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Geome y-awa e Analysis o Whea G ain Hyd a ion P io o Milling
А.U inboe ,
Fe gana S a e Technical Uni e si y, Fe gana, Uzbekis an
[email p o ec ed]
B. Ismailo ,
M.Auezo Sou h Kazakhs an Uni e si y, Shymken ,
Kazakhs an
[email p o ec ed]
Abs ac . This s udy p esen s an analysis o he geome y and sho - ime hyd a ion o wo whea
a ie ies widely cul i a ed in he Fe gana Valley o Uzbekis an “As ” and “Aleksee ich”. Linea
dimensions (leng h, wid h, hickness) we e measu ed wi h a digi al calipe (p ecision 0.001 mm);
mic os uc u e was examined by op ical mic oscopy; and su ace/ olume cha ac e is ics we e
econs uc ed om 3D scans. Hyd a ion kine ics we e assessed g a ime ically a 5 min in e als up
o 30 min unde cold (20–25 °C) and wa m (40–50 °C) condi ions. “As ” g ains we e ound o be
la ge ac oss all axes (leng h 5.6 ± 0.3 mm; wid h 2.45 ± 0.2 mm; hickness 2.05 ± 0.2 mm) han
“Aleksee ich” (5.3 ± 0.2, 2.2 ± 0.2, 1.9 ± 0.2 mm; p < 0.05). Mass gain a 30 min was highe in wa m
compa ed wi h cold condi ions (9.1% s. 4.2% o As ; 8.5% s. 3.9% o Aleksee ich). Box-plo
analysis con i med signi ican ly as e wa e up ake o “As ” unde bo h egimes. An ellipsoidal
mul i-laye di usion amewo k was applied o link g ain geome y wi h p edic ed mois u e-
pene a ion imes (𝑡50,𝑡95). The esul s demons a e ha geome y-awa e condi ioning can imp o e
millabili y and lou quali y while educing epea ed we ing–d ying cycles.
Kali so‘zla : Whea , geome ic pa ame e s, 3D modeling, hyd a ion kine ics, condi ioning,
di usion.
INTRODUCTION
In Uzbekis an, whea plays a cen al ole in
ag icul u al p oduc ion, se ing as he p ima y aw
ma e ial o he milling, ce eal, baking, and pas a
indus ies. The quali y o bo h win e and sp ing whea
is de e mined by a ange o cha ac e is ics ha
signi ican ly a ec he inal p ope ies o p ocessed
p oduc s. G ain quali y assessmen is based on a
combina ion o pa ame e s ha mus con o m o
egula o y and echnical documen a ion s anda ds.
Mode n app oaches o g ain p ocessing a e
aimed a imp o ing he quali y o inished p oduc s,
educing losses, and op imizing echnological
p ocesses. One o he mos c i ical s ages in p epa ing
g ain o milling is hyd a ion, which signi ican ly al e s
he physical, mechanical, and geome ic p ope ies o
he g ain. This p ocess a ec s he size, shape, and
s uc u e o he g ain, di ec ly in luencing milling
e iciency and lou quali y. Modeling he geome ic
pa ame e s o whea g ains du ing hyd a ion allows o
he iden i ica ion o pa e ns essen ial o op imizing
echnological p ocesses and de eloping ad anced
p ocessing me hods.
In ecen yea s, nume ous s udies ha e been
conduc ed on he hyd a ion and milling o whea g ains
unde a ying mois u e le els. S udies [1-4] ha e
in es iga ed a ious aspec s ela ed o he
cha ac e is ics o whea and lou , as well as p ocessing
echnologies. Pa icula a en ion has been gi en o he
in luence o whea a ie y on lou quali y, along wi h
he ela ionships be ween g ain ha dness, endospe m
s uc u e, and physicochemical p ope ies. A
signi ican ocus has also been placed on c op
managemen me hods and hei e ec s on yield and
g ain quali y, con ibu ing o mo e e icien p oduc ion
and p ocess op imiza ion. The physicochemical
p ope ies o g ain a e in luenced by a ious ac o s,
including clima ic condi ions and echnological
p ac ices. Resea ch [5-6] highligh s he e ec s o
empe a u e egimes, p ecipi a ion le els, and o he
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na u al ac o s on yield and g ain quali y. S udies ha e
also explo ed he consequences o hea s ess, i s
impac on pa hogen iabili y, and he p ese a ion o
g ain du ing s o age. Fu he mo e, i is impo an o
examine he e ec s o a ious ea men me hods on
main aining and enhancing g ain quali y, which is
c i ical o he e ec i e ope a ion o ag icul u e and
ood secu i y. Mode n g ain p e-p ocessing me hods,
including he in oduc ion o inno a i e echnical
solu ions such as compac mul i unc ional machines
and mobile g ain d ye s, con ibu e o inc eased
p oduc i i y and educed aw ma e ial losses. Resea ch
in de eloping and op imizing p ocessing condi ions in
specialized equipmen enables signi ican
imp o emen s in p oduc quali y wi h minimal ene gy
inpu . These app oaches g ea ly enhance he e iciency
o pos -ha es g ain p ocessing, os e ing
sus ainabili y and economic bene i s in ag icul u e.
