68
CONVECTIVE GAS.FLO TSIN WETLAND PLANT AERATION
'PETERM. BECKETTand
VILLIAM ARMSTRONG,
JEANARMSTRONG,
S A M U E LH . F , \ 7 J. U S T I N
Depafiments oJ Applied Biologl and 'Applied Matbematics, Uniuers/ty ol' Hull,
U.K., HU6 7RX
Al)sttact
qas flows pertinenr Io pi?nt aeration
va.ious repons olconvectivc lhrougbJtloa ^nd nonlhrcuqblau
m2thematical
models a.e defived to help assess
werlan<l
are
.eviewed,
and
two
simple
in
condirions
(o
dist2nce
diffusion
fhizomes end .oot ae.ation. APart
of
conveclion
and
long
rhe llkely conr.ibutions
f'om venturiindu.ed |Lows (s€c Appendix), bo!h convective types 2re diffusion d€pendcnt, ?nd the
pressurisxtion undedying throughflow convectioos can be explained in terms of blz2l.1it! iru1uce.l
dilfusion,(ofrcnthe.mdly
enhanced),and t e/aat transpi ration. into rhe emefgen t shools ZrrozS,
in
w2rer
lilies
and in the commont.ed Pbragftites ausl/ars(Cav )Trin, ex Steud ,
convecrjons
/]4ou
can considerably improv€ aeration: dnectly, by the rale of convection rhrough rhe .hizomcs. anci
indi.ecrly by increaseddiflusion ofoxyg€n wilhin thc roots and 1o the rhizosph€re Oo rheother hand,
ir is concluded (hat ro, ,r/aughJlotu convecions. caused by the solubilisation 2nd remo val of respire
rory carbon dioxide, c2n never play mor€ than ? minor role in the 2erarion of pa.tiallv subme.ged
shoors ancl of roots The mxthematical modelling shows ttral aerated path lenglh wilhin an orgin i5
always less than the sum of the l€ngths which wouid be aerated by diftusion and convection 2ctin!!
independenily. The con nlburioa of thlouSbllou convection depends upon (he flow velocity 2nd can
bc much less lhan diffuslon ar low velocities and much greal€r at hiSh velocili€s. At equjlib.iun. the
conr.ibution of ,or,-rrlauAbfloa co vection frcm th€ 2tmosphere will nevcr cxce€d one fifth of tha(
ol diifusion and may b€ v€.y much less; also the combined effecr of diffusion 2nd this non th.ough
now convectioo is unlikely ro be more than I 06 times rhar of diffusion alone
l. Introduction
Until quite recentlyit had beengeneraliyassumedthat the only significantven
rilaring mechanismin wetland plants wasthe reciprocating g s-phasedifJusion of
oxygeo and carbondioxide throughthe exceptionallywell-developed,intercon
(lacunal)and non aerenchymatous
intercellularco.tical
nectiogaerenchymatous
gasspacesof shoot and root. Bulk-flowsof gasw€re not unknown e.g , the in
rush of air into mangroveroot systemsexposedon the ebb tide (Scholandere, al.
1955), but the notion that conoection mighr often play a significant role in rhe
're'discovery'of p.essurised
?erationprocesshas now emerged.Firstcame the
'rvinds'in waterlilies(Dacey1979,I980, l98l 1987;Daceyand Klug I979,l9a2a;
,
Schroder et a/. 1986; Grosseand Mevi Schutz 1987; Mevi-Schurzand Gtosse
19UBa,b),
air-flowsin deep water rice (Raskin
then, reportsofmass-(convective-)
Kende
1985).
Latterly,
and
1983,
convective gas-flows in Pbragmites australE
(threetypes;Armstrongand Armstrong1987,l99Oa, 1990b,1990c;Brix 1988),
ar].dinCarexgracilis (Koic lovaet al. 1988)have been reported. Elsewhere,pressure changeswhich might be accompani€dby som€ convective flow have been
found in the submerged "quatic Egeria elegans (Sotrel and Drumgoole 1987;
Sorrel 1989) and in subm€rgedrice seedlings(vaters e, a/. 1989).A potential for
Ptant tik under oryeen depriuation,pp. 283-302
edatedbt M.8. Jackson,D-D Daries and H Lambers
O1991 SPBAcademicPubttshi/18bx, Tbe Ha8ue, The Netbe aflds
2a4
W. Attnstrong et al.
convecrivegas-flowhasbeen noted in '4l/l?/s(Grosseand Schroder1984, 1985)
and, indeed,a potentialfor some convective82sflow probablyexistsin all submerged foot systems,(Curranet al 1q86,Koncalovae/ al I qBB;Becket(el a/.
l98B).
Tl-]isarticlesetsout to review our knowledgeof thesegasflows and to make
of the relativeimportanceof conuectionsand dillusion in the aera
assessments
Somenew informationon convectiveflows is presented.
tion of wetlandspecies.
2. Types of convectiveflow
Isothermalbulk flou of g2scs,technicallya canltectlan,and somctimescalled
transplratlan refetsto gasesbehavingas2 continuumfluid driven alongby x pres'
sure gradient,(Masonand Evans1969).Bulk gas-flowsin plantscan be broadly
groupecl as tbrougbflou o( non tbrougb|Tou conuections(Beckett e/ al 19aa),
but, paradoxically,apa.tfrom venturi inducedfloq/s(seeAppendix),both tyPes
we have r€
of convection are probably initixted by diffusiontype Processes.
frained here from Ih€ usc of the term mlss'flou to describethesemovements,
since diffusion in bin2ry systemscan itselfsometimesresult in a unidirectionzl
transferof massof one con'tponentof a gasmixture without a net volumc flow.
Tbt oughllou conueclrorsc2n be causedby a pressurisationdue ro a Knudsen
difJusion or lransitional Knudsen-dilfusro, of gasesfrom the envi.onmcnt into
the emergentshoot/rootsystem.Th€ gasesv/hich haveenteredthe plant by such
partsat a relativeiyconstantvek>
diffusionarethen convectedthroughsubmerged
city becausea veotingto the atmospheteoccu15at someother point. ln thosespe
ciesin which i t hasbeendiscovered, the wateriiliesand P, ragrnitesaustralis, rl'\e
indeedand ofien
potentialofthrougblau convectionis very apPreciable
xe12ring
involved in
and
the
causai
factors
much llreaterthanthat of diffusionalone.This,
rhc iniriation of ,rroughfou's xe discrssedlzter. l:'reemoleculal Knu.lsen d.i.IJu'
sian tlescribesgas mouementstbrougb tubes (or porous lnedia) ubere pressure
moleculesare so infrequent compared uitb colli
is so lou that collisionsbeLtueen
sions uitb tbe u.1llsoftbe tube, tbat tbe! can bedisl.egar.led.As uitb normal dilfu
sion, net merements oI a speciesarc determined b! concentration graldients. At
dtnospberic pressuretbe Knudsen regitueis realisedonbt uben tube/pore diame'
ters are uerJ)small (motecutaf mean free patb tength, I { 0.I pm; Loeb 1931),
and Knudsen dilfusion c.)elficientsare numet'icallysmaller tban thoseof normal
.tiffusion in whicb molecule molecule collisions dominate, (leuning 1983).
