equation is expressed in the equation ( 17) [START_REF] Colinart | Influence de l'hystérésis sur le comportement hygrothermique d'un enduit de finition intérieure biosourcé[END_REF]. We only consider heat transfers due to conduction, convection and phase change, and we neglect the radiation phenomenon. The final conservation of energy equation is then as:

C F ρ % -div λ∇T -@ 7 C F ∇T -m L ω = 0 (17)

Initial and boundary conditions

The boundary conditions in this paper are Dirichlet type, and the temperatures and relative humidities are directly applied to the exterior surfaces of the sample.

I ω x = 0, t = ω , t T x = 0, t = T , and

I ω x = L, t = ω N t T x = L, t = T N ( 18
)
Where L is the thickness of the sample. The initial conditions are considered uniform in the material and expressed as follows:

I ω x, t = 0 = ω O T x, t = 0 = T O (19)

Input parameters

The input parameters of the heat and mass transfers model are the hygrothermal properties of the material, that were determined using an experimental campaign. The moisture storage capacity Cm is obtained through the water vapor sorption isotherm curves presented later.

The thermal conductivity of the material depends on the temperature and the water content of the material, and it was experimentally determined based on the guarded hot plate method [START_REF] Nf En | Thermal performance of building materials and products -Determination of thermal resistance by means of guarded hot plate and heat flow meter methods -Products of high and medium thermal resistance[END_REF]. The thermal conductivity of the polystyrene mortar can be expressed as a function of temperature as follows:

λ = 0,0005. T + 0,1472 (20)
The thermal conductivity was also measured depending on the hydric state of the material. Its dependency on the water content is expressed in equation 21.

λ = 0,3663. ω + 0,1413 (21)
The water vapor permeability of polystyrene concrete depends on the materials water content, and it was experimentally determined following the cup test method based on the standards NF EN ISO 12572 [START_REF] Afnor | Hygrothermal performance of building materials and products -Determination of water vapor transmission properties[END_REF]. This method allows determining the water vapor permeability at a low and a high relative humidity (3% and 93%

Sorption hysteresis modelling

The coupled heat and mass transfers model will be coupled to a sorption hysteresis model. Therefore, in addition to taking into account the moisture accumulation inside the pores through the moisture storage capacity, it will be able to calculate the real value of water content from the ambient relative humidity. The sorption hysteresis model chosen for this work is the one developed by Carmeliet [START_REF] Carmeliet | Hysteresis and moisture buffering of wood[END_REF], which is a physical model based on the theory of the independent domains and the ink-bottle pore effect, elaborated by Mualem [START_REF] Mualem | A conceptual model of hysteresis[END_REF][START_REF] Mualem | Modified approach to capillary hysteresis based on a similarity hypothesis[END_REF]. In previous works, this model was proven to be the most representative to the hysteretic behavior of cement based materials [START_REF] Oumeziane | Evaluation des performances hygrothermiques d'une paroi par simulation numérique : application aux parois en béton de chanvre[END_REF][START_REF] Lelièvre | Simulation numérique des transferts de chaleur et d'humidité dans une paroi multicouche de bâtiment en matériaux biosourcés[END_REF].

The use of empirical hysteresis models often leads to a hysteretic behavior called "pumping effect". It reflects the fact that the numerical scanning curves do not respect the closing principle. In other words, this means that during a succession of adsorption and desorption cycles, there is a unique water content value for each extremum of relative humidity. Therefore, a material undergoing several cycles of wetting /drying should normally return to its initial relative humidity and water content.

Some researches [START_REF] Zhang | Modelling of sorption hysteresis and its effect on moisture transport within cementitious materials[END_REF][START_REF] Huang | A novel hysteresis model in unsaturated soil[END_REF][START_REF] Werner | Artificial pumping errors in the kool-parker scaling model of soil moisture hysteresis[END_REF] consider that the pumping effect is not a physical characteristic specific to the material, but that it is entirely artificial. It is then considered as errors generated by the calculation algorithms. Mualem model -and therefore Carmeliet model -respects the closing principle and makes it possible to avoid pumping errors, confirming its accuracy in hysteresis modelling [START_REF] Derluyn | Hysteretic moisture behavior of concrete: Modelling and analysis[END_REF][START_REF] Lelièvre | Simulation numérique des transferts de chaleur et d'humidité dans une paroi multicouche de bâtiment en matériaux biosourcés[END_REF].

