Introduction_NN1 
The_AT0 pandemic_AJ0 of_PRF 2019_CRD ,_PUN due_AJ0 to_PRP SARS-CoV-2_NP0 ,_PUN named_VVD COVID-19_AJ0 and_CJC referred_VVN to_PRP as_PRP coronavirus_NN1 ,_PUN has_VHZ been_VBN responsible_AJ0 for_PRP nearly_AV0 two_CRD million_CRD of_PRF deaths_NN2 worldwide_AV0 in_PRP 2020_CRD alone_AV0 ._SENT It_PNP is_VBZ well-established_AJ0 that_CJT this_DT0 virus_NN1 primarily_AV0 spreads_VVZ from_PRP person-to-person_AJ0 contact_NN1 by_PRP respiratory_AJ0 droplets_NN2 produced_VVN when_CJS an_AT0 infected_AJ0 person_NN1 coughs_NN2 or_CJC sneezes_NN2 ._SENT Subsequently_AV0 ,_PUN the_AT0 droplets_NN2 come_VVN into_PRP contact_NN1 with_PRP the_AT0 eyes_NN2 ,_PUN nose_NN1 or_CJC mouth_NN1 of_PRF a_AT0 nearby_AJ0 person_NN1 or_CJC when_CJS a_AT0 person_NN1 touches_VVZ an_AT0 infected_AJ0 surface_NN1 ,_PUN then_AV0 makes_VVZ contact_NN1 with_PRP their_DPS eyes_NN2 ,_PUN nose_NN1 or_CJC mouth_NN1 ._SENT Since_CJS the_AT0 virus_NN1 is_VBZ small_AJ0 ,_PUN 0.06_CRD –_PUN 0.14_CRD microns_NN2 in_PRP diameter_NN1 ,_PUN it_PNP can_VM0 be_VBI contained_VVN in_PRP or_CJC attached_VVN to_PRP such_DT0 emitted_AJ0 droplets_NN2 ._SENT Droplets_NN2 as_CJS small_AJ0 as_CJS one_CRD micron_NN1 can_VM0 carry_VVI enough_DT0 viral_AJ0 load_NN1 to_TO0 cause_VVI an_AT0 infection_NN1 ._SENT A_AT0 particular_AJ0 concern_NN1 is_VBZ the_AT0 interaction_NN1 of_PRF droplets_NN2 with_PRP ventilation_NN1 systems_NN2 ,_PUN which_DTQ can_VM0 capture_VVI emitted_AJ0 pathogens_NN2 ,_PUN but_CJC can_VM0 also_AV0 potentially_AV0 could_VM0 enhance_VVI their_DPS propagation_NN1 ._SENT This_DT0 has_VHZ implications_NN2 on_PRP situation-specific_AJ0 safe_AJ0 distancing_NN1 and_CJC the_AT0 design_NN1 of_PRF building_NN1 filtration_NN1 systems_NN2 ,_PUN air_NN1 distribution_NN1 ,_PUN heating_NN1 ,_PUN air-conditioning_NN1 and_CJC decontamination_NN1 systems_NN2 ,_PUN for_PRP example_NN1 using_VVG UV-c_AJ0 and_CJC related_AJ0 technologies_NN2 ._SENT In_PRP order_NN1 to_TO0 facilitate_VVI such_DT0 system_NN1 redesigns_NN2 ,_PUN fundamental_AJ0 analysis_NN1 tools_NN2 are_VBB needed_VVN that_CJT are_VBB easy_AJ0 to_TO0 use_VVI ._SENT Accordingly_AV0 ,_PUN this_DT0 work_NN1 develops_VVZ a_AT0 combined_AJ0 Digital-Twin_NN1 and_CJC Machine-Learning_AJ0 framework_NN1 to_TO0 optimize_VVI ventilation_NN1 systems_NN2 by_PRP building_NN1 on_PRP rapidly_AV0 computable_AJ0 respiratory_AJ0 emission_NN1 models_NN2 developed_VVN in_PRP Zohdi_NP0 ._SENT This_DT0 framework_NN1 ascertains_VVZ the_AT0 placement_NN1 and_CJC flow_NN1 rates_NN2 of_PRF multiple_AJ0 mobile_AJ0 ventilation_NN1 units_NN2 ,_PUN in_PRP order_NN1 to_PRP optimally_AV0 sequester_NN1 particles_NN2 released_VVN from_PRP respiratory_AJ0 emissions_NN2 such_DT0 as_PRP coughs_NN2 ,_PUN sneezes_NN2 ,_PUN etc._AV0 There_EX0 have_VHB been_VBN dramatic_AJ0 advances_NN2 in_PRP technologies_NN2 associated_VVN with_PRP automation_NN1 across_PRP many_DT0 industries_NN2 ,_PUN which_DTQ have_VHB the_AT0 potential_NN1 to_TO0 drastically_AV0 improve_VVI system_NN1 efficiency_NN1 ,_PUN quality_NN1 and_CJC safety_NN1 ._SENT Some_DT0 approaches_NN2 are_VBB methodical_AJ0 and_CJC systematic_AJ0 ,_PUN while_CJS some_DT0 are_VBB ad-hoc_AJ0 and_CJC haphazard_AJ0 ._SENT In_PRP the_AT0 world_NN1 of_PRF systems_NN2 engineering_NN1 ,_PUN increasingly_AV0 sophisticated_AJ0 and_CJC integrated_AJ0 approaches_NN2 for_PRP digital_AJ0 systems_NN2 are_VBB appearing_VVG at_PRP a_AT0 rapid_AJ0 rate_NN1 ._SENT One_CRD key_AJ0 component_NN1 to_PRP advancements_NN2 in_PRP this_DT0 areas_NN2 are_VBB Digital-Twins_NN2 ,_PUN which_DTQ are_VBB digital_AJ0 replicas_NN2 of_PRF complex_AJ0 physical_AJ0 systems_NN2 that_CJT can_VM0 be_VBI safely_AV0 manipulated_VVN and_CJC optimized_VVN in_PRP a_AT0 virtual_AJ0 world_NN1 and_CJC deployed_VVN in_PRP the_AT0 physical_AJ0 world_NN1 afterwards_AV0 ,_PUN reducing_VVG costs_NN2 of_PRF experiments_NN2 and_CJC accelerating_AJ0 development_NN1 of_PRF new_AJ0 technologies_NN2 ._SENT Digital-Twins_NN2 blend_VVB AI_NN1 ,_PUN machine_NN1 learning_NN1 ,_PUN software_NN1 analytics_NN2 and_CJC data_NN0 to_TO0 create_VVI living_AJ0 digital_AJ0 computer_NN1 models_NN2 that_CJT can_VM0 update_VVI and_CJC change_VVI in_PRP tandem_NN1 with_PRP their_DPS physical_AJ0 counterparts-and_NN1 ultimately_AV0 control_VVB them_PNP in_PRP real_AJ0 time_NN1 ._SENT Updates_NN2 to_PRP the_AT0 Digital-Twin_NN1 are_VBB made_VVN continuously_AV0 in_PRP real-time_NN1 ,_PUN which_DTQ necessitates_VVZ technologies_NN2 like_PRP rapid_AJ0 wireless_NN1 communication_NN1 ,_PUN hyperspectral_AJ0 cameras_NN2 ,_PUN sensor_NN1 fusion_NN1 and_CJC fast_AJ0 simulations_NN2 of_PRF process_NN1 behavior_NN1 ._SENT Today_AV0 ,_PUN there_EX0 is_VBZ no_AT0 shortage_NN1 of_PRF general_AJ0 simulation_NN1 software_NN1 ;_PUN however_AV0 ,_PUN the_AT0 fundamental_AJ0 limitations_NN2 are_VBB ease-of-use_NN1 and_CJC integration_NN1 of_PRF models_NN2 with_PRP in-field_AJ0 data_NN0 and_CJC easy_AJ0 deployment_NN1 for_PRP researchers_NN2 ._SENT A_AT0 core_NN1 issue_NN1 across_PRP all_DT0 domains_NN2 is_VBZ the_AT0 ability_NN1 of_PRF a_AT0 system_NN1 to_TO0 adapt_VVI to_PRP rapid_AJ0 changes_NN2 in_PRP the_AT0 environment_NN1 and_CJC system_NN1 capabilities_NN2 by_PRP autonomously_AV0 modifying_VVG operation-with_NN1 humans_NN2 in_PRP the_AT0 loop_NN1 ._SENT By_PRP developing_VVG these_DT0 tools_NN2 for_PRP food_NN1 systems_NN2 researchers_NN2 ,_PUN we_PNP believe_VVB that_CJT we_PNP can_VM0 enhance_VVI the_AT0 ability_NN1 of_PRF industry_NN1 to_TO0 conduct_VVI research_NN1 that_CJT inevitably_AV0 involve_VVB Digital_AJ0 Twins_NN2 ,_PUN as_CJS well_AV0 as_CJS benefiting_VVG society_NN1 and_CJC industry_NN1 ._SENT 