Non tbrougbJlou canuections?te gener2llycheracerisedby a longitudinal gra
dient of velocity through the plant. Suchconvectionscan be initizted by some
degreeof removalof, ratherthan a fully reciprocalexchangeof, respiratoryoxy
gen aod carbondioxidesomewherein the system(Raskin2nd Kende 1983,1985;
Curran e/ a/. 1986;Koncalov^et al. 1988;Brix 1988;Beckettel al. l9AA), by
(Raskinand Kende 1985),or
a diffusive input of oxygen from photosynthesis
Gransitorily)by Kzrdse, diffusionsinto the shoots.Becauseof th€ velocity gradient, the aeratingpotenti^l of non-tbrougblTou convectiots, although significant
at times, will, in darkness,generally be lessthan th^t of tbroughfloa types; it will
also usuallybe lessimportant than normallong'distaocediffusive transport.tn
fully submergedplantstheremay alsobe short-termpulsedconvectionseffected
Conuectiue gas-Jlous in tuetland plant aeration
285
by variarionsin light flux (Sorreland l)rumgoole 1987;Sorrel 1989),or by the
surface tension effects during the growth aod escapeof oxygen-enriched gasbubbles from leaf gas films (waters et al. 1989). Such convections are, however,
probably of litde signifancein plant aeration.
isothermalin
The convectivegas-flowsdiscussedhere are probablyessentially
therm2l
components.
may
have
supplementary
Convecthey
naru.e,although
tions due to diurnal thermalexpansionsor contractionsare not 2ddressed.
J. Effectivenessof throughflow ^nd non-throughflow convections:
a mathematicalanalysis
wherher convectionis principallyof t tbrougbflotttot non tbrougbflow type, it
will usu2llybe accompaniedby some deg.eeof superimposedlongitudinaldiffusion inducedby respiration.Indeed,the effectsof througbJlouconvectionmight
cori ectivecomponentaswell ?sby a parallel
be modifiedby a ,o n-tbtougbJTou
diffusion.
ln order to appreciatethe r€lalionbetweenconvectionand diffusion,2nd the
significanceof the two types of convection it is necessaryaLsoto considerthe
influenceof respirationon the flows.
3. 1. Tbrough|lou conuection
ofpressuredeficits,and tra..sportbytbrougb'
Convectionsariseasa consequence
js
fol convection stroogly dependent on the viscosity coefficient.For non
turbulent(laminar)flow, the rateof the convectionis gove.nedby the Poisseuille
equationfor flow through paralleltub€sor porous
soiurioo!o the Navier-Stokes
media:
(nra2\a2oAP
Volumeflux : -----li
p
,
(r)
wh€re n is the number of pipes,a is the individualpipe radius,AP is the pressure
gradienr,p rhe densirvand p the viscosityAssumingth2t we havea thlougblloa convection and uoiform respiration alonla
a channelwhich is open at both ends,the concentrationof oxygen will dec.ease
in the directionof motion and there will be a consequentoxygen concentration
gradienrwirhin the moving nuid; this will also createa diffusionalong lhe pathway. Moreover,becauseof the high solubility of 9O2 there may be a volumetric
lossofgas from rhechannelwhich would createa furtherpressuredeficitand l€ad
to an enh2nced flow rate. Convection may be defined as/rrougbflou conoection
when this addition is very smallcompared with the basicPoiss€uilleflow.
V\vecan quantify rhe effecrsofdiffusion a^dthrougbfloa convection asfollows.
Firstly, consider a ,b rougbflou cor,,rectionfor which we assumea constant veloc
ity U parallelto the axisof a channelalong which th€re is uniform respiralionQ.
\vithout diffusionthe oxygenconcentrationwill be depl€teduniformly alongthe
pathway and the length, I, of the channel which can be aeratedis given by
? : u co/Q,
(2)
2a6
W. Arrnstrong et al.
where Co is the oxygen concentrationat the inflow secrion(x = O).
In order ro seethe effectofdiffusion, due the creationof the concentrationgra
dient in the x,direction,it is uecessaryto solve rhe combined convecrion/diffu
sion equationwhich, for steadystate(1.e.,rime independent)flow, is
dc
d2c
ut=oo":
(3)
a
In thiscaselis found by solvingrhc equarionfor C(x)subjecrro rhe boundarycondirions
C = c o a t x= 0 p l u C
s = oandff = or,* = r.
'
(1)
Herethe rhreeboundaryconditionsare necessarybecausealthoughrhe equation
is only ofsecond order we dn nor know aprtoii thc vatueof t The generxlsolu
lion of (3) is
c(x)=a+0"-n(*-) 3-
(t)
\ " /
andsubjecrro (4) rhisyieldsrhe parricular
solurion
." -)
, n{ ' i
' I $f' #
\ ' , 1_1 0
'
. r x )= . o
QD
/
, , - . " p t'
L
r \
D
r ) | o- eDx p {/ - t r P - x\ r J u, . "
/
t/
t
/
in termsof I where f is given by the transcendenral
equation
u
c.r u2
/ u \
."p\-Dt)-O(=r* qo
,
,,,i
(7)
It is worrh noring that thil equarionalso yields rhe length of channelwhich can
be ?eraredby eirher pure diffusion or by pure convecrion. These limirs arc
deducedby setting,in the first case,U = 0 and in rhe secondcaseD = O.
To derivethe limir wirh U = 0 we userhe seriesexpansionfor rhe exponential
function ibr smallvaluesof the 2rgumentto oblain
f
j '
(
u
1/u\,
/u -\r) u
o
(
o i /l t o r
n r * 7 ( b f )
\
/
\ - / )
coU'
, - O o
where O indicatesthat ?11
subsequenrrermsin the seriesare 'of the order of the
third, or higher,power of UllD. This simptifies!o
r / r . t
/ u i , =L o U
u/
"
z \o
(o'/ o-r
(B)
and as U - 0 this yields th€ familiar formula for the length which can be aerated
by diffusion, I e.,
/2DC^\t2
?
(ol
|
^")
\ v . /
In the caseof D = 0 rhe exponenrialterm is unity and we immediarelydeduce
Conuectire gas-flous ln uetland plant aeralian
287
c 9
s o Ui
t
33 : F
t
E
a t y ;
I
;D;
(>
o
_d
c'?
l
.i nri rru
ii
z
;
:-
9
.g
a
a
I
;
E
F
?
*; sE
O
?
z
!
z
I
..9
-.o
i
z
E
.g
E
9 -
2it{l
W. Armstrong et al.
f = CoU/Q which {'as previouslyderivedfrom physicalcoosideratioos,see(2).