In he con ex o his s udy, he analysis o g ain
geome y and hyd a ion p ocesses p io o milling
ep esen s a i al a ea o esea ch ha suppo s he
op imiza ion o ce eal p ocessing echnologies. S udies
[9-12] emphasize he impo ance o mo phological
changes in g ains du ing hyd a ion, which di ec ly
in luence hei beha io du ing milling. Analyzing he
geome ic pa ame e s o g ains and how hey change
du ing hyd a ion helps iden i y key pa e ns ha can
imp o e g ain p ocessing e iciency and lead o he
p oduc ion o highe -quali y lou . Hyd a ion plays a
c ucial ole in ensu ing he quali y o inal p oduc s
such as lou . The p ocess enhances he physical and
mechanical p ope ies o he g ain, acili a ing
p ocessing and inc easing milling e iciency.
Hyd a ion ensu es he uni o m dis ibu ion o mois u e
wi hin he g ain, minimizing aw ma e ial loss and
maximizing p oduc yield. Gi en he g owing demand
o high-quali y ood p oduc s, op imizing hyd a ion
has become a i al objec i e in mode n g ain
p ocessing. Hyd o he mal ea men , in ol ing he
combined ac ion o wa e and hea , is implemen ed
using wo p ima y me hods: cold and apid
condi ioning. In cold condi ioning, g ains a e
mois ened wi h wa e a oom empe a u e and le o
es o a ce ain pe iod. Rapid condi ioning in ol es
ea ing he g ain wi h mois s eam, inc easing i s
mois u e con en by 1.5-2.0% and aising i s
empe a u e o 45-55°C in a sho ime (20-40
seconds). The choice o me hod depends on g ain
cha ac e is ics such as a ie y, glu en quali y, and
ke nel anslucency.
Fo whea cul i a ed in he Fe gana Valley o
he Republic o Uzbekis an-cha ac e ized by a
anslucency ange o 40-60% and subop imal glu en
quali y-cold condi ioning is p e e able. Due o local
geog aphical and clima ic condi ions, he dominan
whea a ie ies g own in he egion include “As ” and
“Aleksee ich”. One p omising di ec ion o imp o ing
he hyd a ion p ocess is he modeling o g ain shape
and i s in luence on mois u e abso p ion and
dis ibu ion wi hin he g ain s uc u e. Mode n 3D
modeling echniques enable de ailed in es iga ions o
hyd a ion kine ics, aking in o accoun he geome ic
and mo phological p ope ies o he g ain. These
ad ancemen s c ea e oppo uni ies o au oma ion and
p ocess con ol, as well as he de elopmen o
inno a i e echnologies and equipmen . 3D modeling
enhances he accu acy o expe imen al da a, educes
he cos o da a acquisi ion, and minimizes ene gy
consump ion by p e en ing he need o epea ed
mois ening and d ying be o e milling. In eg a ing
ma hema ical and compu e modeling in o he
au oma ed con ol sys ems (ACS TP) o milling
en e p ises inc eases p ocess e iciency and educes
en i onmen al impac by p omo ing esou ce-e icien
p ac ices.
Acco ding o s udies [11-21], he shape o a
whea g ain can be conside ed an i egula geome ic
igu e (see igu e 1). Howe e , o ma hema ical
modeling and nume ical analysis o mois u e
dis ibu ion wi hin he g ain, i s shape is o en
app oxima ed as a egula body, such as an ellipsoid o
a pa aboloid o e olu ion. In ou iew, he mos
e ec i e app oach combines expe imen al and
heo e ical modeling echniques. Using mode n
compu a ional ools (including 3D modeling), i is
possible o de e mine quan i a i e cha ac e is ics o he
g ain’s geome ic pa ame e s, such as leng h,
hickness, and po osi y. These geome ic pa ame e s
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a e hen used in mois u e dis ibu ion simula ions
du ing hyd a ion. A well-s uc u ed hyd a ion p ocess
no only imp o es lou quali y bu can also enhance
ene gy e iciency by a oiding epea ed mois ening o
d ying s eps. Thus, modeling he geome ic pa ame e s
o g ains is a ele an ask ha con ibu es o mo e
accu a e p edic ions o key cha ac e is ics.
Figu e 1. A) Schema ic ep esen a ion o
whea : whole g ain; B) g ain c oss-sec ion.