The_AT0 presented_AJ0 work_NN1 also_AV0 involves_VVZ blending_VVG Machine-learning_NP0 with_PRP Digital_AJ0 Twins_NN2 ,_PUN whereby_AVQ simulations_NN2 iteratively_AV0 learn_VVB from_PRP their_DPS mistakes_NN2 and_CJC constantly_AV0 evolve_VVB to_TO0 improve_VVI and_CJC optimize_VVI the_AT0 model_NN1 ,_PUN safely_AV0 in_PRP a_AT0 virtual_AJ0 environment_NN1 ._SENT This_DT0 rapid_AJ0 simulation_NN1 should_VM0 be_VBI designed_VVN to_TO0 run_VVI rapidly_AV0 in_PRP tandem_NN1 with_PRP a_AT0 real_AJ0 system_NN1 ._SENT Accordingly_AV0 ,_PUN the_AT0 Digital-Twin_NP0 and_CJC Machine-Learning_NP0 in_PRP this_DT0 framework_NN1 combines_VVZ these_DT0 rapidly_AV0 computable_AJ0 models_NN2 with_PRP genomic_AJ0 Machine-Learning_NP0 methods_NN2 to_TO0 ascertain_VVI the_AT0 placement_NN1 and_CJC flow_NN1 rates_NN2 of_PRF multiple_AJ0 mobile_AJ0 ventilation_NN1 units_NN2 ,_PUN in_PRP order_NN1 to_PRP optimally_AV0 sequester_NN1 particles_NN2 released_VVN from_PRP respiratory_AJ0 emissions_NN2 such_DT0 as_PRP coughs_NN2 ,_PUN sneezes_NN2 ,_PUN etc._AV0 Specifically_AV0 :_PUN 
A_AT0 model_NN1 is_VBZ developed_VVN for_PRP the_AT0 propagation_NN1 of_PRF emitted_AJ0 particles_NN2 that_DT0 is_VBZ rapidly_AV0 computable_AJ0 ,_PUN 
A_AT0 qualitative_AJ0 analysis_NN1 of_PRF the_AT0 model_NN1 is_VBZ discussed_VVN ,_PUN 
A_AT0 numerical_AJ0 discretization_NN1 for_PRP the_AT0 flow_NN1 of_PRF the_AT0 distribution_NN1 of_PRF particles_NN2 is_VBZ constructed_VVN ,_PUN 
A_AT0 genomic-based_AJ0 Machine-Learning_AJ0 algorithm_NN1 to_TO0 optimize_VVI the_AT0 mobile_AJ0 ventilation_NN1 systems_NN2 is_VBZ developed_VVN and_CJC 
Numerical_AJ0 examples_NN2 are_VBB provided_VVN ._SENT 
Remark_NN1 1_CRD 
It_PNP is_VBZ now_AV0 widely_AV0 accepted_VVN that_CJT masks_NN2 are_VBB an_AT0 integral_AJ0 part_NN1 of_PRF controlling_VVG the_AT0 spread_NN1 of_PRF infectious_AJ0 diseases_NN2 ,_PUN such_DT0 as_PRP COVID19_NN1 ._SENT There_EX0 are_VBB three_CRD general_AJ0 categories_NN2 of_PRF face_NN1 masks_NN2 :_PUN (_PUL 1_CRD )_PUR Cloth_NN1 Masks_NN2 (_PUL for_PRP the_AT0 general_AJ0 public_NN1 )_PUR ,_PUN which_DTQ provides_VVZ some_DT0 protection_NN1 to_PRP the_AT0 wearer_NN1 ,_PUN but_CJC mainly_AV0 serves_VVZ to_TO0 stop_VVI the_AT0 spread_NN1 of_PRF viruses_NN2 (_PUL 2_CRD )_PUR Surgical_AJ0 Masks_NN2 (_PUL for_PRP healthcare_NN1 workers_NN2 and_CJC the_AT0 general_AJ0 public_NN1 )_PUR ,_PUN which_DTQ provides_VVZ partial_AJ0 protection_NN1 and_CJC (_PUL 3_CRD )_PUR N95_CRD Respirators_NN2 (_PUL primarily_AV0 for_PRP healthcare_NN1 workers_NN2 )_PUR ,_PUN which_DTQ provides_VVZ high_AJ0 level_NN1 of_PRF protection_NN1 and_CJC use_VVB charged_AJ0 fibers_NN2 (_PUL electrets_NN2 )_PUR to_TO0 attract_VVI particles_NN2 of_PRF all_DT0 sizes_NN2 ._SENT N95_CRD masks_NN2 are_VBB excellent_AJ0 at_PRP trapping_VVG very_AV0 small_AJ0 particles_NN2 (_PUL below_AV0 0.1_CRD micron_NN1 )_PUR ,_PUN since_CJS their_DPS motion_NN1 is_VBZ random_AJ0 (_PUL Brownian_AJ0 )_PUR ,_PUN due_AJ0 to_PRP collisions_NN2 with_PRP other_AJ0 particles_NN2 ,_PUN air_NN1 molecules_NN2 ,_PUN etc._AV0 ,_PUN which_DTQ will_VM0 force_VVI them_PNP to_TO0 