In o.der to seerhe quantilativeeffectof thesecontributionswe coosiderdara
.elevanrro rhe convectionand diffusionofoxygen in air, D = 0.205 cmzs I and
C() = 0.000269g cm I, for a rangeof valuesfor the respiratoryactivity and
rbroughflov/ velocities.Table I displaysvaluesof the length I which v"'ill be
2eraredin eachcasebyi (i) pure diffusionaspredictedby (9);(ii) pure con! ccrion
aspredictedby (2);and (iii)by combineddiffusionand convectionwith I s2tisfy
ing equation(7)
pointsregardingthe likely effecoveness
The resultsrevealsomevery interesting
Firsrly,it is clearthat 2eratedpath length cannot be
of througbJloucottvecrions.
dererminedby simplysummiogthe lengthswhich would be aeratedby diffusion
and convectionactingindependentlyThe t.ue aeratedlength is alwayslessthan
this figure.Secondly,and asexpected,asconvectionvelocity increases,so does
the influcnceof diffusiond'minish lghat is particularlyinteresting,howc\ cr, is
so to doesthe velocityneecledfor convec_
that as respiratorydemandincreases,
tive aeraLion
to'overtake'thatofdiffusiveaeration.Hence,with a respiratoryrate
pg
l0
mm ls 1, the influenceof convectionis already''i times greater
of only
than diffusion if the convectivevelocitv 1510 mrn mln I. wrth rcsPirztionat
100pg mm Js r, however,the convectiveeffectis only one-thirdgreater,whilst
at 200 pg mm Js'r, the diffusiveeffectis marginallythe greaterone. This is a
consequence
ofthe factthatlis inverselyproportionalro Q for pure convertion,
see(2), but is inverselyproportionaito Q"' for pure diffusion,see(9). It should
be noted also that the additiveeffectsof convectionand diffusion are greatest
eould 2chievesimiler degree:r,,f
when the two processes,
ectingindependently,
I | .1ncl
whefe
aeration;for example,comparelhe situation
Q = 200 pg mm
L l = 1 0 . 0m m m i n ' l , w i t h a n y o t h e r v 2 l u € so f U .
ow conuection
J.2 Non-throuqhfl
lf we next considerrespirationwithin a channelopen at one end onl,v,and wherc
there is no externallygeneratedpressurelfadient, then in lhe absenceof respi12
tion, the diffusiveprocesswould ultimalelyyield a fully mixed gas at constant
pressurewithio the path and without any volume (or mass)transportak)ng fiIc
channei.vith the addition of respiration,howevef, thesewill be a volumetric
lors of oxygen leadingto a concentrationgradient(which promotes diffusion).
Further, if the CO2 releasedin respiratioois solubilisedto some e)(tentraLher
than being reciprocalltexchangedinto the gas phase,x Prcssuredeficit will
developwhich hasthe cffectof suckinggasinto the channel.Thus 2gainwe have
both convectionand diffusionbut in this c?set-herate of coovection decreases
from the open end to the closedend where, becausethere cao be no outflow,
the non tbrougbflo?r,type Fhere
lhe convectionrate is zero. This characterises
convectionis a direct conscquenceof lon€:itudina!dtffusionalong the chanoel
(Beckettet al. 1988:seealso equation(13) as D * 0) and is, by its nature, a
relativelyslow flo$; it is importantto distinguishthis from the Late(aldiffusion
betweenthe channel,leafand water which is,of course,lhe fundameotaldriving
influenceFor most casesof non tbroughflou conveciion, viscositycan probably be
ignoredin mathematical
treatmenrsHo!r'ever,from (1) it is clearthat for a Siven
Conuectiue 4as-flous in uetlqnd plant aeraliotl
249
pressuredeficit, the slower the flow the greatermust be the viscosityand so it
seemsparadoxical to assertthat viscosity is unimPortant in the non'througbJlou
convection where the motion is slowest. The neglect of v tscosityrn flon'tbrougb
flou conuectioncan be explainedin the light of the physic2lforcesat work; in
Poiseuilleflow the only hiodranceto motion is the viscousstresson the boundary
and ignoring viscositythereforeremoves any restrictionon the throughflow,
'sucking' effect of the respiration
whereas in the non-tbroughfloa./case it is the
which pullsthe gasalongthe channel.This suckingis effectivelyspreadacrossany
which would only
sectionand is virtually independentof the viscousresislance
be manifestat the boundaries;this is the conventionalbasisfor consideringcom
pressibleflow in pipesvr'herethe rate of adiustmentof gasto densitychangesis
governed nor by viscositybut by the speedof propagationof sound In models
of non-tbrougbfloaconvectionthe convectiveelementof gastransportis there
in order to makeup
fore effectivelyallowedto attainwhatevervalueis necess2rl'
by the respiratoryactivity.
for the volumetriclosscause<-l
The quan!itativecontriburionsby diffusionand conv€ctioaio the non'tbrougb
flou c se can be deducedfrom equation(3) but with the modiFicationth2t the
velocity is now dependenton distance2long the pathi thal is we solve
d
dx
drc
(uc)= D - - Q
(t0)
clx"
againsubjecrto the boundaryconditions(4). It should be noted thzt io this trcat
ment all CO2releasedin respirationis solubilisedratherthan being reciprocallv
exchangedwith oxygeninto the gasphase.In order to solve(10)we ireed2 speci
fied form for U(x);assuminguniform .espirationalong the chennelthe velocitv
decreaseslinearlyaccordinSto
(l t)
U(x) = Uo (1 - x/1)
where Uo is the inflow vebcity at x = 0. Furthermorefrom consideretionsof
globalconservation,
thc nass inflow at x = 0 must equate!o the totzl ferpilltiorl
i n t h e c h a n n e i s ot h a tU o i s g i v e nb y p t j o = l Q . T h i s f o r m o f U ( x ) c a n b € p r o v e n
(llecke:(let al. 1988),but is readilyexpleinedon the grouodstirrt
mathematically
there can bc no flow beyond the point *here the channelceasesto be eerobic.