The objec i e o his s udy is o analyze he
cha ac e is ics o he mos widely cul i a ed whea
a ie ies in he Fe gana Valley o he Republic o
Uzbekis an and o de elop compu e models o hei
g ains. The de eloped compu a ional model enables
he de e mina ion o op imal mois u e pene a ion
imes o di e en g ain laye s, which is c ucial o
imp o ing he e iciency o he hyd a ion p ocess and
o e all lou p oduc ion.
2. METHODS AND MATERIALS
This s udy ocuses on analyzing he geome ic
pa ame e s o wo whea a ie ies “As ” and
“Aleksee ich” and hei in luence on mois u e
abso p ion du ing he hyd a ion p ocess. A
combina ion o mode n expe imen al echniques,
including mic oscopic analysis and digi al 3D
modeling, was employed o ob ain comp ehensi e
da a. To in es iga e he ela ionship be ween g ain size
and hyd a ion beha io p io o milling, wo whea
a ie ies we e selec ed based on hei p e alence
wi hin he ag o-indus ial sec o o he Fe gana Valley,
Republic o Uzbekis an. The choice o “As ” and
“Aleksee ich” a ie ies is jus i ied by hei widesp ead
cul i a ion in he egion and he dis inc i e
physicochemical and geome ic cha ac e is ics ha
signi ican ly impac he hyd a ion p ocess. The “As ”
a ie y is indigenous o Uzbekis an, whe eas
“Aleksee ich” was in oduced om he Russian
Fede a ion. The geome ic pa ame e s ob ained
h ough hese in es iga ions se e as aluable inpu s
o ma hema ical models used in p ocessing ope a ions
such as d ying o o e ly mois g ains o ehyd a ing
excessi ely d y ones.
2.1. Selec ion o whea a ie ies and hei
cha ac e is ics
The geome ic pa ame e s o whea g ain-
including linea dimensions, shape, su ace a ea, and
su ace a ea- o- olume a io-ha e a signi ican impac
on hyd a ion p ocesses. Whea g ains can a y in shape
om o al and o oid o elonga ed, wi h he ollowing
dimensional anges: hickness - 1.4 o 2.7 mm, wid h -
1.4 o 3.6 mm, and leng h - 4.3 o 6.4 mm. The “As ”
and “Aleksee ich” whea a ie ies we e de eloped by
local b eede s and a e well-adap ed o he clima ic
condi ions o Uzbekis an, including he Fe gana
Valley. Thei cha ac e is ics a e summa ized in Table
1.
Table 1. Ag onomic and quali y cha ac e is ics
o he whea a ie ies “As ” and “Aleksee ich”.
As shown in Table 1, he “As ” and
“Aleksee ich” a ie ies exhibi s able adap a ion o
a id and ho clima ic condi ions, making hem
pa icula ly sui able o egions cha ac e ized by high
empe a u es and limi ed humidi y. These a ie ies all
in o IDK (Indi idual Quali y G oup (classi ica ion
based on glu en con en and g ain anslucency)) G oup
2, indica ing compliance wi h speci ic quali y
s anda ds, including glu en con en and g ain
anspa ency. These ai s make bo h a ie ies sui able
o s udies aimed a op imizing hyd a ion p ocesses.
Acco ding o hei physical s uc u e, ana omical
composi ion, and geome ic cha ac e is ics, he mass
a io o g ain componen s a ies wi hin ce ain anges.
Fo lou p oduc ion, a high endospe m pe cen age is a
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c ucial indica o o quali y, as he endospe m con ains
he majo i y o he s a ch and p o ein ha de e mine he
ex u e, nu i ional alue, and baking p ope ies o
lou . The “As ” and “Aleksee ich” a ie ies exhibi
highe endospe m con en , con ibu ing o he
p oduc ion o high-quali y whi e lou . Depending on
p ocessing goals, di e en ypes o lou a e chosen:
o b ead baking, lou wi h a high endospe m con en
is p e e ed, while whole-g ain lou wi h a balanced
composi ion is ecommended o heal hie nu i ion.
Figu e 2 p esen s a compa a i e diag am o he
dis ibu ion o key g ain componen s o he “As ” and
“Aleksee ich” a ie ies.
Figu e 2. Compa a i e Diag am o he Main
G ain Componen s o he “As ” and “Aleksee ich”
Va ie ies. A) “As ” a ie y; B) “Aleksee ich” a ie y;
(1-ge m, 2-endospe m, 3-b an)
In Figu e 2a, he main g ain componen s o he
“As ” a ie y a e shown, consis ing o h ee laye s: he
ge m, endospe m, and b an. Each laye is cha ac e ized
by a speci ic pe cen age ha e lec s i s sha e in he
o al g ain composi ion.
- In Figu e 2A-1, he ge m- he i al ep oduc i e
pa o he g ain-accoun s o 1.4% o 3.8% o
he o al g ain mass. I p o ides he nu ien s
and ene gy equi ed o sp ou ing.
- In Figu e 2A-2, he endospe m, he main
componen , se es as a nu ien ese oi
(p ima ily s a ch) o he de eloping seedling.
