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\begin{document}

\title{Effect of functional lipids on the quality of walnut butter prepared
from defatted walnut meal by ball mill grinding}



\author[1]{Yuxin Xie}%
\author[2]{Nan Jiang}%
\author[2]{Hongchen Su}%
\author[2]{Feng Tan}%
\author[2]{Xi Cheng}%
\author[2]{Jiyan Wang}%
\author[1]{Hao Hu}%
\affil[1]{Affiliation not available}%
\affil[2]{Huazhong Agricultural University}%


\vspace{-1em}



  
  \date{May 24, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Abstract In this study, walnut butter was produced by mixing functinal
lipids with defatted walnut meal. Three kinds of functional
lipids(FL), medium-chain triglycerides (MCT), diacylglyceroe (DG), and
conjugated linoleic acid glycerides (CLA), were used to make functional
lipids walnut butter(FLWB) and their physical properties as well as
microscopic morphology were compared with commercial walnut butters. The
FLWBs were prepared by grinding FL and defatted walnut meal through the
ball milling technique. The mixing ratios of FL and defatted walnut meal
were 6:4, 6.5:3.5, 7:3. It was found that the fluidity of FLWB was
increased with the addition amount of FL, but the particle size of FLWB
was decreased with the addition amount of DG or CLA. As the additions of
DG and CLA increased from 60\% to 70\%, the D (4,3) of DG-WB and CLA-WB
decreased by 36.23\% and 20.88\%; the flowability index increased by
15.74\% and 168.91\%. As the addition of MCT increased from 60\% to
70\%, there was no significant difference in D (4,3) of MCT-WB, but the
flowability index increased by 717.34\%. Microrheological properties
indicated that both FLWB and commercial walnut butter exhibited
viscoelastic characteristics. The rheology showed that the FLWB was
non-Newtonian pseudoplastic fluids, which was similar to the commercial
walnut butter. The DG-WB and CLA-WB were closer to the commercial walnut
butter, compared with MCT walnut butter. The microstructure further
indicated that the walnut butter with 65\% CLA addition was closer to
the commercial walnut butter.%
\end{abstract}%



\sloppy


\textbf{The effect of functional lipids on the quality of walnut butter
prepared from defatted walnut meal by ball mill grinding}

Yuxin xie\textsuperscript{a,b,c}, Nan Jiang\textsuperscript{a,b,c},
Hongchen Su\textsuperscript{a,b,c}, Feng Tan\textsuperscript{a,b,c}, Xi
Cheng\textsuperscript{a,b,c}, Jiyan Wang\textsuperscript{a,b,c}, Hao
Hu\textsuperscript{a,b,c,}*

\textsuperscript{a} College of Food Science and Technology, Huazhong
Agricultural University, Wuhan, Hubei 430070, PR China

\textsuperscript{b} Key Laboratory of Environment Correlative Dietology,
Huazhong Agricultural University, Ministry of Education, PR China

\textsuperscript{c} Hubei Key Laboratory of Fruit \& Vegetable
Processing \& Quality Control (Huazhong Agricultural University), Wuhan,
Hubei 430070, PR China

\textbf{*} Corresponding Author: Dr. Hao Hu

College of Food Science and Technology, Huazhong Agricultural
University, No. 1, Shi Zi Shan Road, Wuhan 430070, China.