In this casethc solution for C(x), io terms of the aerobiclength {, ls
(
( ott xi
c ( x =) p j r - e x p ( - _ l-J- l ' / )\ )
I
\
2Do
/
ttzt
\i/hile f is given by
(
C..\)tt:
r=l.- a "s"( ;))
( rl )
we can againdeducethe formula,(9), for the l€ngth f which is a€ratedby pure
diffusion on takingthe limit as(Co/p) - O. \ve can zlso deducethat it is impos
sible to aerateany length of rhe channelif there is no diffusion;settingD = 0 in
( 13)yields I = 0. The consequenceof this last observationis centralto the argu
ment of Beckett e/ dl. (1988), when assettif'gtn ii nan-througbflott conve.riun
the role of convectionis secondaryto that of diffusion
290
W. Armsttong et al.
Tabte 2 lhe te^grh ot a channet which can be a€rared by difiusion or diffusion/conv€c0on rn zo,
througbJlou convecrio^ ior 2 range of respiration .a(es
a
Lengrhby
Lengrhby
(psmm rs r)
Lengrbby
uo
(mm)
l0
50
ro0
200
2i0
100
500
lr09l
496 |
150.8
24AO
2 2 19
202 5
1 5 69
l o 5 02
4961
142.1
244a
210.0
t9l 7
t 4 a5
o.49
2.21
221_9
992
702
49.6
2 7l
150
40.5
ll 4
l t l
The analysisshows fh2r not only is convection rorally dependenton having
somelongirudin2ldiffusion,bur alsothat rhe oxygen which is convectedinro the
channelis, a{ besr,able to aerar€only one fifth of thar which can be aeratedby
diffusion alone, (seeTable 2). As wirh tbroughfloa convection,howeve., the
effectsof diffusion and convecrion are nor simply additive: as can be seen in
Table2 rhe occurrenceof convectionincreasesthe aeratedpath by only a small
fractionof rhar which can be aeratedby diffusion alone. Furthe.more,if CO,
lossesby solubilisationare only a fracrionof the total CO2 produced ,n resp',a:
tlon, the cffectsof convectionwill be quite negligible.It should b€ emphasised
that Table 2 displaysresultsfor a rangeof.espiration rates;it is not meaningful
to stipulate a range of velociries, as was the case fot tbrougbJlo4l convecrion,
becausegiven any specificvalue of Q tt\erc is a unique convectionrare which
mustbe consjsrentwith rhe'suction'causedby the respiraroryactivity.The respi
ration rareschosenfbr Table 2 cover a rangewhich includesthe value used in
T a b l ei .
4. Examplesof rfi.ooghtos, convection
4 l. lvatet lilies
The first recen! reportsof a tbrougbJTotuconvecrion in plants were rhoseof Dacey
(i980, l98l) and Daceyaod KIug (1982a,b).Usiqgrhe waterllly Nupbar tutea,
they noted the following: (i) small, bur significanrly.aised,gaspressures(upro
250 Pa)in the youngestemergentleavesduringrdaylighrhours,(and somerimes
alsoat night, if lakewarerswere warm; Daceyand Klug 1982b),(ii) an ioflow of
gasesfrom the atmosphereinto theseleaves(Lheinflux leaves)againstthc prcssure
gradient, (iii) by meansof an erhane t(acer gas, a convection from these inJtu:x
lezv€sto rhizome and back to the atmosphere through older, more mature (and
morc pote\s) efflur leaves,and (iv) thar there was a diurnal rhyrhm ro cheflow:
ilows increased from near zero at dawn, peaked around mid-day and declined
again ro ca. zero at dusk. The convective flows at mid-day were particularly
impressive with petiolar velocities from the influx leavesof upto 50 cm min I
Conuecliue qas-J7au)sin tuetland plarlt aeration
291
(volumefluxr 60 ml min-l) and,exceptfor the higherwater-vapour(humidity)in
rhe gas of ccccche
midrib of these inJlux leaves,there was no measurabledifference
berweenrhe composirionof the lacunargasesand atmosphere-Isotopestudies
confirmed rhar most of the oxygen in the flow originated in the external atmo
and integratedpredictionsfrom the pressure:
spher€and nor in phorosynthesis,
flow dar2indicated Lher22 L.of at( (4.6 L of oxygen) could be moved down a single
perioicduring rhe hoursof daylight.From a considerationof the data in Table I
it will bc cvident thatsuch ratesof flow should appreciablyimprove the aeration
of lhe submergedrhizomes;thesemay be as far as 2 m below the water surface.
A diurn2l patternof oxygen abundancein the rhizome,often varying from less
rhan l0ol, 02 (v/v) at night, to near ambient(217" 02 v/v) during daylight,and
which .efiecredrhe patte.nof convectiveflow supportsthis view. It sboul.l be
noled tbat tbe dat.t in Table I deriue Irom tbe assumption aI I OOoZporositl in
afi orgdn; to translorm tbe data for louer porosities, tbe aerate.l patb lengtb
sbould be nultiplie.l by tbe fractional potositj G.9., 0.5 u'hereporosities are
5O%).
It had previouslybeenthoughtthat raisedlevelsofoxygen in water liliesduring
and that diffusionwas the maior
of photosynthesis,
the d?y were a consequence
mechanismofgastransportboth at night and during the day(Laing1940).Daccy's
datasuggestthat convectiondominatesin the day,diffusional night, and that the
lower oxygen ievelsin the rhizomesat night might resultin someadditionaloxy
a! this stage,however,
gen stressin partsof the root system.It should be srressed
aerationin
petioles
aerated
by
convection,
a.e directly
lhat alrhoughrhizomeand
rhe roor systemitselfshould alwaysbe dominatedby diffusionunlessthereis an
as yet'unknown additionaltyp€ of convection.Henc€,the vTlueaf rhe tbrougb
tol convectianto root aeration,will be due !o enhancedoxygenconcentrations
at the root-shootiuctionsand, thereforeenhancedO2 diffusionfrom this point
onwards into the root (seePbragmites below). Convection will of course be of
benefit in reducingCO2levelsin rhizomeand root also;futthermore,it will help
remove gasesdiffusing into the root system from the sediments(D2cey and Kluli
r919).
There have alsobeenreports ofconvective flows in lr'rnproldes peltata (Grosse
and Mevi-Schutz1987),and Nelunbo nucikra (Lotus - Dacey 1987;Mevi-Schu!z
and G.ossel988a,b),and we haverecentlyobservedvery substantialflows frorn
rhe leaves of Nympbaea alba (Lrmsuor'g and Armstrong unpublisbed data).
Tbrougb|lou i^ Nelurnbo is p rticulatly interesting, with inJlu, N\d eIJlux appar
andGrosse1988a).
ently occurringwithin the sameleaf,(Dacey1987;Mevi-Schutz
Air is thought to enter the leafacrossthe expanseof the lamr\", ^nd petiola{ influx
channels t.ansport the gasesto the rhizome. Efilux cnannelsin the same petiole
rransportthe ventinggasesback to the atmospherevia a highly porous disclike
regionat the centreof the laminadirectly abovethe petiole.The only dataavaila
ble on the ralesof convectionin Nelumbo are thoseof Mevi-Schutzand Grosse
(1988a),who estimatedvolume fluxes as 10 cml min i. Al(hough this is some
what lower than the maxima of 60 ml min-t reported by D^cey for Nupbar, it \s
neverthelessa substantialflow and translatesinto a petiolar velocity of ca. 30 cm
min-r, a quite similarfigureto petiolarvelocitiesof Dacey.Usingsoap-filmflowmerers,we hav€ detectedflows of 50 cm min-t (15 cm3 min t) 1n NlmPbaea,
W Armstrang et dl
but if convecrionis deliberatelyblocked, whereasyounger leavesmay dev€lop
higher pressuresthan older, more expanded leaves,ir is our experiencerhar
the potentialfor convecfionfrom the older le2vesis grearerand in proporuon ro
rheirgreaterarea.\ve alsofind that whereasan infrz-redlight sourcewill enhance
convection,considerableflows can still develop in darknessprovided rhat the
atmosphereis moving and is relztivelydry.