I cons i u es 83% o 85% o he g ain mass,
making i he mos signi ican componen in he
“As ” a ie y.
- In Figu e 2A-3, he b an, o ou e p o ec i e
laye , plays a c ucial ole in shielding in e nal
issues om ex e nal ac o s. I makes up 1.1%
o 1.8% o he g ain mass-a ela i ely small
sha e, ye impo an o p o ec ion and
p ese a ion.
Figu e 2B depic s he g ain s uc u e o he
“Aleksee ich” a ie y, which also consis s o he ge m,
endospe m, and b an, hough wi h sligh di e ences in
hei p opo ional composi ions:
- In Figu e 2B-1, he ge m cons i u es 1.2% o
3.4% o he g ain mass, sligh ly less han ha
o he “As ” a ie y, hough s ill essen ial o
sp ou ing.
- In Figu e 2B-2, he endospe m makes up 81%
o 85% o he g ain mass-simila o “As ”,
indica ing compa able nu ien con en
suppo ing seed de elopmen .
- In Figu e 2B-3, he b an accoun s o 1.1% o
1.2%, sligh ly lowe han in he “As ” a ie y.
Despi e i s modes sha e, i plays a p o ec i e
ole in p ese ing in e nal g ain issues.
In summa y, bo h “As ” and “Aleksee ich”
a ie ies sha e simila ana omical s uc u es wi h mino
pe cen age di e ences, which may in luence hei
esis ance o ex e nal s esso s and nu i ional alue. To
analyze he geome ic pa ame e s o he g ain,
compu e modeling, mic oscopy, and expe imen al
echniques we e used. The physicochemical p ope ies
o he g ain we e de e mined in acco dance wi h he
na ional s anda d (GOST) [23] and in e na ional
quali y s anda ds [24]. Hyd a ion pa ame e s we e
assessed by measu ing changes in g ain mass a e
imme sion in wa e a a ious empe a u es and ime
in e als. Thus, he selec ion o he “As ” and
“Aleksee ich” a ie ies is jus i ied by hei
cha ac e is ics and widesp ead cul i a ion, allowing
he esul s o be e ec i ely applied in eal-wo ld
p oduc ion o op imizing echnological p ocesses.
2.2. Me hodology o measu ing g ain
dimensions
To ensu e he p ecise measu emen o he
geome ic pa ame e s o whea g ains, a
comp ehensi e me hodology was employed in his
s udy, inco po a ing mode n ins umen s ha p o ide a
high deg ee o accu acy and ep oducibili y. In
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pa icula , he digi al calipe Mi u oyo 500-196-30
om he Mi u oyo Absolu e Digima ic Calipe se ies
was u ilized o de e mine he linea dimensions o he
g ains (leng h, wid h, and hickness). This ins umen
o e s measu emen p ecision up o 0.001 mm, making
i especially e ec i e o applica ions whe e e en he
sligh es dimensional a ia ions a e o scien i ic
signi icance. Fo mo e de ailed analysis and high-
esolu ion isual obse a ion o he whea g ains, an
op ical mic oscope Mo ic BA310E was used. This
de ice is capable o magni ica ion up o 1000x and
o e s excellen op ical esolu ion. I enabled ho ough
examina ion o he mic os uc u e o he g ains and
accu a e measu emen s o hei dimensions a he
mic ome e scale. The supe io op ical capabili ies o
he mic oscope we e essen ial o s udying he
ana omical and s uc u al ea u es o he g ains in he
con ex o hyd a ion p ocesses. In addi ion, o cons uc
h ee-dimensional models o he g ains and o
in es iga e hei su ace mo phology in de ail, a 3D
scanne EinScan P o 2X Plus was employed. This
de ice is capable o gene a ing highly accu a e 3D
ep esen a ions o objec s, enabling no only he
assessmen o linea dimensions bu also he
calcula ion o g ain olume and su ace a ea wi h high
p ecision. This app oach allows o a mo e
comp ehensi e analysis o he g ain’s geome ic
pa ame e s, which is pa icula ly impo an in s udies
o hyd a ion, whe e su ace a ea and olume di ec ly
in luence he a e and e iciency o wa e abso p ion.
Figu e 3. Geome ic ep esen a ions o whea
g ain o he “As ” a ie y: A) Op ical mic og aph o
c oss-sec ion (scale ba =200 µm); B) 3D scanne
image o in ac g ain.
Using he a o emen ioned ins umen s, p ecise
geome ic cha ac e is ics o whea g ains we e
ob ained and subsequen ly analyzed wi hin he
amewo k o his esea ch. Figu e 3 p esen s he
images o he whea g ains acqui ed ia he op ical
mic oscope and 3D scanne , clea ly demons a ing he
high quali y and eliabili y o he collec ed da a, as well
as hei compliance wi h he me hodological
equi emen s o he s udy.
