Advances in Multiphase Flow and Heat Transfer

Volume: 1

Marangoni Motion of Multiphase Compound Drops

Author(s): O. M. Lavrenteva and A. Nir

Pp: 158-212 (55)

DOI: 10.2174/978160805080210901010158

* (Excluding Mailing and Handling)

Abstract

Compound drops are comprised of two of more immiscible phases. They occur in many natural and technological processes and environments, e.g. the atmosphere, liquid membranes and liquid bi-layers, direct contact heat exchange and phase separation processes. Compound liquid-liquid drop can model a living eukaryotic cell. Two-phase compound drops may consist of two touching, partially or completely engulfed parts, or have more complex geometry. Most processes involving multiphase drops are accompanied by intensive heat and mass transfer and, thus, a significant influence of Marangoni flow is anticipated, i.e. fluid motion induced variation of surface tension due to surfactant or temperature gradient along the interface. In the case of completely engulfed drop, Marangoni effect induces a relative motion of the inner particle towards the center of the outer one or in the opposite direction and, thus, stabilizes or destabilizes the liquid shell. In this chapter we overview the theoretical advances concerning the motion of multiphase compound drops of various types induced by externally imposed temperature and concentrations gradient and spontaneous Marangoni motion of such systems due to heat and mass transfer between the phases including the results of our ongoing research. Most of the works on the subject are devoted to quasi-stationary Stokes flow and non-deformable spherical interfaces corresponding to the case of small Reynolds and capillary numbers. Solutions of the Stokes equations are obtained making use of special coordinate systems (bi-spherical, toroidal, or tangent spheres), depending on the compound drop type.

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      • 13. app/Models/UserAccess/UserAccess.php:1266
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      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59772390 and j.to_ip >=59772390 )) and ((j.from_date <= 1739834840 and j.to_date >= 1739834840 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 735) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59772390 and j.to_ip >=59772390 )) and ((j.from_date <= 1739834840 and j.to_date >= 1739834840 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 735) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59772390 and j.to_ip >=59772390 )) and ((j.from_date <= 1739834840 and j.to_date >= 1739834840 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 735)
      720μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 842 and `b`.`banner_from_date` <= 1739834840 and `b`.`banner_to_date` >= 1739834840 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.51msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 842
      • 3: 1739834840
      • 4: 1739834840
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='160d810a7830d816d0d59c55a7bf8efe'
      310μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Keywords
    1Keywords.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        UKM0OC8tswa1dogVMTDexbTMwN801FwCGwQfy7Cx
        uc_cart_id
        160d810a7830d816d0d59c55a7bf8efe
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/735" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/735
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
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        request_cookies
        0 of 0
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        response_headers
        0 of 0
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-17 23:27:20GET/chapter/735112193