It canbe deducedfrom equation(1),that providedthe resistance
ro convecUon
throughthe plantsis low, the'dynamic'pressuresdevelopedin rhe /ztzJr le2ves
will be, and ooly ne€d to b€, smallto drive appreciableflows (seelater).
4. 1.1. Tbepbenonerul untler4ting pressurisation
One can become easily confusedby the terminolo€i)'used to describe rhe
phenomenawhich causethe pressurisation
and consequentconvectionstn warcr
ltlies: tber/no'diffusiofl, thermal transpiration, tbermo osmosis. Each refers io
thermallyinducedor enhanceddiffusivegas-movemenrs
of a Koudsen-or transitionalKnudsentype (Leuning1983)acrossa pariition In warer lilies this parrition must be the leaf surfaceand/()rsome internal porous structure(Schroder
et al. 1986).
Pressurisations
occur becausethe various mechanismseffectively induce a
diffusiveinflux of air ratherthan (J2 or N2, and this influx is nor balancedin a
normal w^y by rhediffusiveeffluxofanother species(seebelow) A warerlily leaf
will tend to pressurise
until the pressure€itherovercomesthe partition restsr.utce
to bulk flow sufficientto inducea reversePoisseuilleflow equal in magnitudeto
the diffusion,or until it is sufficientto forcea Poisseuille
flow oFequalmallnirude
th.ough the plant.
The letms tbermo-osmosisar.d tbermal transpiration oltefi seem to have been
usedsynonymously.In context,howevet, tbermal tfttnspiration seemsto have
historicalprecedence2nd to havebeenmore rigorouslydefined.Furthermorc,rr
should be noted that Denbeighand Raumann(1951) used tbet'ma-osmosis
to
which
describemovementsin
the diffusingspeciesdissolvedin rhe parririon.
(Feddersen1873),hashisroricalprecedeoce(Merger1873,
7-bermo-di.ffusion,
1874;Ohno 1919;Ursp.ung1912),but seemsro havebeen appliedto p.essurisa
tionsand flows which were humidity-inducedand rhermallyenhancedasweu as
temperatureinduced.Its conrinueduse is probably inadvisable.
Tbermal transpi/"a/io, is a very specific term used to describe a temperature,
induceddiffusionacrossporouspartitionswhere the gaseson each side are dry
(Reynolds1879);net movementis usuallyfrom rhe colder ro rhe warmerside,and
the flux can create,and move againsr,a pressuregredienr ln rhe warer lily leaf,
however,the gasesare not dry but very moist,"nd during rhe day there will usu
ally b€ a gradientof humidity between rhe leaf 2nd rhe drier, exrernal,2amo
sphere.However,if the internalremperature
of the l€afis higherthan outside,and
the pore dimensionsa.e within the Knudsenregime,there ought to be a thermal
transpiration
componentin anyp.essurising
diffusion.The rheoryunderlyingthis
the.maltranspirationcomponenthasbeen dealt wirh in some detail by Schroder
et al. (1986).Under idealcondirions,i.e., if pore diametersin rhe leaf'spartirion
were < < l0 7 m, and ifconvectiveventingthrough rhe rhizomewere prevented
in some way, thermaltranspirationshould lead ro an equilibrium pressurera(ioi
Canuectiue gds-floLNs in uetlarul pldnt aeratio,l
P1 = P, (Tt/T,) "'
293
(r4),
where P, (armosphericpressure)is approx. i0l kPa. At an externaltemperature
('l,) of 296"K and ao internal leaf tempcrature(Ti) of 298'K, the pressure
differeorialfrom l€af to atmospherewould be a42 Pa.Ail the indicationsare that
pore diamerersare, in fact, only oo the fringesof the Knudsenregime(1.e.,not
<< I but rather < X),and hencethe tendencyto pressu.isein a non-ventingsys
and the pressures
will b€ largely
rem would be confoundedby pa.titionleakiness,
fl()w back rhroughthe leafsurface
dissipatedin a concomitantr€versePoisseuille
to the atmosphere;hence,the'static'pressurcdifferentialdevelopedfor a AT of
2'K would be very very much smallerthan 142 Pa.A sm2llstaticpressuredoes
nor necessarily
imply that therewillbe a slow llow unde. throughflowconvection
to throughflowis negligible;never'
conditions,however,particularlyif rcsist2nce
rheless,th€ indic2tions?re that tbermallranspi.ationmav makeonly 2 smallconrribution ro the throughflowswhich havebeenobserved,and, if the temperatu.e
differentialsare reversed,any contribution from thermaltranspirationwill be a
negativeone.
is undoubtedlyofmuch
The humidity differentialbetweenleafandarnlosphere
greaterimportaocethan thermaltranspiratior-r
for creztingthe diffusiveinfluxes
of air which induce convectivethroughflowsriodeed,it would seemthar burnidiry incluce.ldifJusio, (Dufour 1874;Kundt I 877),is the matordriving force for
such throughflow convcctions(see also Dacev I987; Mevi'Schulzand Grosse
l9BBb):ir can funcrion isorhermally,and with, as weLlas against,a temperature
gradient,and can be rhefmallyenhanced.(Afmstronfland Armstrong,unpub
lished)-Thesephenolnenacan be explainedin relativelysimpletermsasfollowsl
Consideran upright cylinder topped by a porous membrane(po.e diameters
<< \) and containingfree'watcrto within a very shortdistanceof th€ membrane.
air at atmospheri(pres
If rhe atmospbereabove !he membraneis w?ter-saturated
(composition
volume
epprox.97%
N2
and
Ar:
sure,
by
O,,
3% H2o-vapour;par
tial pressuresapprox. 98 kPa and 3 kPa respectively),
the atmospherewithin the
chamberv/ill also be water saturated,and, if there is no tempe.atu.edifferential,
therewill be no net fluxesof any gasacrossthe membrane,or a pressuredifferen
tial. lf dry air at atmosphericp.essurel0l kPa,(composition100% 02, N2 and
Ar), is no$/ passedover th€ membrane,a water vapourgradientwill immediately
be createdberween lhe chamberand the armosphere,and ao 02-N2 gradient
betweenthe atmosphe.eand the chambcr.lf rhe membraneis very thin, and the
bouodary layersabove the membraneare kepr ro a minimum, the gradientswill
be very steep,and will causea rapid diffusionof air into the chamberand a rapjd
diffusionof water'vapouroutwards.lf, however,.thewater'vapourin the cham
ber is replac€dby evaporatioofrom the free-watersurfaceasrapidly as it is lost,
the water'vapourcon!ent (andwater vapourpartialpressure)
in the chamberwill
gas-pressure
tend to be sustained,while the total
in the chamberwill risebecause
ofthe inflow ofthe air. Indeed,the inflow ofg?seswill continueuntil the pr€ssure
risessufficientlyto drive a Poissueille
ourflow, or until the concentrationsof O2
and N2 insidethe chamberequal thoseoutside.Ideally,this will occur when the
total internalpressureapproachesoumericallythe atmosphericpressureplus the
saturatedwater vapour pressufeat that tempe€ture accordingto the equation
W. Armstrong .'t .il
l',=l',+P-,-P*"
(15)
where Pwiand P_aa(e the vapour pressuresinsideand outsidethe leaf respectively (Dacey1987).At 296"K rhiswould amounrro approx. 104.t kpa,and2 pres,
sure differential,AP, of approx. 2808 Pa would have been creared.