Table 1 p esen s he esul s o he geome ic
measu emen s o whea g ains o he “As ” and
“Aleksee ich” a ie ies, ob ained using he digi al
calipe . These esul s con i m he high p ecision o he
measu emen s and hei alignmen wi h he esea ch
objec i es.
2.3. 3d Modeling o whea g ain
To in es iga e he geome ic cha ac e is ics o
whea g ains and analyze hei shape, olume, and
su ace a ea, his s udy employed 3D modeling
echniques. This app oach enhanced measu emen
accu acy and acili a ed a deepe unde s anding o he
hyd a ion p ocesses o he g ain. This sec ion ou lines
he ools and so wa e used, he s eps in ol ed in
cons uc ing 3D models, and he analysis o he
esul ing models. A 3D model o he whea g ain
a ie y “As ” was de eloped using Au odesk 3ds Max
so wa e. In he ini ial s age, he whea g ain was
scanned using he EinScan P o 2X Plus 3D scanne .
Figu e 4. 3D models o “As ” whea g ain: A)
Ini ial scan model; B) Mesh cons uc ion; C)
Pa ame e ized model p epa ed o analysis; D) 3D
isualiza ion o he whea g ain’s shape.
This p ocedu e yielded de ailed digi al images
wi h high p ecision. Scanning was conduc ed in wo
modes: High-Resolu ion Mode o cap u ing de ailed

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geome ic ea u es, and Rapid Scan Mode o
p elimina y shape analysis. The ob ained digi al
models we e hen impo ed in o 3ds Max, whe e noise
a i ac s in oduced du ing scanning we e emo ed,
and he g ain dimensions we e pa ame e ized.
Pa ame e iza ion in ol ed iden i ying key me ics
(leng h, wid h, hickness) and gene a ing a mesh model
composed o nume ous iangles, which enabled
accu a e ep oduc ion o he g ain su ace. In he inal
s age, he 3D models we e e i ied using SolidWo ks.
This e i ica ion in ol ed compa ing he 3D model
dimensions o hose ob ained ea lie using he digi al
calipe . Su ace a ea and olume calcula ed om he
models we e c oss- alida ed wi h expe imen al da a,
and mesh adjus men s we e made o minimize
disc epancies. The 3D models c ea ed se ed as a
ounda ion o he p ecise de e mina ion o geome ic
p ope ies, including su ace a ea, olume, and shape.
These da a we e hen analyzed o es ablish co ela ions
be ween he g ain’s geome ic pa ame e s and i s
hyd a ion beha io . Figu e 4 p esen s examples o 3D
models o he “As ” whea g ain de eloped using he
desc ibed me hodology.
The applica ion o 3D modeling signi ican ly
imp o ed he accu acy o geome ic analysis, which is
essen ial o op imizing hyd a ion p ocesses and
enhancing whea p ocessing quali y unde eal-wo ld
indus ial condi ions. Based on he analysis shown in
Figu e 4, i was obse ed ha he g ain su ace exhibi s
g oo es o inden a ions. Du ing hyd a ion, he a e o
mois u e pene a ion h ough hese g oo es
signi ican ly exceeds he di usion a e h ough o he
su ace a eas. This e ec mus be conside ed when
compa ing ma hema ical modeling esul s wi h
expe imen al da a ha e lec he empo al and spa ial
dis ibu ion o mois u e con en . The esea ch indings
suppo he selec ion o “As ” and “Aleksee ich”
whea a ie ies based on hei geome ic p ope ies and
he analy ical me hods applied. The use o mode n
measu emen ools-such as he digi al calipe , op ical
mic oscope, and 3D scanne -ensu ed high da a
accu acy and allowed o de ailed examina ion o
c i ical g ain pa ame e s and hei impac on hyd a ion
p ocesses.
The in eg a ion o 3D modeling echniques
enabled a mo e comp ehensi e analysis by p o iding
p ecise da a on shape, su ace a ea, and olume. The
combined use o hese ools and me hods no only
enhanced he eliabili y o he esul s bu also
con i med hei p ac ical ele ance o op imizing
hyd a ion and whea p ocessing echnologies. These
conclusions a e pa icula ly aluable o imp o ing he
quali y o ag o-indus ial p oduc ion in he Fe gana
Valley and o he egions wi h simila clima ic
condi ions. The esul s ob ained can be in eg a ed in o
echnological wo k lows, he eby inc easing he
e iciency and p oduc i i y o g ain p ocessing
ope a ions.
2.4. Hyd a ion p o ocol and s a is ical
analysis.