E-mail: huhao@mail.hzau.edu.cn, Tel.: +86-15971475341

\textbf{Abstract}

In this study, walnut butter was produced by mixing functinal lipids
with defatted walnut meal. Three kinds of functional lipids(FL),
medium-chain triglycerides (MCT), diacylglyceroe (DG), and conjugated
linoleic acid glycerides (CLA), were used to make functional lipids
walnut butter(FLWB) and their physical properties as well as microscopic
morphology were compared with commercial walnut butters. The FLWBs were
prepared by grinding FL and defatted walnut meal through the ball
milling technique. The mixing ratios of FL and defatted walnut meal were
6:4, 6.5:3.5, 7:3. It was found that the fluidity of FLWB was increased
with the addition amount of FL, but the particle size of FLWB was
decreased with the addition amount of DG or CLA. As the additions of DG
and CLA increased from 60\% to 70\%, the D (4,3) of DG-WB and CLA-WB
decreased by 36.23\% and 20.88\%; the flowability index increased by
15.74\% and 168.91\%. As the addition of MCT increased from 60\% to
70\%, there was no significant difference in D (4,3) of MCT-WB, but the
flowability index increased by 717.34\%. Microrheological properties
indicated that both FLWB and commercial walnut butter exhibited
viscoelastic characteristics. The rheology showed that the FLWB was
non-Newtonian pseudoplastic fluids, which was similar to the commercial
walnut butter. The DG-WB and CLA-WB were closer to the commercial walnut
butter, compared with MCT walnut butter. The microstructure further
indicated that the walnut butter with 65\% CLA addition was closer to
the commercial walnut butter.

\textbf{Keywords} : Defatted walnut meal; Walnut butter; Functional
lipids; Vibratory ball mill; Processing characteristics

\textbf{Introduction}

Walnut is one of the most widely grown nut food in the world, which is
popular due to its high economic value. China accounts for 48\% of the
world's walnut productions (Qu et al., 2016). Most walnut is used for
walnut oil (WO) extraction, while many defatted walnut meals are
produced during this processing. Defatted walnut meal contain more than
40\% protein and have high levels of arginine and glutamic acid, while
other essential amino acids for the human body (Sun et al., 2019).
Defatted walnut meal are often used as animal feed or directly wasted in
landfills (Feng et al., 2021). At present, there have been studies on
the extraction of active ingredients from defatted walnut meal, such as
walnut protein or active peptide (Feng et al., 2021). In addition to
this utilization, there is still a need to further improve the
comprehensive utilization of defatted walnut meal.

Traditionally, walnut kernels were roasted and then ground to make
walnut butter. (Zhaohua et al., 2020). However, the fat content of
walnut butter is high, while excessive intake of high-fat foods can
increase the risk of obesity and cardiovascular disease (Lu et al.,
2019). Therefore, the development of Low-fat and functional walnut
butter is becoming a new trend in the nut industry. In order to reduce
oil amount of walnut butter, some previous studies produced the product
by adding water rather than oil. However, the higher the moisture
content of the walnut butter, the more likely it is to have a negative
impact on the sensory properties (Mehdi et al., 2019). The oils in
walnut butter are beneficial to enhance the processing characteristics
and stability of the product, so it is better to use oil as the mobile
phase of walnut butter. Therefore, using choice of functional lipids
(FL) to replace the oil in traditional nut butters may maintain the
quality of nut butter.

FL, such as medium-chain triglycerides (MCT), diacylglyceroe (DG), and
conjugated linoleic acid glycerides (CLA), could meet people's need for
flavorful oils and reduce fat energy intake. Moreover, FL has many
beneficial physiological effects such as losing weight and reducing
blood lipid. MCT has good antioxidant stability, which is naturally
found in foods such as palm oil and coconut oil (Walker et al., 2017).
DG is a trace component of natural vegetable oils, which can be used as
a substitute for animal fat in meat processing. These meat products
usually had better stability (Miklos et al., 2011). CLA is a
physiological active material, which have potentially antitumor and
anti-atherosclerosis effects (Belury, 2002).

Traditionally, walnut butter were usually ground by stone mills,
high-speed grinders, and colloid mills (Wagener and Kerr, 2018). It is
hard to obtain small walnut butter particle sizes by one time of
grinding using the above mentioned traditional grinding methods. So a
secondary grinding is necessary for walnut butter to reach a specific
particle size range. Vibration ball milling is a new ultrafine grinding
technology. Ball milling could exert collisional, compressive, shear,
and frictional forces on the sample during the collision processing. The
frictional process could lead to local heating, causing thermochemical
reactions (Steiner et al., 2016). Therefore, after ball milling
treatment, the processed material undergoes reversible internal
structural rearrangement. This process can create new active surfaces or
result in covalent bond breakage, and thus changing the molecular
conformation and chemical bonding of the material (Karinkanta, 2014;
Marti, 2004). Based on the above mentioned information, ball milling
technology is gaining more and more attention as a new, efficient and
green grinding technology in the food field. Vibration ball milling may
effectively reduced the particle size of walnut butter with only one
time of grinding. Consequently, this study aimed to make comprehensive
utilization of defatted walnut meal to make a healthier and marketable
FLWB by vibration ball milling technology.