If by somesustainedinpul of heat,a temperarure2'K aboveambienrcould be
maintainedwithin the chamber,the warer vapourpressorewould risero 3 i 66 p?,
and a temperatureenhanced humidiry induced diffusion would h?ve been
achieved.If on the other hand, rhe ev2porationof warerled ro a deciineio cham,
ber temperaturethe humidity induc€ddiffusionwould give a pressLrre
differenrial
below 2808 Pa.Nevertheless,
whether the remperaruredifferenrialwas posirive,
neg2tiveor zero,the potenti2lfor pressurisation
is consid€rablygrearerrhan rhe
342 Pa deducedearlierfor tbermal ttanspiration.
Humidity-inducedflow depending 2s it does on humidiry diffe.enri2Ls
mey
involve differentials
within the leefirself- it is wrong to assumethat rhe leafgases
wili be wholly water-saturated
throughour,(\(/ardand Bunce l986) Ag?in,how
ever, it must be str€ss€dthar, in pracrice,th€ full potenrialsfor pressurisarion
by
humidicy-induceddiffusion and rhermal rranspirarionare also nor realjsedbe
causeof l€af leakiness
(Dacey l98l, 19f17).
A nice exampleof rhis is seenin dara
oo Nelumbo,Dac€y(1987),wherc, qrirh venting preveotedand a zero remperature differentialat 2l'C, rhe roralpressuredifferenrialdevelopedwasonly 700 pa
instead of a potenllal 2490 Pa.
The potential for pressu.isarionby thertual transpitation and b)' humidiry
differentialsin water liliesand gardenbeaoshasbeen examinedrheoreticallyby
Idso ( 1981).V\Ve
canalsodeduce rhe relative effectsof bumidit!-/nctuced presstrisatlon and thermal tt ansplration from lhe relationship between AT and Ap found
by Daceyfot Nelu/n o; this p rovidessomegood evidencefor ihe exisrenceof rhe
thermaltranspirationcomponent:under iclealconditionsthe potenrialfor sraric
pressurisation
at 21"C with iso{hermalconditionsrs 2490 P^; ia Nelumboit was
700 P2; with " LT of 2"C rhe porenrialfor ideal pressurisarion
will be 2808 Pa
(humidity componenr)+ 312 (the.maitranspirationcomponent),a {otalpressure
riseof approx. 27yo;\n Nelumbo rhe roralrisein AP for this AT wasalsoapprox.
2Jy". ^^d we can estimarerharrhe rhermaltranspirarioneffectwith ? AT of 2 "C
was approx. I I "/" and inkeepingwirh rhe predicrions.If AT ris€sro 6.C (e.9.,as
in bright sunlight - Dacey 198t , I 987) rhe idealpressurisatioo
would raiseAP !o
3564 Pa (humidity compenenr) + 1028 Pa (rhermalrranspirarioncomponenr),
i.e-, the thermaltranspirarioncomponenr is noy 22y" and the total rise in AP,
64.5y". Fot Nelun o the rise w^s 64"/". Again,therefore,we have confirmalion
of a tbelmal transpiration effecr^nd canseethat as a propoftion of the total con
vectingforce it can vary considerably,e.9.,from zero where AT = O,to22"/" at
a AT of 6"C. Theseconsiderations,
at leastpa(tly explainwhy sunlightand infrared illumination have the enhancing€ffectson pressutisarion
and convecrioo
reportedin the literature.The very low ratesofconvecrion that havebeennored
at night may be a consequenceof high atmospherichumiditiesand perhapsa
negativethermal rranspiration.More information is needed on the funcrioning of
the humidity-inducingcomponeot in the water lilies,however.Ir is not yet clear
how stomatemay control the p.ocess,but Schroderetal. (1986),idenrifyrhe cell
Cc)floectiuegas-Jlous ln uetland plant aeration
o.048
oo
t
o . 0 4 0t -
400
;
o.o32Yo
o
\
300
o.o243o
ir
qq
s 200
o
5
o . 0 16
o
Q
t
100
o.o08
(!
(./)
200
Light Flux
600
800
Qmot i2 t^)
Ik /'lheeffcdoivaryinglightflux(PAR)onslaticp.essuredifferentixis.con!e.liveflowzndrem
perarure differenrials. Almospheric humidities ilso shown. l\ Pblaqmites thl7t)rie bearing i young
s h o o t s ( 0 . 2 1 0 l 2 m r a u )w a s u s e d .
layerbeneaththe palisadetissueas the micro-porouspartition.From this it could
to occLrr,there must be
be concludedthat, for humidity-inducedpressurisation
very significanthumidity gradientsthrough the palisadelaver Our studieson
Nympbaeashow th2t considerableflows are posgiblein darknessunder isother
mal conditionsprovided rhatthe atmosphereis movingand drv, but one canspec
ulatethat it may be the closingof the stomataat night which reducethe humidity
llradient2crossthe partition rather thao the incr€asingatmospherichumidity.
4.2. Pbragmites ausrralrs (Seealso Appendix)
A convective throughflow in the common rced Phragmites44.r/,.4rs was also dis
coveredrecently(Armstrongand Armstrong1987,l99O^,b).A humidity-induced
diffusive inflov/ of atmospheric gas€sthrough stomata oo the leaf sheathsand
296
W. Atmstrong et al.
Rhizome
3
>
o
,"8
o
o
Advent.Root
;t
L at e r a l s
;}
o's
Control
o
1000
a
Light
o
o.o
C on v e c t i a n
o.o
o
2
4
6
Time
8
10
12
14
16
th)
Fig 2. Pbragmites:effectsof light and dark periodson convecdvefloR s, on oxygen concentrerions
of g2s€svenling f.om rhizome, and on roor,oxygen efflux. Rhizome lengrh was 65 mmi I culnrs
presenr(heights0 6 m); depth of culm subm€rgencewes 170 mmj rhe adventirious.oor was young
2nd65 mm long(diam.approx.l 5 mm);rh€hrerrl roos weri aprox l5 mm longrnd iormeda dense
coetingon oldcr advenlitious100ts The conrrol el€crrodewas l0 mm xnay from larer?lrools.
culm nodes appearsto be the major driving force, again supplemenred (or re'
duced) to varving degreesby thermal modification and rherm2lrranspirerion.