Hyd a ion expe imen s we e conduc ed on n =
50 indi idual g ains pe a ie y (“As ” and
“Aleksee ich”), wi h h ee independen eplica es a
each empe a u e condi ion. P io o hyd a ion, g ains
we e cleaned, so ed by size o emo e ou lie s, and
equilib a ed a labo a o y oom empe a u e (22 ± 1
°C). Each eplica e was imme sed in dis illed wa e a
a ixed g ain- o-wa e a io o 1:20 (w/ ) o ensu e
excess wa e a ailabili y. Two empe a u e egimes
we e es ed: cold hyd a ion (20–25 °C) and wa m
hyd a ion (40–50 °C). Wa e ba hs (±0.5 °C p ecision)
we e used o main ain cons an empe a u e, and no
agi a ion was applied du ing he expe imen s.
Hyd a ion ime poin s we e se a 5, 10, 15, 20, 25, and
30 minu es. A each in e al, g ains we e emo ed,
gen ly blo ed wi h il e pape o elimina e su ace
mois u e, and immedia ely weighed using an analy ical
balance (±0.001 g). The ela i e change in g ain mass
was calcula ed using he ollowing equa ion:
∆𝑚(%)=100×𝑚𝑡−𝑚0
𝑚0
whe e 𝑚𝑡 is he g ain mass a ime , and 𝑚0 is
he ini ial d y mass.
All measu emen s a e epo ed as mean ±
s anda d de ia ion (SD). S a is ical analysis was
pe o med using one-way ANOVA, ollowed by
Tukey’s HSD pos -hoc es o assess pai wise
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di e ences be ween a ie ies and empe a u e egimes.
The signi icance h eshold was se a α = 0.05. E ec
sizes we e es ima ed using Cohen’s d, and 95%
con idence in e als (CI) we e calcula ed o all mean
alues. Boxplo s (Figu e 6) display he dis ibu ion o
g ain dimensions and hyd a ion da a. In each plo , he
cen al line indica es he median, boxes ep esen he
in e qua ile ange (IQR), whiske s ex end o 1.5 ×
IQR, and indi idual poin s beyond he whiske s a e
conside ed ou lie s.
2.5. Da a analysis
P e-p ocessing and quali y con ol. All aw
measu emen s (leng h, wid h, hickness, and hyd a ion
mass o e ime) we e sc eened o en y e o s and
biologically implausible alues. Ou lie s we e
iden i ied as poin s beyond 1.5×IQR in p elimina y
boxplo s and we e inspec ed agains expe imen al
no es (e.g., chipped ke nels, incomple e blo ing).
Unless a p ocedu al e o was documen ed, alues
we e e ained o p ese e na u al a iabili y; summa y
plo s (Fig. 6–7) display hese poin s anspa en ly.
Desc ip i e s a is ics. Fo geome ic pa ame e s
and hyd a ion ou comes, mean ± s anda d de ia ion
(SD) and 95% con idence in e als (CI) we e epo ed,
wi h CIs compu ed as 𝑥±𝑡0.975,𝑑𝑓𝑠/√𝑡. Dis ibu ional
summa ies we e isualized using boxplo s (Fig. 6) and
ime-cou se cu es (Fig. 7).
Assump ion checks. P io o pa ame ic
in e ence, no mali y o esiduals was assessed using
Shapi o–Wilk es s and Q–Q plo s, and homogenei y o
a iances ac oss g oups was e alua ed by Le ene’s
es . When assump ions we e no ully me , obus CIs
(bias-co ec ed and accele a ed, BCa) we e ob ained
ia nonpa ame ic boo s ap (10,000 esamples), and p-
alues we e complemen ed by e ec sizes.
In e en ial compa isons.
- Geome y (Table 2; Fig. 6): Be ween- a ie y
di e ences in leng h, wid h, and hickness we e
es ed wi h one-way ANOVA ( ac o : Va ie y)
o each dimension, ollowed by Tukey’s HSD
o pai wise con as s. E ec sizes we e
exp essed as Cohen’s d wi h 95% CI.
- Hyd a ion endpoin (30 min): Mass gain (%) a
30 min was analyzed using wo-way ANOVA
wi h ixed ac o s Va ie y (As , Aleksee ich)
and Tempe a u e (20–25 °C, 40–50 °C),
including he in e ac ion e m. Tukey’s HSD
con olled he amily-wise e o a e o simple
e ec s. Pa ial η2 was epo ed o indica e
ac o impo ance.