collide_VVI with_PRP an_AT0 electrically_AV0 charged_VVN "_PUQ sticky_AJ0 "_PUQ fiber_NN1 ._SENT It_PNP is_VBZ also_AV0 excellent_AJ0 in_PRP trapping_VVG large_AJ0 particles_NN2 (_PUL above_AV0 0.3_CRD microns_NN2 )_PUR ,_PUN since_CJS their_DPS motion_NN1 is_VBZ effectively_AV0 linear_AJ0 across_PRP the_AT0 mask_NN1 (_PUL because_CJS of_PRF their_DPS inertia_NN1 )_PUR and_CJC will_VM0 collide_VVI with_PRP a_AT0 fiber_NN1 ._SENT It_PNP has_VHZ more_DT0 difficulty_NN1 trapping_VVG medium-sized_AJ0 particles_NN2 (_PUL 0.1_CRD microns-0.3_CRD microns_NN2 )_PUR ,_PUN which_DTQ travel_VVB with_PRP airflow_NN1 patterns_NN2 ._SENT N95_NP0 means_VVZ that_CJT it_PNP traps_VVZ at_PRP least_AV0 95_CRD %_NN0 of_PRF the_AT0 particles_NN2 ._SENT However_AV0 ,_PUN there_EX0 are_VBB problems_NN2 ,_PUN due_AJ0 to_TO0 mask_VVI ill-fitting_AJ0 ,_PUN re-use_VVB due_AJ0 to_PRP shortages_NN2 ,_PUN use_NN1 of_PRF alcohols_NN2 and_CJC solvents_NN2 for_PRP mask_NN1 cleaning_NN1 ,_PUN etc._AV0 ,_PUN which_DTQ may_VM0 damage_VVI the_AT0 mask_NN1 or_CJC neutralize_VVB the_AT0 fiber_NN1 charge_NN1 ._SENT Furthermore_AV0 ,_PUN the_AT0 proper_AJ0 donning_NN1 and_CJC doffing_VVG (_PUL removal_NN1 from_PRP face_NN1 )_PUR of_PRF a_AT0 mask_NN1 is_VBZ nontrivial_AJ0 ,_PUN due_AJ0 to_TO0 strap_VVI elongation_NN1 ,_PUN facial_AJ0 hair_NN1 ,_PUN etc._AV0 Therefore_AV0 ,_PUN one_PNI must_VM0 assume_VVI that_CJT some_DT0 particles_NN2 get_VVB through_AVP ,_PUN regardless_AV0 of_PRF the_AT0 mask_NN1 type_NN1 ._SENT Accordingly_AV0 ,_PUN in_PRP workplaces_NN2 ,_PUN some_DT0 type_NN1 ventilation_NN1 is_VBZ needed_VVN ,_PUN generally_AV0 involving_VVG HEPA_NN1 (_PUL High_AJ0 Efficiency_NN1 Particulate_NN1 Absorbing_AJ0 )_PUR grade_NN1 filters_NN2 ,_PUN which_DTQ remove_VVB 99.95_CRD %_NN0 of_PRF the_AT0 particles_NN2 equal_AJ0 to_PRP 0.3_CRD microns_NN2 in_PRP size_NN1 ,_PUN with_PRP efficiency_NN1 increasing_VVG for_PRP particles_NN2 larger_AJC or_CJC smaller_AJC than_CJS this_DT0 size_NN1 ._SENT Such_DT0 filters_NN2 were_VBD started_VVN by_PRP the_AT0 German_AJ0 military_NN1 in_PRP WWII_NN1 for_PRP gas_NN1 masks_NN2 ,_PUN whereby_AVQ increases_NN2 in_PRP mask_NN1 efficiency_NN1 were_VBD noted_VVN by_PRP simply_AV0 adding_VVG a_AT0 piece_NN1 of_PRF paper_NN1 (_PUL cellulose_NN1 )_PUR to_PRP the_AT0 mask_NN1 ._SENT Such_DT0 systems_NN2 started_VVD commercially_AV0 in_PRP the_AT0 1950s_CRD for_PRP decontamination_NN1 control_NN1 in_PRP hospitals_NN2 ,_PUN nuclear_AJ0 facilities_NN2 ,_PUN homes_NN2 vehicles_NN2 ,_PUN etc._AV0 They_PNP are_VBB comprised_VVN of_PRF randomly_AV0 arranged_VVN fiberglass_AJ0 fibers_NN2 between_PRP 0.5_CRD and_CJC 2.0_CRD microns_NN2 ._SENT As_CJS with_PRP N95_CRD masks_NN2 ,_PUN they_PNP are_VBB designed_VVN to_TO0 capture_VVI a_AT0 range_NN1 of_PRF particles_NN2 by_PRP similar_AJ0 mechanisms_NN2 ._SENT Another_DT0 common_AJ0 term_NN1 is_VBZ '_PUQ MERV_NN1 '_POS Minimum_AJ0 Efficiency_NN1 Reporting_NN1 