Responsivenessto light tn Pbragmites canbe considerable, (Fig- 1), bur at pres€nr
is believed to be more a function of stomatal mov€ments rhan of rempe.ature
differentials,although temperaturedifferentials do have an enhancingeffect. The
Conuectil)e gas-JTotrsin uetland plant aeration
297
convection in Pb,"agmiles is from the living culms to the ext€nsively aerenchymarous rhizomes,with ventingoccurringvia old or broken culms.
In rhe field, convectiveflows upto 80 cm min livolume flux 16 cm3 min-l)
have been reco.ded from single shoots, and in the laboratory it has been shown
rharrhe convectionappreciablyimprovesthe aerationof both rhizome and roots,
(seeFig. 2). Improved ae€tion in the roots is, of course,2 consequencelargely
of convectionenhancedoxygen concentrationsat the root shoot iunction, and
althoughtheremay be a smallnon throughflowconvectionin the roots, roor aera
rion will be largelydiffusiondominated(seelate.).Again,as in the water lilies,
pel seappearsto havelittleeffecton the convection,and volume
phorosynrhesis
inflow of gasesacrossthe leafsheathsand culm nodesapproximately equalsrhat
vented, and the concentr2tionsof oxygen in the gasespassingdown the living
culms a.e little differentfrom thoseof atmosphericair when account is tak€n of
i h e r n c r e a 5 ehdu m i d i l ).
By enhancingthe oxygensupplyto the root system,the convectionsin Prr4g
/nitesmay pl^y ^nimportantrole in rhesuirabiliryofthis speciesfor sewagepurification by what has becoineknown as the rool zone treatment',(reviewed by
Lawson1985).Oxygendiffusingfrom rootsirlto w?terloggedreed beds supplied
w i r h e f f l u e n r c\ r n 5 u p p o r It h e b r , t e r r r lo x r d i ) r n gr e r ,r r , r n .N H , > N O , > N O ; .
while in anaerobicpocketsof the soii nTosaic,rhe nitratesare reducedand escape
as oxidesof nitrogenand nitrogengas.Similarly.oxidation reactionsare needcd
for the removal of S-compounds,
COD and heavv mer2ls.
4.3. Nuclepore membranes
Becauseof the petiolar anatomy in water Lilies,and the unwreldy na..uteof Pbragn //esshoots, the study of tbrougbfloa conuectionin rbesespeciescan be difficult.
phenomenaexnefl.
An alternativemeansof studyingaspecrs
of rhe pressurisation
mentally is to mimick the leaf partitionsby meaosof Nucleporepolycarbonate
micro porous membranes.Dacey(l987) usedsuch membranesfor comparrsons
wirh Nelumbo in regardto differentialsepar2tionratesof Ar and N2 from 2rr Ln
accordancewith Knudsendiffusivities.
Nucleporemembraneshavediscretepores
rather than a mesh-work,and can be obtainedwith specificpore sizesdown to
0.015 pm diameter.ve have madean exrensivesrudy of the humidity-induced
component of the convectionusingthesemembranes,examiningthe effectsof
such fac!orsaspore size,pore frequency,membranearea,wind velocity, humidi
ty and temperaturedifferentials.
Detaiiswili bc publishedelsewhere(Armstrong
preparation).ln
znd Armstrong,in
brief, rhe datashow that whilst the potential
for pressurisation
is an inversefuncrion of pore diameter,po.e frequenclesare
alsoexrremelyimportantfor determioingconveclionrates.Hencefor memb12nes
of equal area,flow ratescan be greaterwith pore diametersonly on the fringes
of the Knudsenregime(e.g-,1 0 pm), rhanwirb membraneshavingpore diameters
well within the Knudsenregime(e9.,0.015 am), provided that the porositiesof
the former ale very much greaterthanof the latter.Convectiveflow ratesfor any
given membranea(elinearlyrelaredro rhe sraricpressur€differentialsdeveloped
unde. non-rhroughflowconditions;they increaserepidly wirh wind velocity
up to I m min I and declinecurvilinearlyas a function of increasinladistance
294
IY Armstrong et al.
between the membmne and the fre€ wate. surface;this is analogousto the devel
opmentofsignificantwater vapourgr2dientswitb leaves(Vard and Bunce1985).
The relalionshipbetweenhumidity differentialsand rhe staticpressuredifferen
tialsunder isorhermalconditionsis a linearone, wirh zero AP occurringar zero
humidity (Armstrongand Armstrongl99O^in press),and this hasd€monsrrated
the criricalimportanceof humidiry-inducedconvection.It hasnot beenpossible
to demonstrate a very significant thermal transpiration effect with Nuclepore
membranes,however:pressuredifferenrialsin humidifiedchambersriseby only
approx.6.57oper "K (numericallyequalto rhe rempcrarure
eohancementof rhe
whereas
humidity component),
in Nelumbothe figu.e was approx. 13y..\fi dty
chambersonly minimzl effecrsarrriburableto thermalrranspirationhave been
noted. This may be a function of the very thin membranes(10 #m) and it could
be rharpartirionrhickness(and hencepore lengrhs)may be criticalto rhe main,
tenanceof tempe.aturedifferenrials.
5. Examples of non-throighllow
convection
5.1. Deep-uaterrice
Attention was recently focussedon non tbroughJlow convecrions by repofts of
massflows of air which it was claimedwere the majoamechanismfor aeration
in deep water .ice', (Raskinand Kcnde 1983,1985).Theseconvecriveflows occur
via the narrow, but continuousgasfilms which coat rhe submergedleafsurfaces
and connect with the atmospherear rhe floodv/arersurfacewhere the leavesare
emergent-They arisebecauserespirarorycarbon dioxide produced in rhe submergedpartscan be lost into the surroundingflood waters12rherthan moving up
the films to the atmospherein diffusivereciprocitywith oxygen.The rendency
is, therefore,for gaspressuresto fall within the films and rhis is {e-dressedby a
convective inflov/ of air from rhe atmosphe.e.In daylight,becauseof photosynthesis,CO2 will be absorbedfrom rarherth2n releasedto the water, and ihe
oxygen released,being comparitivclyinsoluble,can causea revers2lof the convection (Raskinand Kende l9B5).
\ve havealreadyanalysedand commenredupon rhisrypeof convectionin Sec
tion 3.2 and in derailelsewhere(l)eckeuet dl. 1988).Raskinand Kendeshowed
that the convection was grealesrimmediarelyafrer partialsubmergencein the
dark,or in darknessfollowing a period of photosynthesis;
the flow rhen declined
considerablyin a few hours ro 2 quasiequilibriumstate.So far as roors are concerned,by the time this equilibriumstatehas been arrained,the oxygen supply
fiom convecaionis insufficienrfor growth or significantrhizosphereoxygenarion
in apicalregions,(Fig. 3).