- Full ime-cou se: Because epea ed
measu emen s we e aken ac oss ime wi hin
eplica es, mass-gain ajec o ies we e modeled
using a linea mixed-e ec s amewo k:
𝑦𝑖𝑗𝑘𝑙=𝛽0+𝛽1𝑉𝑎𝑟𝑖𝑒𝑡𝑦𝑖+𝛽2𝑇𝑒𝑚𝑝𝑗+𝛽3𝑡𝑘
+𝛽4(𝑉𝑎𝑟𝑖𝑒𝑡𝑦×𝑇𝑒𝑚𝑝)𝑖𝑗
+𝛽5(𝑉𝑎𝑟𝑖𝑒𝑡𝑦×𝑡)𝑖𝑘
+𝛽6(𝑇𝑒𝑚𝑝×𝑡)𝑗𝑘+𝑢𝑙+𝜖𝑖𝑗𝑘
whe e a andom in e cep 𝑢𝑙 accoun ed o
eplica e (and o g ain, when acked), and ∈𝑖𝑗𝑘𝑙
deno ed he esidual. Time (min) was ea ed as
con inuous and was ep esen ed wi h a es ic ed cubic
spline (3 kno s) o cap u e cu a u e. Signi icance was
de e mined by likelihood- a io es s (nes ed models)
wi h Sa e hwai e deg ees o eedom. Model
adequacy was checked h ough esidual diagnos ics
(homoscedas ici y and independence ac oss ime).
Empi ical kine ics and cha ac e is ic imes. Fo
each condi ion (Va ie y×Tempe a u e), hyd a ion
kine ics we e summa ized by i ing a Weibull- ype
up ake model o he mean cu e ( eplica e-le el i s
we e used in sensi i i y analysis):
𝑋(𝑡)=𝑋∞[1−𝑒𝑥𝑝{−(𝑡/𝜏)𝛽}]
whe e 𝑋∞ deno es he asymp o ic gain, τ a scale
pa ame e , and β a shape pa ame e . Cha ac e is ic
imes we e compu ed analy ically:
𝑡50=𝜏(𝑙𝑛2)1/𝛽, 𝑡95=𝜏(𝑙𝑛20)1/𝛽
Unce ain y (95% CI) o 50 and 95 was
es ima ed by nonpa ame ic boo s ap (10,000
esamples). The esul ing alues a e epo ed in Table
4 alongside di usion-model p edic ions.
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Physics-based model alida ion. Ag eemen
be ween expe imen al da a and di usion simula ions
(Sec ion 3.3) was quan i ied using he oo -mean-
squa e e o (RMSE) o he ime cou ses and
absolu e/ ela i e e o s in 50 and 95:
𝑅𝑀𝑆𝐸=√1𝑁∑(𝑋𝑒𝑥𝑝(𝑡𝑘)−𝑋𝑚𝑜𝑑𝑒𝑙(𝑡𝑘))2
𝑁
𝑘=1
Mean absolu e pe cen age e o (MAPE) was
addi ionally epo ed o in e p e abili y. Pa ame e
sensi i i y (±20% a ound baselines in Table 3) was
p opaga ed o 50 and 95 and summa ized using pa ial
ank co ela ion coe icien s (PRCC).
Mul iple es ing and epo ing. The o e all
signi icance h eshold was se a α=0.05. Pos -hoc
compa isons used Tukey’s HSD. Alongside p- alues,
e ec sizes (Cohen’s d, pa ial η2) and 95% CIs we e
p esen ed o emphasize p ac ical signi icance.
So wa e and ep oducibili y. S a is ical
analyses we e conduc ed in R (lme4, emmeans, ca ) o
Py hon (s a smodels, pingouin, sciki -pos hocs), and
igu es we e gene a ed wi h ggplo 2 o ma plo lib.
Di usion simula ions we e un in COMSOL
Mul iphysics 6.1. Analysis sc ip s and da a a e
a ailable om he co esponding au ho upon
easonable eques .
3.RESULTS
This s udy p esen s he esul s o he analysis o
geome ic pa ame e s o whea g ains om he “As ”
and “Aleksee ich” a ie ies, as well as an in es iga ion
in o he hyd a ion p ocess and i s e ec on changes in
g ain mass. The measu emen s e ealed signi ican
di e ences in he size and shape o he g ains, which
di ec ly in luence he a e and ex en o mois u e
abso p ion. Pa icula emphasis was placed on he
e ec o wa e empe a u e on he in ensi y o
hyd a ion, as well as on he modeling o mois u e
dis ibu ion wi hin he g ain using ad anced 3D
echniques. The indings p o ide aluable insigh s in o
he dynamics o wa e up ake and highligh he c i ical
ole o g ain mo phology in hyd a ion e iciency. The
ob ained da a se e as a ounda ion o he op imiza ion
o hyd a ion and milling p ocesses. Such op imiza ion
is expec ed o signi ican ly imp o e lou quali y and
educe aw ma e ial losses du ing indus ial
p ocessing.
3.1. Measu emen o geome ic pa ame e s
o whea g ain
An essen ial aspec o he whea g ain hyd a ion
p ocess is he conside a ion o i s geome ic
cha ac e is ics, as he shape and size o he g ains
signi ican ly in luence he a e and ex en o mois u e
abso p ion. In his s udy, linea dimensions o whea
g ains om he “As ” and “Aleksee ich” a ie ies
we e measu ed, e ealing subs an ial di e ences in
hei geome ic pa ame e s. Figu e 5 illus a es he
p incipal geome ic pa ame e s o whea g ains,
including leng h, wid h, and hickness. The main
diag am p esen s a op iew o a g ain, clea ly
indica ing i s leng h and wid h, while an enla ged
segmen highligh s he hickness measu emen . These
pa ame e s a e c i ical o analyzing he physical
p ope ies o he g ain, which plays a signi ican ole in
op imizing s o age, p ocessing, and anspo a ion
p ocesses in he ag icul u al and ood indus ies.