The sorption hysteresis model developed by Carmeliet allows calculating modelled hysteresis loops from the main adsorption and desorption isotherm curves. It is based on the theory of independent domains, considering the ink-bottle shaped pores. It expresses the water content in the scanning curves in different expressions, whether it is a wetting or a drying, in terms of water content in the main sorption isotherms, and some specific values such as saturation point.

The equation describing the water content in adsorption scanning curves is recalled below.

ω #W ,XY RH, i = ω Z[, + \1 -A RH Z[, ^ ω #W RH -ω #W RH Z[, . (22)
The "i" indicates the inversion point which is the exact time of going from an adsorption to a desorption (and vice versa). In equation [START_REF] Rode | Moisture Buffering of Building Materials[END_REF], the "i" here marks the inversion between the i-1 th desorption scanning curve and the i th adsorption scanning curve.

The equation describing the water content in desorption scanning curves is expressed in [START_REF] Lelièvre | Simulation numérique des transferts de chaleur et d'humidité dans une paroi multicouche de bâtiment en matériaux biosourcés[END_REF]. In this case, the "i" marks the inversion between the i-1 th adsorption scanning curve and the i th desorption scanning curve, as explicated in figure 3.

ω W_ ,XY RH, i = ω Z[, -\1 -A RH ^ ω #W RH Z[, -ω #W RH , ( 23
)
Where

A RH = `ab $-[ B`b $- bBc [ B`b $- (24)

Fig.3 Schematic representation of the i th inversion point

The water content associated to each varying value of relative humidity is calculated whether it is a wetting or a drying. For that, we need to know and memorize the inversion points. It is then necessary to indicate a transition criterion between the different phases of wetting/drying, along with a list of the inversion points [START_REF] Oumeziane | Evaluation des performances hygrothermiques d'une paroi par simulation numérique : application aux parois en béton de chanvre[END_REF]. Equation [START_REF] Jiang | Modelling of water vapour sorption hysteresis of cement-based materials based on pore size distribution[END_REF] expresses the condition of the transition from the adsorption curve to the desorption curve, and vice versa.

When the inversion criterion is less than zero, there is a transition from a sorption phase to the other, and the new inversion point is added to the list.

L Z0 = RH n -RH n -1 × RH n -1 -RH Z[, (25)
RH(n) represents the relative humidity of the material at the time n, RH(n-1) at the time n-1, and RHi-1 corresponds to the relative humidity of the last identified inversion point.

The iterations in the program stand for the time. There is an inversion if the inversion criterion is less than zero. In this case, this new point is saved and becomes the last identified inversion point. The values of relative humidity and water content are therefore calculated at each time, and the water capacity is calculated differently whether it is an adsorption or a desorption.

As shown in figure 4 Comsol has several solvers all based on finite elements method, then chooses the most suitable one to ensure stability and convergence of the solutions. The time dependent solver is computing the solution to a possibly nonlinear system of equations at each time step via a set of iterative techniques based upon Newton's method. These Newton's method techniques for solving a nonlinear system of equations evaluate a function, as well as its derivative, at every time step. This derivative is also known as the Jacobian and is relatively expensive to compute. Therefore, the software will try to minimize reevaluating the Jacobian, by default. If the nonlinear solver has difficulty converging, it will reduce the requested time step size and try to compute the solution.

Fig. 4 Hysteresis modelling steps

Materials and methods

In this study, the coupled heat and moisture transfers model developed is based on phenomenological modelling, where the relevance of the prediction is conditioned by a reliable evaluation of the input data. The hygrothermal properties that constitute the input parameters of the implemented model were experimentally determined using standard laboratory methods. A part of this section was dedicated to a fine, experimental characterization of the intrinsic hydric and thermal properties of the material. The material of interest in this work is a polystyrene mortar made of recycled expanded polystyrene granules and a CEMII cement as a binder [START_REF] Maaroufi | Characterization of EPS lightweight concrete microstructure by X-ray tomography with consideration of thermal variations[END_REF][START_REF] Maaroufi | Influence of recycled polystyrene beads on cement paste properties[END_REF].