Value_NN1 (_PUL 1987_CRD ASHRAE_NP0 )_PUR ,_PUN which_DTQ is_VBZ designed_VVN to_TO0 report_VVI the_AT0 worst_AJS case_NN1 performance_NN1 of_PRF a_AT0 filter_NN1 ,_PUN ranging_VVG 0.3_CRD –_PUN 10_CRD microns_NN2 ,_PUN with_PRP a_AT0 scale_NN1 rating_NN1 of_PRF from_PRP 1_CRD –_PUN 16_CRD (_PUL highest_AJS at_PRP 95_CRD %_NN0 )_PUR ._SENT It_PNP is_VBZ essential_AJ0 ,_PUN that_DT0 ventilation_NN1 systems_NN2 be_VBI given_VVN much_AV0 more_DT0 attention_NN1 than_CJS ever_AV0 before_AV0 ._SENT 
Remark_NN1 2_CRD 
We_PNP remark_VVB that_CJT some_DT0 systems_NN2 also_AV0 employ_VVB UV-c_AJ0 light_NN1 for_PRP further_AJC decontamination_NN1 ,_PUN in_PRP combination_NN1 with_PRP the_AT0 ventilation_NN1 system_NN1 ._SENT A_AT0 dosage_NN1 of_PRF 1_CRD 𝐽_NN1 /_PUN 𝑐𝑚2_NN1 is_VBZ considered_VVN adequate_AJ0 to_TO0 destroy_VVI COVID19_NN1 ._SENT Many_DT0 commercial_AJ0 mobile_AJ0 UV-c_NN1 light_NN1 systems_NN2 now_AV0 exist_VVB ._SENT UV-c_NN1 light_NN1 254_CRD –_PUN 265_CRD nm_NN1 is_VBZ considered_VVN optimal_AJ0 ._SENT Wavelengths_NN2 above_PRP this_DT0 range_NN1 are_VBB not_XX0 effective_AJ0 ,_PUN while_CJS wavelengths_NN2 below_AV0 produce_VVB ozone_NN1 ,_PUN which_DTQ is_VBZ dangerous_AJ0 (_PUL Zohdi_NP0 )_PUR ._SENT Heating_NN1 contaminated_VVN at_PRP 70_CRD °_NN0 C_ZZ0 for_PRP 60_CRD min_NN0 is_VBZ effective_AJ0 ,_PUN but_CJC impractical_AJ0 in_PRP a_AT0 large_AJ0 workplace_NN1 setting_VVG with_PRP sensitive_AJ0 equipment_NN1 and_CJC people_NN0 ._SENT For_PRP example_NN1 ,_PUN decontamination_NN1 based_VVN on_PRP UV_AJ0 technology_NN1 has_VHZ become_VVN ubiquitous_AJ0 ,_PUN with_PRP many_DT0 variants_NN2 now_AV0 being_VBG proposed_VVN ._SENT UV_AJ0 light_NN1 varies_VVZ in_PRP wavelength_NN1 from_PRP 10_CRD to_PRP 400_CRD nm_NN2 ,_PUN thus_AV0 making_VVG it_PNP shorter_AJC that_DT0 visible_AJ0 wavelengths_NN2 and_CJC larger_AJC than_CJS X-rays_NN2 ._SENT Short_AJ0 wave_NN1 UV_AJ0 light_NN1 (_PUL UV-c_NP0 )_PUR can_VM0 damage_VVI DNA_NN1 and_CJC sterilize_VVB surfaces_NN2 making_VVG in_PRP useful_AJ0 in_PRP the_AT0 medical_AJ0 industry_NN1 ._SENT This_DT0 was_VBD first_ORD noted_VVN in_PRP 1878_CRD (_PUL Downes_NP0 and_CJC Blunt_NP0 )_PUR when_CJS the_AT0 effect_NN1 of_PRF short-wavelength_AJ0 light_NN1 killing_NN1 bacteria_NN2 was_VBD discovered_VVN ._SENT By_PRP 1903_CRD it_PNP was_VBD known_VVN the_AT0 most_AV0 effective_AJ0 wavelengths_NN2 were_VBD around_AV0 250_CRD nm_NN2 (_PUL UV-c_NP0 )_PUR ,_PUN for_PRP which_DTQ Niels_NP0 Finsen_NP0 won_VVD a_AT0 Nobel_NP0 Prize_NN1 (_PUL for_PRP skin-based_AJ0 tuberculosis_NN1 eradication_NN1 using_VVG UV_AJ0 light_NN1 )_PUR ._SENT Contaminants_NN2 in_PRP the_AT0 indoor_AJ0 environment_NN1 are_VBB almost_AV0 entirely_AV0 organic_AJ0 carbon-based_AJ0 compounds_NN2 ,_PUN which_DTQ break_VVB down_AVP when_CJS exposed_VVN to_PRP high-intensity_AJ0 UV_AJ0 at_PRP 240_CRD –_PUN 280_CRD nm_NN2 ._SENT Despite_PRP the_AT0 attractiveness_NN1 of_PRF