\textbf{Materials and Methods}

\textbf{2.1 Materials}

Commercial walnut butter-1 (SS1, purchased from Shengyuan Agricultural
Technology Co., Ltd), commercial walnut butter-2 (SS2, purchased from
Tianjin Jizhou Green Food Group Co., Ltd), commercial walnut butter-3
(SS3, Purchased from Nanshizhao Food Group Co., Ltd); defatted walnut
meal(purchased from Hebei Chenxing Biotechnology Co., Ltd); medium-chain
triglyceride(purchased from Wuhan Kangcan Biotechnology Co., Ltd),
diglyceride(purchased from Xi'an Huageng Biotechnology Co., Ltd), and
conjugated linoleic acid lipid (Purchased from Qingdao Aohai
Biotechnology Co., Ltd, all three FL are food grade). All chemicals were
purchased from Sinopharm Chemical Reagent Co.,Ltd. They included: Methyl
red indicator, methyl blue indicator, petroleum ether, sodium dodecyl
sulfate.

\textbf{2.2 Preparation of FLWB}

Preparation of FLWB was according to a previous method with optimization
(Mostafa et al., 2019). The oil phase (MCT, DG, CLA) and defatted walnut
meal were premixed in the weight ratios of 6:3, 6.5:3.5 and 7:3. Then
the premixed samples were further ground in a ball milling (RETSCHMM
400, Retsch, Germany) tank. The walnut butter prepared with three
functional lipids were noted as MCT-WB, DG-WB, CLA-WB. In the case of
MCT: walnut butter prepared with 60\%, 65\% and 70\% MCT was noted as
MCT-6, MCT-6.5 and MCT-7. The FLWB was stored in 25 mL sealed sample
bottles at 4 \selectlanguage{ngerman}± 2°C (taken within three days). Before analysis, the
samples were removed from the freezer and kept at 25 ± 2°C for 1 h for
subsequent tests.

\textbf{2. 3 Measurement of particle size}

Particle size measurement are performed according to the previous method
(Liu et al., 2007). The walnut butter was dissolved in sodium dodecyl
sulfate (SDS) solution (0.1\%) at a ratio of 1:50 (w/v), then stirred
with a magnetic stirrer and shook with a vortex shaker until the walnut
butter was well dispersed. The particle size of the samples was measured
using a particle size analyzer (Mastersizer 2000, Malvern, UK). The
walnut butter to be measured was added to 1000 mL of deionized water and
the stirring paddle speed was set to 2000 rpm. The degree of shading was
kept in the range of 10 - 15\%. The refractive index of the dispersed
phase (aqueous phase) was 1.330. The refractive index of the oil phases
is shown in Table S1. The volumetric mean particle size D (4, 3) was
used to indicate the sample particle size. The measurements were
repeated at least three times for each sample.

\textbf{2. 4 Color of walnut butter}

The determination of color was referenced to a previous method (Sun et
al., 2015). The color parameters of walnut butter were determined with a
colorimeter (Ultrascan VIS, HuntereLab, USA). Where L* reflected the
brightness of the product, a* indicated a red-green value and b*
indicated a yellow-blue value. The measurements were repeated at least
three times for each sample.

\textbf{2.5 Determination of rheological properties}

\textbf{2.5.1 Measurement of oil viscosity}

The rheological properties of walnut butter were measured based on a
previous method (Mostafa et al., 2019). The viscosity of the oil was
determined using a DHR 2 rheometer (Waters, USA). Experimental
conditions: an aluminum plate of 60 mm with a taper of 1.007° was
selected, plate spacing was set to 500 \selectlanguage{greek}μ\selectlanguage{english}m, the temperature was set to
25\selectlanguage{ngerman}°C, and the frequency variation range was set to 1 - 100
s\textsuperscript{-1}.