Computing the coupled heat and mass transfers involves the experimental determination of the hygrothermal properties of the material. The experimental campaign aimed to measure the water vapor permeability using the wet cup/dry cup method based on the EN ISO 12572 norm [START_REF]ASTM Annual book of standards, Standard test method for water vapor transmission of materials[END_REF], the thermal conductivity using the Guarded Hot Plate method based on the NF EN 12667 norm [START_REF] Nf En | Performance thermique des matériaux et produits pour le bâtiment -Détermination de la résistance thermique par la méthode de la plaque chaude gardée et la méthode fluxmétrique -Produits de haute et moyenne résistance thermique[END_REF], and the heat capacity using a 3D sensors calorimeter.

In addition, the implementation of the hysteresis model requires the determination and modelling of the main adsorption and desorption curves of the material. The experimental isotherm curves were determined using the gravimetric technique that is based on continuous successive weightings. The test was performed on a very recent vapor sorption analyzer that allows measuring the mass evolution of the samples. For the polystyrene mortar, the main isotherms are modelled using the equation below [START_REF] Carmeliet | Hysteresis and moisture buffering of wood[END_REF], which proves a good adequacy between the experimental and the modelled curves, as shown in figure 5.

ω RH = ω # /1 - 0 $- d 1 [ , 0 e (26)
A and n are empirical calibration coefficients. These parameters were adjusted using the experimental data presented in figure 5. The fitting parameters are presented in table 2, and are different whether it is adsorption or desorption. The root mean squared error between the experimental data and the adjustment curves is 0,2%.

Table 2. Fitting coefficients for the main sorption isotherms

During the daily variations of relative humidity and temperature, the water content inside building materials varies according to the intermediate sorption isotherms. In order to characterize experimentally the intermediate curves of the expanded polystyrene mortar, the total water content is measured at the equilibrium when subjecting the material to different relative humidity levels. The experimental method used here was the gravimetric technique that is based on continuous successive weightings. The test was performed on three cubic samples of 10x10x10 mm 3 dimensions previously dried at 60°C. The temperature was fixed at 23°C and the relative humidity variations are presented in figure 6. Table 3. Experimental hydric and thermal conditions

Results and discussion

In the following, the experimental and numerical results are presented. First, the intermediate adsorption and desorption curves of the polystyrene mortar are presented, in addition to the experimental and modelled moisture storage capacity curve. Afterwards, the experimental water content profiles inside the samples, along with the simulated water content profiles are presented simultaneously in order to compare both. The three different experimental protocols presented in table 3 are treated separately, in order to compare between the experimental and simulated profiles in each case.

Main and intermediate sorption curves

The experimental adsorption and desorption curves of the polystyrene mortar are presented in the figure 9. Given that the sample was initially at a dry state, the first curves are the main adsorption and desorption isotherms, while all the others represent the intermediate curves. The scanning curves are all located between the main curves, which represent an envelope curve. They have the same look and vary in the same way, they even present the abrupt decrease in desorption around 30% of relative humidity. After four cycles of the wetting and drying cycles presented in figure 6, the intermediate curves overlap, thus the 4th adsorption curve and the 3rd desorption curve are imbricating. These results come from the water accumulation in the materials porosity and the sorption hysteresis phenomenon, since the relative humidity conditions are narrowed down after each cycle. The hysteresis model is also used to model the moisture storage capacity of the material in order to evaluate its accuracy. Moisture storage capacity is defined as the derivative of the water content in relation to the relative humidity; it can then be obtained from the sorption curves. In order to verify the accuracy of the hysteresis model, modelled moisture storage capacity of polystyrene mortar is compared to the experimental in figure 11.

During the adsorption phase, the modelled moisture capacity shows very good concordance with the experimental curve, since the highest difference is only 8%. In desorption, the model give less adequate results and display bigger differences up to 30%. However, the variations of the modelled curves look like the experimental ones, and the model allows preserving the shape of the experimental curve.

Fig. 11 Experimental and modelled moisture storage capacity of polystyrene mortar

Water content evolution through time

In the following, the experimental water content profiles inside the samples are presented.