using_VVG UV-c_AJ0 light_NN1 ,_PUN the_AT0 literature_NN1 has_VHZ shown_VVN that_CJT it_PNP is_VBZ difficult_AJ0 to_TO0 ensure_VVI that_CJT all_DT0 surfaces_NN2 are_VBB completely_AV0 decontaminated_VVN due_AJ0 to_PRP shadowing_VVG effects_NN2 ._SENT Thus_AV0 ,_PUN the_AT0 use_NN1 of_PRF ultraviolet_AJ0 germicidal_AJ0 irradiation_NN1 (_PUL UVGI_NP0 )_PUR is_VBZ effective_AJ0 only_AV0 as_CJS a_AT0 component_NN1 in_PRP a_AT0 multistage_NN1 process-it_NN1 alone_AV0 carries_VVZ the_AT0 risk_NN1 of_PRF residual_AJ0 contamination_NN1 ._SENT Thus_AV0 ,_PUN purely_AV0 UV-c_AJ0 protocols_NN2 should_VM0 be_VBI adopted_VVN if_CJS there_EX0 is_VBZ no_AT0 other_AJ0 choice_NN1 ._SENT However_AV0 ,_PUN they_PNP can_VM0 be_VBI an_AT0 integral_AJ0 part_NN1 of_PRF a_AT0 multistage_NN1 process_NN1 involving_VVG a_AT0 combination_NN1 of_PRF (_PUL a_AT0 )_PUR gas_NN1 vapors_NN2 and_CJC (_PUL b_ZZ0 )_PUR heat_NN1 and_CJC humidity_NN1 ._SENT The_AT0 topic_NN1 of_PRF decontamination_NN1 technologies_NN2 is_VBZ of_PRF paramount_AJ0 interest_NN1 (_PUL see_VVB references_NN2 Anderson_NP0 et_NP0 al._NP0 ,_PUN Battelle_NP0 ,_PUN Boyce_NP0 et_NP0 ._SENT al._NP0 ,_PUN Card_NN1 et_NP0 al._NP0 ,_PUN Heimbuch_NP0 and_CJC Harish_NP0 ,_PUN Heimbuch_NP0 et_NP0 al._NP0 ,_PUN Ito_NP0 and_CJC Ito_NP0 ,_PUN Lin_NP0 et_NP0 al._NP0 ,_PUN Kanemitsu_NP0 ,_PUN Lindsley_NP0 et_NP0 al._NP0 ,_PUN Lore_NP0 et_NP0 al._NP0 ,_PUN Marra_NN1 et_NP0 al._NP0 ,_PUN Mills_NP0 et_NP0 al._NP0 and_CJC Nerandzic_NP0 et_NP0 al._NP0 )_PUR ,_PUN and_CJC the_AT0 corresponding_AJ0 simulation_NN1 of_PRF such_DT0 processes_NN2 has_VHZ recently_AV0 been_VBN undertaken_VVN in_PRP Zohdi_NP0 and_CJC is_VBZ a_AT0 topic_NN1 of_PRF ongoing_AJ0 research_NN1 ._SENT 
Reduced_AJ0 Order_NN1 Particle-Fluid_NN1 Interaction_NN1 Model_NN1 
In_PRP its_DPS most_DT0 basic_AJ0 form_NN1 ,_PUN a_AT0 cough_NN1 can_VM0 be_VBI considered_VVN as_PRP a_AT0 high-velocity_AJ0 release_NN1 of_PRF a_AT0 random_AJ0 distribution_NN1 of_PRF particles_NN2 of_PRF various_AJ0 sizes_NN2 ,_PUN into_PRP an_AT0 ambient_AJ0 atmosphere_NN1 (_PUL Fig._NN1 1_CRD )_PUR ._SENT We_PNP refer_VVB the_AT0 reader_NN1 to_PRP Wei_NP0 and_CJC Li_NP0 ,_PUN Duguid_NP0 ,_PUN Papineni_NP0 and_CJC Rosenthal_NP0 ,_PUN Wei_NP0 and_CJC Li_NP0 ,_PUN Zhu_NP0 et_NP0 al._NP0 ,_PUN Chao_NP0 et_NP0 al._NP0 ,_PUN Morawska_NP0 et_NP0 al._NP0 ,_PUN VanSciver_NP0 et_NP0 al._NP0 ,_PUN Kwon_NP0 et_NP0 al._NP0 ,_PUN Tang_NP0 et_NP0 al._NP0 ,_PUN Xie_NP0 et_NP0 al._NP0 ,_PUN Gupta_NP0 et_NP0 al._NP0 ,_PUN Wan_NP0 et_NP0 al._NP0 ,_PUN Villafruela_NP0 et_NP0 al._NP0 ,_PUN Nielson_NP0 Zhang_NP0 and_CJC Li_NP0 ,_PUN Lindsley_NP0 et_NP0 ._SENT al._NP0 and_CJC Burridge_NP0 et_NP0 al._NN1 for_PRP extensive_AJ0 reviews_NN2 of_PRF coughs_NN2 and_CJC other_AJ0 respiratory_AJ0 emissions_NN2 ._SENT We_PNP will_VM0 consider_VVI the_AT0 model_NN1 problem_NN1 in_PRP Fig._NN1 1._CRD 
Assumptions_NN2 