Figu e 5. Geome ic pa ame e s o whea g ain:
leng h, wid h, and hickness.
Table 2 summa izes he a e age geome ic
cha ac e is ics o whea g ains om he “As ” and
“Aleksee ich” a ie ies. As shown, he a e age leng h
o “As ” g ains (5.6 mm) sligh ly exceeds ha o
“Aleksee ich” g ains (5.3 mm). Simila ly, di e ences
a e obse ed in wid h and hickness: he a e age wid h
o “As ” g ains is 2.45 mm compa ed o 2.2 mm o
“Aleksee ich”, and he hickness is 2.05 mm e sus 1.7
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mm, espec i ely. These a ia ions in linea
dimensions may be a ibu ed o he gene ic ai s o he
a ie ies and he condi ions unde which hey we e
cul i a ed. Unde s anding hese geome ic di e ences
is impo an o p edic ing g ain beha io du ing
hyd a ion, as size in luences bo h he speed and
uni o mi y o mois u e pene a ion. Thus, he da a
p esen ed in Table 2 p o ide a basis o u he analysis
and modeling o p ocesses ela ed o g ain hyd a ion
and p ocessing.
Table 2. A e age geome ic cha ac e is ics o
whea g ain a ie ies
Pa ame e
As (mm)
Aleksee ich
(mm)
Leng h
5.6
5.3
Wid h
2.45
2.2
Thickness
2.05
1.9
Figu e 6 p esen s an analysis o he a ia ions
in geome ic pa ame e s o “As ” and “Aleksee ich”
whea g ains. This isualiza ion clea ly depic s he
ange o changes in g ain leng h, wid h, and hickness,
as well as he median alues o each pa ame e . Figu e
6A in shows ha “As ” g ain leng h a ies om 5.0 o
6.2 mm, wi h a median close o he uppe bound,
whe eas “Aleksee ich” g ain leng h anges om 4.8 o
5.6 mm, wi h a median nea he cen e o he ange.
This indica es ha , on a e age, “As ” g ains a e longe
han “Aleksee ich” g ains. Figu e 6B demons a es
ha “As ” g ain wid h anges om 1.8 o 3.1 mm,
while “Aleksee ich” g ains a y be ween 1.6 and 2.3
mm. The wide alue ange and highe median con i m
ha “As ” g ains a e gene ally b oade . Figu e 6C
shows he hickness dis ibu ion: “As ” g ains ange
om 1.7 o 2.4 mm, while “Aleksee ich” g ains all
wi hin 1.4 o 2.0 mm. The median hickness o “As ”
g ains is g ea e han ha o “Aleksee ich”, u he
a i ming “As ”'s supe io i y in his dimension.
Figu e 6. Compa ison o geome ic pa ame e s o
whea g ains om “As ” and “Aleksee ich” a ie ies:
A) leng h. B) wid h. C) hickness. Boxplo s show
median (cen e line), in e qua ile ange (box),
whiske s o 1.5×IQR; poin s beyond whiske s a e
ou lie s.
The diag am analysis con i ms ha he “As ”
a ie y has ad an ages ac oss all h ee geome ic
pa ame e s-leng h, wid h, and hickness-compa ed o
he “Aleksee ich” a ie y. These di e ences a e likely
due o a ie al gene ic ai s and should be conside ed
when selec ing a a ie y o speci ic g owing
condi ions o p ocessing pu poses. The esul s can also
be used o op imize echnological p ocesses associa ed
wi h g ain handling and ea men .
3.2. The hyd a ion p ocess and mass change
o whea g ain
The hyd a ion p ocess o whea g ains was
in es iga ed unde a ying wa e empe a u es and
ime in e als. Changes in g ain mass indi ec ly
indica e he a e o mois u e di usion and he quan i y
o wa e abso bed by he g ain. Expe imen al esul s
e ealed ha he mos signi ican mass inc ease
occu ed when he g ains we e ea ed wi h wa m wa e
(40-50°C), whe eas hyd a ion in cold wa e (20-25°C)
p oceeded a a slowe a e. Figu e 7 illus a es he
changes in g ain mass as a unc ion o wa e
empe a u e and p ocessing ime.
G ain mass was measu ed e e y 5 minu es,
beginning a he 5 h minu e and concluding a he 30 h
minu e o ea men . Figu e 7 p esen s he g aphs
depic ing he change in mass o whea g ains om wo