They are compared to the numerical profiles obtained through simulations using the hysteresis model presented in the previous parts. A non-hysteresis model will also be used in order to assess the importance of the phenomenon consideration in the hygrothermal transfers modelling in building materials. The results of each experimentation is presented apart from the others below. The discrepancy in the first cycle could result from a delay of the model, due to the initial conditions. In fact, the material is initially conditioned at 60% of relative humidity, which corresponds to a water content of 2.8% kg/kg before going through the first adsorption. In the model, the initial water content put in the input parameters corresponds to that. Afterwards, at the end of each desorption cycle, the sample has a water content of about 3.5% kg/kg.

Therefore, during humidification where the relative humidity is at 85%, it is easier for the material to reach the maximum water content (4.7% kg/kg) when it is at 3.5% kg/kg than when it is at its initial value. In reality, polystyrene mortar is not very hygroscopic, and so it quickly reaches the maximum water content even when it is at the initial water content.

Short lasting cycles at constant temperature

The second experiment consists of short lasting cycles at constant temperature, and the water content profiles are presented in figure 13. The water content curve simulated with the nonhysteresis model has the same shape as the experimental curve, and their amplitudes are similar. The real water content values are underestimated since the numerical curve is below the experimental, and the relative gap increases a little more with each cycle, until reaching a maximum value of 7% in the last cycle.

Using a non-hysteresis model in simulating the hygrothermal behavior of building materials is not a wise choice. Indeed, it is not advised to underestimate the water content in building walls in hygrothermal transfer simulations, because of water accumulation that could degrade the construction if not taken into consideration.

In a second time, the numerical curves acquired using the hysteresis model show the effect of the sorption hysteresis phenomenon. This latter is less apparent in the experimental results because of the drying period that is higher than the humidification. The numerical profiles have the same amplitude as the experimental, but show a slight increase in time. However, the displayed relative difference is only of 2.5% corresponding to barely 0.07% kg/kg, and the simulated curves are in good agreement with the experimental.

The hysteresis model uses the main adsorption and desorption isotherm curves as input parameters, which are based on equilibrium measurements. On the other hand, the measurements in this test are carried out in dynamic regime, which may explain the differences between the experimental and numerical results.

Short lasting cycles at varying temperature

The third experimentation is based on short lasting cycles at a varying temperature, corresponding to the daily variations of temperature and relative humidity. As can be seen in figure 14, the experimental curve shows a discrepancy in the first cycle, where the water content is lower than in the others. This is due to a malfunctioning of the climatic chamber, which did not secure the required temperature and relative humidity during the first cycle.

Given that the real climatic conditions recorded inside the chamber are used in the numerical simulations, the simulated water content profiles display the same behavior in the first cycle. In this experimentation, the simulated water content curve using the non-hysteresis model is not located below the experimental curve, contrary to the two previous tests. In fact, the water content values are overestimated, and the high values obtained could be due to the varying temperature and its effect on moisture transfers. In addition to that, the amplitude of the simulated curve is significantly lower and corresponds to only 40% of the real one. The relative difference gradually increases as cycles progress, and attain a maximum value of 16%.

The curve obtained using the hysteresis model shows a very good concordance with the experimental one. Although the water accumulation due to hysteresis is slightly greater in simulated curves, only a small difference is observed. Indeed, the highest relative gap is about 5%, which can be considered as included in the precision range of the sensors. The hysteresis model also allows to maintain the shape and the amplitude of the experimental water content profiles, unlike the non-hysteresis model.

Conclusion

In this paper, we presented an experimental and numerical study of the water vapor sorption hysteresis phenomenon in expanded polystyrene mortar. First, a coupled heat and mass transfer model was presented allowing the sorption hysteresis consideration through the physical model of Carmeliet. Afterwards, the experimental setup was presented, along with the protocols and hygrothermal conditions. The experimental profiles were then compared to the simulated ones in order to assess the influence of hysteresis consideration in hygrothermal modelling of building materials.

