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This article presents the evolutionary history of immersed boundary methods (IBMs), tracing their origins to the very beginning of computational fluid dynamics in the late 1950s all the way to the present day. The article highlights the advancements in this simulation methodology over the last 50 years and explores the interplay between IBMs and body-conformal grid methods during this time. Drawing upon the authors’ combined experience of more than 40 years in this arena, the perspective offered is personal and subjective. By employing a critical and comparative approach through the chronological lens, we hope that this article empowers the reader to understand both the capabilities and limitations of these methods, and to pursue advancements that fill the key gaps and break new ground. 

A reduced-order model of face mask aerodynamics and aerosol filtration is introduced. This model incorporates existing empirical data on filtration efficiency for different types of face masks, as well as the size distribution of exhaled aerosol particles. By considering realistic peripheral gap profiles, our model estimates both the extent of peripheral leakage and the fitted filtration efficiency of face masks in terms of outward protection. Simulations employing realistic peripheral gap profiles reveal that, for surgical masks, 80% or more of the total exhaled airflow could leak through the mask periphery, even when the average peripheral gap measures only 0.65 mm. However, the majority of exhaled aerosol particles do not follow the flow path through the peripheral gaps but, instead, impact directly on the mask fabric. As a result, these face masks can filter out approximately 70% of the exhaled particles despite the significant peripheral leakage. To validate our model, we compare its predictions with experimental data, and we find a reasonable agreement in estimating the outward protection provided by surgical masks. This validation underscores the reliability of our model in assessing the efficacy of surgical masks. Moreover, leveraging the insights gained from our model, we explore the impact of mask usage on the transmission of respiratory viruses within communities. By considering various scenarios, we can assess the potential reduction in viral spread achieved through widespread mask adoption. 

Although face masks have been used for over a century to provide protection against airborne pathogens and pollutants, close scrutiny of their effectiveness has peaked in the past two years in response to the COVID-19 pandemic. The simplicity of face masks belies the complexity of the physical phenomena that determine their effectiveness as a defense against airborne infections. This complexity is rooted in the fact that the effectiveness of face masks depends on the combined effects of respiratory aerodynamics, filtration flow physics, droplet dynamics and their interactions with porous materials, structural dynamics, physiology, and even human behavior. At its core, however, the face mask is a flow-handling device, and in the current review, we take a flow physics–centric view of face masks and the key phenomena that underlie their function. We summarize the state of the art in experimental measurements, as well as the growing body of computational studies that have contributed to our understanding of the factors that determine the effectiveness of face masks. The review also lays out some of the important open questions and technical challenges associated with the effectiveness of face masks. 

Recent studies have shown that the effectiveness of the face masks depends not only on the mask material but also on their fit on faces. The mask porosity and fit dictate the amount of filtered flow and perimeter leakage. Lower porosity is usually associated with better filtration; however, lower porosity results in higher perimeter leakage. The resulting leakage jets generated from different types of faces and different mask porosities are of particular interest. Direct numerical simulations of the flow dynamics of respiratory events while wearing a face mask can be used to quantify the distribution of the perimeter leaks. Here, we present a novel model for porous membranes (i.e., masks) and use it to study the leakage pattern of a fabric face mask on a realistic face obtained from a population study. The reduction in perimeter leakage with higher porosities indicates that there would be an optimal porosity such that the total leakage and maximum leakage velocities are reduced. The current model can be used to inform the quantification of face mask effectiveness and guide future mask designs that reduce or redirect the leakage jets to limit the dispersion of respiratory aerosols. 

The use of face masks by the general population during viral outbreaks such as the COVID-19 pandemic, although at times controversial, has been effective in slowing down the spread of the virus. The extent to which face masks mitigate the transmission is highly dependent on how well the mask fits each individual. The fit of simple cloth masks on the face, as well as the resulting perimeter leakage and face mask efficacy, are expected to be highly dependent on the type of mask and facial topology. However, this effect has, to date, not been adequately examined and quantified. Here, we propose a framework to study the efficacy of different mask designs based on a quasi-static mechanical model of the deployment of face masks onto a wide range of faces. To illustrate the capabilities of the proposed framework, we explore a simple rectangular cloth mask on a large virtual population of subjects generated from a 3D morphable face model. The effect of weight, age, gender, and height on the mask fit is studied. The Centers for Disease Control and Prevention (CDC) recommended homemade cloth mask design was used as a basis for comparison and was found not to be the most effective design for all subjects. We highlight the importance of designing masks accounting for the widely varying population of faces. Metrics based on aerodynamic principles were used to determine that thin, feminine, and young faces were shown to benefit from mask sizes smaller than that recommended by the CDC. Besides mask size, side-edge tuck-in, or pleating, of the masks as a design parameter was also studied and found to have the potential to cause a larger localized gap opening.