Following_AJ0 formulations_NN2 for_PRP physically_AV0 similar_AJ0 problems_NN2 associated_VVN with_PRP particulate_NN1 dynamics_NN0 from_PRP the_AT0 fields_NN2 of_PRF blasts_NN2 ,_PUN explosions_NN2 and_CJC fire_NN1 embers_NN2 (_PUL Zohdi_NP0 )_PUR ,_PUN we_PNP make_VVB the_AT0 following_AJ0 assumptions_NN2 (_PUL Zohdi_NP0 )_PUR :_PUN 
We_PNP assume_VVB the_AT0 same_DT0 initial_AJ0 velocity_NN1 magnitude_NN1 for_PRP all_DT0 particles_NN2 under_PRP consideration_NN1 ,_PUN with_PRP a_AT0 random_AJ0 distribution_NN1 of_PRF outward_AJ0 directions_NN2 away_AV0 from_PRP the_AT0 source_NN1 of_PRF the_AT0 cough_NN1 ._SENT This_DT0 implies_VVZ that_CJT a_AT0 particle_NN1 non-interaction_NN1 approximation_NN1 is_VBZ appropriate_AJ0 ._SENT Thus_AV0 ,_PUN the_AT0 inter-particle_NN1 collisions_NN2 are_VBB negligible_AJ0 ._SENT This_DT0 has_VHZ been_VBN repeatedly_AV0 verified_VVN by_PRP "_PUQ brute-force_AJ0 "_PUQ collision_NN1 calculations_NN2 using_VVG formulations_NN2 found_VVN in_PRP Zohdi_NP0 ._SENT 
We_PNP assume_VVB that_CJT the_AT0 particles_NN2 are_VBB spherical_AJ0 with_PRP a_AT0 random_AJ0 distribution_NN1 of_PRF radii_NN2 𝑅𝑖_NN1 ,_PUN 𝑖_NP0 =_NP0 1_CRD ,_PUN 2_CRD ,_PUN 3_CRD ..._PUN 𝑃𝑛_NP0 ,_PUN where_AVQ 𝑃𝑛_NP0 is_VBZ the_AT0 total_AJ0 number_NN1 of_PRF particles_NN2 ._SENT The_AT0 masses_NN2 are_VBB given_VVN by_PRP 𝑚𝑖_NP0 =_NP0 𝜌𝑖43𝜋𝑅3𝑖_NP0 ,_PUN where_AVQ 𝜌𝑖_NP0 is_VBZ the_AT0 density_NN1 of_PRF the_AT0 particles_NN2 ._SENT 
We_PNP assume_VVB that_CJT the_AT0 cough_NN1 particles_NN2 are_VBB quite_AV0 small_AJ0 and_CJC that_CJT the_AT0 amount_NN1 of_PRF rotation_NN1 ,_PUN if_CJS any_DT0 ,_PUN contributes_VVZ negligibly_AV0 to_PRP the_AT0 overall_AJ0 trajectory_NN1 of_PRF the_AT0 particles_NN2 ._SENT The_AT0 equation_NN1 of_PRF motion_NN1 for_PRP the_AT0 𝑖𝑡ℎ_AJ0 particle_NN1 in_PRP the_AT0 system_NN1 is_VBZ equation_NN1 (_PUL 2.1_CRD )_PUR with_PRP initial_AJ0 velocity_NN1 𝑣𝑣𝑖_NN1 (_PUL 0_CRD )_PUR and_CJC initial_AJ0 position_NN1 𝑟𝑟𝑖_NN1 (_PUL 0_CRD )_PUR ._SENT The_AT0 gravitational_AJ0 force_NN1 is_VBZ ΨΨ𝑔𝑟𝑎𝑣𝑖_NP0 =_NP0 𝑚𝑖𝑔𝑔_NP0 ,_PUN where_AVQ 𝑔𝑔_NP0 =_NP0 (_PUL 𝑔𝑥_NP0 ,_PUN 𝑔𝑦_NP0 ,_PUN 𝑔𝑧_NP0 )_PUR =_NP0 (_PUL 0_CRD ,_PUN 0_CRD ,_PUN −9.81_CRD )_PUR 𝑚_NP0 /_PUN 𝑠2_CRD ._SENT 
For_PRP the_AT0 drag_NN1 ,_PUN we_PNP will_VM0 employ_VVI a_AT0 general_AJ0 phenomenological_AJ0 model_NN1 equation_NN1 (_PUL 2.2_CRD )_PUR where_CJS 𝐶𝐷_NN1 is_VBZ the_AT0 drag_NN1 coefficient_NN1 ,_PUN 𝐴𝑖_NP0 is_VBZ the_AT0 reference_NN1 area_NN1 ,_PUN which_DTQ for_PRP a_AT0 sphere_NN1 is_VBZ 𝐴𝑖_NP0 =_NP0 𝜋𝑅2𝑖_NP0 ,_PUN 𝜌𝑎_NP0 is_VBZ the_AT0 density_NN1 of_PRF the_AT0 ambient_AJ0 fluid_NN1 environment_NN1 and_CJC 𝑣𝑣𝑓_NN1 is_VBZ the_AT0 velocity_NN1 of_PRF the_AT0 surrounding_AJ0 medium_NN1 which_DTQ ,_PUN in_PRP the_AT0 case_NN1 of_PRF interest_NN1 ,_PUN is_VBZ air_NN1 ._SENT We_PNP will_VM0 assume_VVI that_CJT the_AT0 velocity_NN1 of_PRF the_AT0 surrounding_AJ0 fluid_NN1 medium_NN1 (_PUL 𝑣𝑣𝑓_NN1 )_PUR is_VBZ given_VVN ,_PUN implicitly_AV0 assuming_VVG that_CJT the_AT0 dynamics_NN0 of_PRF the_AT0 surrounding_AJ0 medium_NN1 are_VBB unaffected_AJ0 by_PRP the_AT0 particles_NN2 ._SENT We_PNP will_VM0 discuss_VVI these_DT0 assumptions_NN2 further_AV0 ,_PUN later_AV0 in_PRP the_AT0 work_NN1 ._SENT 