The developed experimentations aim to highlight the sorption hysteresis phenomenon via submitting the samples to multiple cyclic conditions, varying in temperature and relative humidity. High precision sensors were inserted in the samples in order to record the water content evolution during the time of the experiment. The experimental profiles were later compared to simulated ones, obtained using the hysteresis model coupled to the hygrothermal transfer model, and also a non-hysteresis model used to evaluate the influence of considering hysteresis in numerical simulation.

The three different experimentations showed the same conclusion: Sorption hysteresis consideration allows obtaining a better adequacy between simulated and experimental results.

In fact, the simulated curves using the hysteresis model had the same shape and amplitude as the experimental ones, and the difference did not exceed 7%. On the other hand, the nonhysteresis model showed numerical curves that either highly underestimated or overestimated the real water content values. Moreover, their amplitude did not match the experimental one, and the relative gaps were significantly important and reached 28%.

The water vapor sorption hysteresis phenomenon highly affects the hygrothermal transfers in building materials, as it causes water accumulation in the pores. Its consideration allows to a better apprehension of the real water content in porous materials and thus a better understanding of the hygrothermal behavior of buildings.

  , MATLAB software was used to compute the hysteresis model, coupled to COMSOL Multiphysics where the hygrothermal model was implemented. The experimental values of ambient relative humidity and the main adsorption and desorption curves are first introduced in MATLAB where the hysteresis model allows the calculation of the corresponding values of water content, in addition to the moisture storage capacity. These values are then imported into COMSOL along with the input parameters consisting in the hygrothermal properties of the material of interest. The resolution in Comsol is based on the finite elements method following three basic steps, namely pre-processing, solver, and postprocessing. It generates a set of equations for all the involved physical models and implements them in a single iteration scheme, which is repeated until convergence is reached.

Fig. 5

 5 Fig.5 Main adsorption and desorption isotherm curves of polystyrene mortar

Fig. 6 Fig. 7

 67 Fig.6 Relative humidity variation during the determination of the intermediate isotherms

Fig. 8

 8 Fig.8 Experimental setup diagram

Fig. 9

 9 Fig.9 Main and intermediate sorption isotherm curves of the polystyrene mortar

Fig. 10

 10 Fig.10 Experimental and modelled main and intermediate sorption curves of the polystyrene

4. 2 . 1 .

 21 Long lasting cycles at constant temperatureNumerical and experimental results of the water content profiles in the samples submitted to long lasting cycles at constant temperature are presented in figure12. Using the nonhysteresis model, the evolution of water content represents a curve below the experimental results and underestimates the actual values. In the adsorption phase, the difference between the experimental and simulated curves is relatively low, and the highest relative gap observed is 5%. On the contrary, during desorption, the non-hysteresis model underestimates the real water content values. The difference in this case is highly significant and the simulated values show relative gaps reaching 28%.The profiles obtained with the hysteresis model show a good adequacy with the experimental results, except the first adsorption cycle where the difference is relatively high. Indeed the numerical values of water content are lower than the experimental ones, and a 7% relative difference is recorded at the peak of the first cycle. Concerning the remaining cycles, the numerical curves are in good concordance with the experiments and the relative differences do not exceed 2%.

Fig. 12

 12 Fig.12 Experimental and numerical water content profiles in the first test

Fig. 13

 13 Fig.13 Experimental and numerical water content profiles in the second test

Fig. 14

 14 Fig.14 Experimental and numerical water content profiles in the third test

Table 1 .

 1 Input parameters

	ρs (kg/m3)	537	Cp (J/kg.K)	971
	Tref (K)	273,15	Cpv (J/kg.K)	1860
	δv (kg/m.s.Pa)	3,22.10 -12 at low RH	m (-)	0,3
		1,2.10 -11 at high RH
	Lv (J/kg)	2,5.10 6

). Hence, water vapor permeability will have two different values whether the ambient relative humidity is high or low.

Acknowledgments

The Region and the European Union support the project < CPER BATIMENT DURABLE. Axis 2 MADUR Project: High-performance building materials with low environmental impact, sustainable and resilient > within the framework of the « Operational Program FEDER/FSE 2015-2020 » and Energy saving certificate program of the French Ministry of Ecological and Solidarity Transition "SmartReno Support" 2019-2021.

CRediT authorship contribution statement

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.