宋若水 劉薇禛平 張禹

Abstract：

COVID-19 spreads through patients exhalation droplets， hence a comprehensive understanding of muco-saliva fragmentation provides crucial insight. This paper scrutinizes a study of the breakup of mimic of contagious viscoelastic exhalation fluid， conducted by MIT researchers： “Visualization of sneeze ejecta： steps of fluid fragmentation leading to respiratory droplets”， in which the authors profoundly contributed to the understanding of hazardous sneeze ejecta caused by sneezing. In this article， some of their nicely incorporated experimental methods and break through will be described and analyzed with the integration of fluid dynamics.

1.Introduction

1.1 What the research is about

MIT researchers observation indicates disintegration of muco-saliva occurs not only in trachea， but outside human airway after ejection， which explains the high infectivity of airborne influenza strains like influenza and SARS （1）. However， uncertainties on the range of droplet distribution determined by droplet size and the detail of fluid fragmentation persist within the field （1）. They have visualized the four stages of the mucus decomposition through high-speed videography. The researchers also measured physical quantities like relaxation time， Reynold number， and Deborah number.

1.2 Why this research is important

This work over ejecta disintegration is concerned with the production of droplets of muco-salivary liquids and the viscoelasticity of this material controls the fragmentation of this liquid as it is ejected by sneezing and coughing events. Thus， providing insights into the formation of the droplets is the reason why this research is contributive.

To better understand the innovation of this research， it is helpful to consider previous work and how it could be expanded. First of all， the fluid dynamicsof violent expirations remains poorly understood relative to industrial flows.Second， coughs and sneezes， neurological reflex actions triggered by irritation of the nose or trachea， are two typical ways of spreading contagious droplets （2）. Albeit the mechanism of sneezing is analogous to that of coughing， little is known about the dynamics after pharynx constriction in a sneeze （3，4）.

Hence this research is innovative for these aspects. First， the MIT researchers unveiled the fluid dynamics of sneeze and the features of each stages. Second， through the calculation of the relaxation time， important dimensionless numbers relevant to the problem of sneeze ejecta， the Deborah number and the Reynolds number were estimated， along with many other fluid dynamics features. The researchers discovered the crucial role viscoelasticity plays in mucus fragmentation. Moreover， B. E. Scharfman et al.， the conductors of this research focused on sneezing， an uncommon subject， and compared the dynamics with that of coughing （5，6，7）， which provides tremendous and insight into the formation of sneeze-induced droplets.

2.Review

2.1 Methods and evaluation

2.1.1high-speed video camera filming

In this research， the researchers aimed to directly visualize the fragmentation of sneeze ejection. They chose to use high-speed videography and illumination to highlight droplets against black backdrop to obtain optimal lighting to reveal the droplets in space and time.

In order to gain more comprehensive insight into the distinction of distribution between sneeze and cough ejecta the researchers also visualized cough-induced ejection of muco-saliva at the exit of mouths using controlled groups.

2.1.2calculation of physical features

The Relaxation time， λ， is the time it takes for a viscoelastic material to return to equilibrium following a perturbation. Bourouiba and coworkers cite the muco-saliva fluid relaxation times reported in Simon J. Harwards et al. where extensional rheology of human saliva （8） was analyzed using the Maxwell Model. When a deformation is applied to the dashpot in the form of a step strain， this model produces an exponential decay that can be fit to obtain the relaxation time. Henceforth with the stress the relaxation time can be calculated through integral.

Deborah number （De） quantifies the effect of viscoelasticity by prescribing the relative magnitude of the polymer relaxation time λ and the timescale of fragmentation τ， De =λ/τ. To estimate the fragmentation time， Bourouiba et al. consider another dimensionless group， the Weber number， which is the ratio of the momentum stress to capillary stress in the droplet. De is also represented by the ratio of solid stress Fs over viscous stress Fv， De= Fs/ Fv. Thus， when De is smaller than 1， the material exhibits fluid-like mechanical effects; De is larger than 1， the material exhibits solid-like mechanical effects; and when De approaches 1， the material exhibits viscoelastic mechanical effects.

The magnitude of Reynolds number reflects the flow status. Using the flow speeds from the recordings in Figs. 3， estimate the Reynolds number Re = Q/（dν）， where d is the mouth diameter， Q is the flow rate， determined by evaluating the total volume of air and droplets exhaled over the duration of the emission， and ν is the viscosity of the gas phase.

2.2Results

Since the relaxation time cited varies significantly， 2.24 ms≤λ≤76.2 ms， the resulting Deborah number also ranges widely， 0.65≤ De≤ 78.73. While in Bhats et al. research Deborah number is reported to the within0.004 and 0.5.

In the work of B. E. Scharfman et al.， the total duration of the sneeze was 134.5 ms with an estimated Reynolds number for the gas cloud of ReG = 105， indicating that the sneeze ejection is drastic and fully turbulent.

By juxtaposing the droplets propagation of cough and sneeze， as shown in Fig 2 and 3， the difference between a sneeze and a cough is evident. While sneeze ejecta is still relatively condensed and pendant in the air after 0.34 seconds 70 centimeters away， droplets of cough ejecta can barely be detected by bare eye after 0.15 seconds.

As shown in Fig4， when the mucus first burst out of human airway， it is flattened into sheet; then as the muco-salivary liquid stretches further， the bag structure bursts and mucus on the ligament configurates like beads-on-string due to the spontaneous Rayleigh-Plateau instability. Finally， beads merge and droplets form.

姓名：宋若水

城市：北京市

年級：12年級

目標專業(yè)：生物醫(yī)學(xué)工程專業(yè)

在撰寫本篇研究報告前，我閱讀了有MIT研究員B. E. Scharfman等人的研究論文《Visualization of sneeze ejecta： steps of fluid fragmentation leading to respiratory droplets》。從中我了解了流體動力學(xué)及軟質(zhì)材料的相關(guān)內(nèi)容，如雷諾數(shù)、松弛時間、Deborah數(shù)等無綱常量的物理意義、定義式及計算式。此外我了解了如何從文章摘要中抓取一篇論文的重要信息及如何撰寫評論性論 文。