Qualitative_AJ0 Behavior_NN1 of_PRF the_AT0 Simplified_AJ0 Model_NN1 
A_AT0 simplified_AJ0 Stokesian_NP0 model_NN1 ,_PUN which_DTQ can_VM0 be_VBI solved_VVN analytically_AV0 provides_VVZ some_DT0 physical_AJ0 insight_NN1 ,_PUN is_VBZ discussed_VVN in_PRP Zohdi_NP0 ._SENT A_AT0 summary_NN1 of_PRF that_DT0 analysis_NN1 is_VBZ as_CJS follows_VVZ ._SENT For_PRP a_AT0 (_PUL low_AJ0 Reynolds_NP0 number_NN1 )_PUR Stokesian_NP0 model_NN1 ,_PUN the_AT0 differential_AJ0 equation_NN1 for_PRP each_DT0 particle_NN1 is_VBZ equation_NN1 (_PUL 2.3_CRD )_PUR where_CJS 𝑐𝑖_NP0 =_NP0 𝜇𝑓6𝜋𝑅𝑖_NP0 ,_PUN where_AVQ 𝜇𝑓_NN1 is_VBZ the_AT0 viscosity_NN1 of_PRF the_AT0 surrounding_AJ0 fluid_NN1 (_PUL air_NN1 )_PUR and_CJC the_AT0 local_AJ0 Reynolds_NP0 number_NN1 for_PRP a_AT0 particle_NN1 is_VBZ 𝑅𝑒_NP0 =_NP0 def2𝑅𝑖𝜌𝑎_NP0 |_NP0 |_NP0 𝑣𝑣𝑓−𝑣𝑣𝑖_NP0 |_NP0 |_NP0 𝜇𝑓_NN1 and_CJC 𝜇𝑓_NN1 is_VBZ the_AT0 fluid_AJ0 viscosity_NN1 ._SENT The_AT0 trends_NN2 are_VBB equation_NN1 equation_NN1 ._SENT 
In_PRP summary_NN1 
Large_AJ0 particles_NN2 travel_VVB far_AV0 and_CJC settle_VVB quickly_AV0 and_CJC 
Small_AJ0 particles_NN2 do_VDB not_XX0 travel_VVI far_AV0 and_CJC settle_VVI slowly_AV0 ._SENT 
Remark_NN1 3_CRD 
The_AT0 ratio_NN1 of_PRF the_AT0 Stokesian_NP0 drag_NN1 force_NN1 to_PRP gravity_NN1 is_VBZ equation_NN1 ,_PUN which_DTQ indicates_VVZ that_CJT for_PRP very_AV0 small_AJ0 particles_NN2 ,_PUN drag_NN1 will_VM0 dominate_VVI the_AT0 settling_AJ0 process_NN1 and_CJC for_PRP larger_AJC particles_NN2 ,_PUN gravity_NN1 will_VM0 dominate_VVI ._SENT 
Simulation_NN1 of_PRF the_AT0 Model_NN1 :_PUN Cough_NN1 Particle_NN1 Generation_NN1 and_CJC Propagation_NN1 
For_PRP the_AT0 general_AJ0 model_NN1 ,_PUN in_PRP order_NN1 to_PRP more_DT0 accurately_AV0 model_VVB the_AT0 effects_NN2 of_PRF drag_NN1 ,_PUN one_PNI can_VM0 take_VVI into_PRP account_NN1 that_CJT the_AT0 empirical_AJ0 drag_NN1 coefficient_NN1 varies_VVZ with_PRP Reynolds_NP0 number_NN1 ._SENT 
For_PRP example_NN1 ,_PUN consider_VVB the_AT0 following_AJ0 piecewise_AJ0 relation_NN1 (_PUL Chow_NP0 )_PUR :_PUN equation_NN1 ,_PUN equation_NN1 ,_PUN equation_NN1 ,_PUN equation_NN1 and_CJC equation_NN1 ,_PUN where_AVQ ,_PUN as_CJS in_PRP the_AT0 previous_AJ0 section_NN1 ,_PUN the_AT0 local_AJ0 Reynolds_NP0 number_NN1 for_PRP a_AT0 particle_NN1 is_VBZ 𝑅𝑒_NP0 =_NP0 def2𝑅𝑖𝜌𝑎_NP0 |_NP0 |_NP0 𝑣𝑣𝑓−𝑣𝑣𝑖_NP0 |_NP0 |_NP0 𝜇𝑓_NN1 and_CJC 𝜇𝑓_NN1 is_VBZ the_AT0 fluid_NN1 replaced-dns_VVZ 1We_AJ0 note_NN1 that_CJT in_PRP the_AT0 zero_CRD Reynolds_NP0 number_NN1 limit_NN1 ,_PUN the_AT0 drag_NN1 is_VBZ Stokesian_NP0 ._SENT In_PRP order_NN1 to_TO0 solve_VVI the_AT0 governing_AJ0 equation_NN1 ,_PUN equation_NN1 (_PUL 3.1_CRD )_PUR ._SENT 