The earlier mathematicalsecrior' oA non-tbroughfioz, convection demonsrrated that the convection is sub-ordioarero diffusion in the aeration process even
where all respiratory CO2 is losr ro solution, and it is clear that thar even during
the rapid initial phase, oxygen consumption from the gas-filmsand aerenchyma
reserveirsare more important for the plant than the convecting gases:for every
Jite oxygefl moleculesdepleted from these reservoirsonly o/re oxygen molecul€
Conuectiue 8.ts JTous in uetland plant aeration
299
n]
f
o
1
2
3
4
5
6
7
Time after pattial submetgence (h)
F€ .l Root inle.nal oxygen o, root exlcosion ., and non-throughflowconvectivegasflow ^ , in
agar:wat€r
mediumin theda.k Tbe root m€di
rice par(ially submergedto 0.5 m inai. s2turated0-05%
um war anaerobic.The apicaloxygenregimeofs€l€ct€d1()06wasmonitoredpolarographicallyusing
sleevingPl-el€c(fod€s(Armstrong1979).Root €xt€nsionwasmeasuredi, rrr with a vcrnie. mrcro
scope. Convective 8as-now was measuredby soapfilm flow melersart2chedto the heade. spacc
enclosingrhe em€rgenilexf cnds (Afte. Beckettet al. lgaa).
is drawo into the film in the air flow. lt hasbeen calculatedthzt non-tblougbJlou
conuection alone might only adequatelyaerate40 mm of rice leaf compared with
2O2 mmby dilJusio, alone, and that in the presenceofdiffusion, convection can
only extend the aeratedpath by approx. 10 mm (Beckette/ 4/. 1988).Further,it
is evident that without longitudinaldiffusion(D = 0, equation(13))there could
be oo convection.and also,that convectionwill becomelessassolutionconcen
r r a r i o n so f C O , b e ,o m e g s q J 1 q 1
concerning the eco'physiologyofdeep-wateriice, the problemofsudden sub
mergence by flash floods is partly overcome by (i) rapid internodal growth to
regainemergence(Metrauxand Kende l98l), and (ii) the production of a new
c(op of roors at th€ uppermost node (personalobservation).This ensuresthat a
functional root system will occur in a position as nea. normal as possible. \ve
would suggestthat the gas films on the leavesate more funclional for lateral gasexchangesof both O2 and CO2with the floodwaters,and for the escapeof ethene,
than for inducing influxes of air from the atmosph€re.Becausethe leaf is ridged
and gas films rather than water occupy the furrov/s in which the stomatalie, this
will substantially reduc€ resistanceto gesexchangewith the water. The function
100
W. Armstrong et al.
of the films as lateralgas€xchangerswas firsr suggestedby Raskinand Kende
(1983).In pracrice,rhe deep-waterrice plant may eventuallybreakaway from rhe
originalroot systemburied in the sedimentsand which presumablywill be dead
becauseof the inadequacyof either convectionor diffusionro mainrainaerarion
at depthsof >2 m and at temperaturesof >30"C.
5.2. Roots and rbtzomes
con
Just as the solubilisationof respiratoryCO2 cen induce a non-rbrougb|Tour
vectionalongthe leafsurfacegas-filmsof deep water rice,so too can it crearethc
potential for non throughflow convection in submergedroors and rhizomes,
(Koncalovaet al. 1988;Brix l9B8; Cwrun et al. I986; and orhers).lt hasalready
been pointed out, however, that such non-tbroLlgbflou convection must always
be sub-ordinzrero diffusion in the aerationprocess,and hence rhe derivarion
of diffusioo equationsto model rhe long distanceoxygen rranspor! ln ruors
(Luxmoore,Stolzyand Letey 1970;Armsrrongand Beckerr1987;De Willigenand
VanNoordwitk 1989)is fully jusrified.Concerningroor sysrems,
ir is probablerhxr
in flooded soils the rhizosphereoften will be highly chargedwith CO2,parricu
larly if the soilsareon the acidsideof neurraliry,and rhiswill diminishsrill furrher
the potentialfor an inducrionofconvection. Raskinand Keode(1985)noted thar
non throughflow convecaionin deep-waterrice was halted if rhe submcrsing
medium was chargedwith CO2.The work of Koncalovaet al. (1988)on rhe roor
Aerariooof Cdrexgracilis C]utt.,is particularly p€rtinent here, and rhey sumnre se
their findingsasfollows.'Two processes
appearto be of importancein the venrilarton of Carex roots: (1) the diffusion of oxygen aloog rhe oxygen gradienr fronr
the atmosphereto the internal gasspacesat the roots; and (2) the massflow of air
d.iven by the pressure difference of carbon dioxide between rhe internal gas
spacesand the root medium.\vhen the pressureofcarbon dioxide is lower in the
root medium than in the root, the massflow follows rh€ s?medirectionasdiffu
sion,enhancingrhe internaloxygensupply ro rhe roots.Vhen the pressur€of ca.
bon dioxide is higher in the root medium than in the roots, rhe oxygen suppl,v
is depressedby the mass-flowdirected againstdiffusion.Sincea medium wirh
high biological oxygen demand may produce large amounts of carbon dioxide,
mass-flowis suggestedto play a negative role in the ventilation of roots growing
uoder such conditions'.
Acknowl€dgments
\Ve should like to thank th(] NaturalEnvironment Resea.chCouncil, rhe \g2ter
Research
Centr€ and the YorkshireWater Authority for financialsupport.
References
Armstrong,J. anclArmstrong,W. 1987.Cotract Reports6 aod 7 to Water ReseerchCcnr.c, UK
Armstrong,J. and Armsrrong,ii(. 1990a.A convecrivethroughflow of g?f;esin Pbragmitesausiatis
Aqual Bol (i. press)
Conuectiuegas-flous in u)etllnd plant aeration
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Appendix
LoPbragmites austlalrs, a third causeof convectiv€ throughflows has now b€en
found (Armstrong and Armstrong l99}c): Ventu inciuceclpressutedifferentials
c.eatedwhen winds blow over rhe long (often > 2 m) and p€rsistent,dead (and
often broken)floweringculms.Theseold shoors,which remainconnecredto the
gas-space
systemofthe undergroundrhizomenetwork,area characteristic
feature
of thisplant.The air dmwn out by aheVenruriefffcr is replacedby an inflow from
t h e a t m o s p h e r ien t o o t h e r , L r l m sb r o k e nm u c h c l o s p rr o g r o L l n dl c v e l .
ln preliminarystudies,staticpressures
developedin no flow (blockedrhrough
flow) conditionshave amounredro -2 5 to -30 Pa at averagewind speedsof
10-35 km h I. These^re 55 650/"of the valuesto be €xpectedusing the well
known relationship.
AP = - y, p Vr. In the rhroughflowstate,flow velociriesof
t
3 100 mm min (60 2000 mm] min r)from rhizometo individualculms h2ve
been reco.ded at wind speedsof 10 15 km h '. Alrhough wind speedsvary
enormously,such convectionsshould, neverth€less,
play a significantrole in
Pblagmites aeration(seeTable I ), parricularly at night, and in winter when living
shootsa.e not presentto support humidity-inducedflows.