\textbf{2.5.2 Measurement of apparent viscosity}

The apparent viscosity of walnut butter was measured with the shear rate
from 1 s\textsuperscript{-1} to 100 s\textsuperscript{-1} using a
rheometer at 25°C. The hydrodynamic variation curves of the walnut
butter were recorded.

\textbf{2.5.3 Frequency scanning}

Strain scan results were used to determine the linear viscoelastic
region (LVE) of the walnut butter. The samples were placed as uniformly
as possible between the plates. The frequency was fixed at 10 rad/s or 1
Hz and the stress variation range was set to 0.01\% - 100\%.

The viscoelastic properties of the walnut butter was determined by
selecting the small amplitude dynamic frequency scan mode. Depending on
the measurement, the strain was fixed at 0.01\% (linear viscoelastic
region). In the linear state, the scanning frequency was set from 0.1
rad/s to 100 rad/s. The numerical changes of the energy storage modulus
(G') and the energy dissipation modulus (G'') were recorded.

\textbf{2.5.4 Determination of thixotropy}

A two-step steady state flow procedure was used to increase the shear
rate from 0 s\textsuperscript{-1} to 150 s\textsuperscript{-1}. And
immediately afterward decrease it from 150 s\textsuperscript{-1} to 0
s\textsuperscript{-1} at the same rate of change. The variation of shear
stress and viscosity with the shear rate were recorded throughout the
process. The obtained data were simulated curvilinearly using the cross
model.

\textbf{2.6 Microrheological characterization}

The microrheological properties were determined with reference to a
previous method (Mengjie et al., 2021). The microrheological properties
of walnut butter were investigated using a microrheometer (Rheolaser
Master, France). The freshly prepared walnut butter was placed in a 4 mL
cylindrical glass tube to observe the Brownian Motion of the particles.
The setting time was 4 h, and the temperature was 25°C. The changes in
the mean square displacement (MSD) curve, the elasticity index (EI),
solid-liquid balance index (SLB), and the flow index (FI) of the sample
particles were recorded using Rheosoft Master software 1.4.0.0 software.
The elasticity index (EI), solid-liquid balance index (SLB), and the
flow index (FI) were obtained from the mean square displacement (MSD)
curves. EI was the inverse of the height value of the plateau zone in
the MSD curve. SLB was the slope value of the elastic plateau zone of
the MSD curve. FI was the inverse of the characteristic decorrelation
time corresponding to the decorrelation time required to reach the
correlated scatter plot (Fernandes and Salas Mellado, 2018).

\textbf{2.7 Microstructure of walnut butter}

The microstructures were observed using a Nikon Eclipse Ti-S (Nikon
Instruments Inc, USA) microscope. After taking 1 \selectlanguage{greek}μ\selectlanguage{english}L of sample on a slide
and smearing it well, the microstructure of FLWB was observed with a 40x
objective. The images were acquired as quickly as possible for better
image assurance.

\textbf{3. Results and discussion}

\textbf{3.1 Particle Size Distribution}

As shown in Fig. 1, the particle size distribution curves of the three
commercially available walnut butter were similar (Fig. 1A). However,
from Fig. 1 B it was observed that SS3 had the smallest D (4,3) value
(33.55 \selectlanguage{ngerman}± 0.41 \selectlanguage{greek}μ\selectlanguage{english}m), which was significantly different from SS1 (50.76\selectlanguage{greek}μ\selectlanguage{english}m)
and SS2 (55.14\selectlanguage{greek}μ\selectlanguage{english}m) (P\textless{}0.05). The fluidity of walnut butter
increased with the reduction of particle size, which may result in a
finer texture when consumed (Nam et al., 2014). Compared to commercial
walnut butter, the FLWB prepared with MCT, DG, or CLA and defatted
walnut meal showed a single-peak particle size distribution with a
central peak width range of 1.78 -- 796.21 \selectlanguage{greek}μ\selectlanguage{english}m for all samples (Fig. 1A).
It was noticed that adding 65\% of CLA or 70\% CLA significantly moved
the prominent peak of the particle size distribution to the left. It was
found that the average particle size of DG walnut butter and GLA walnut
butter decreased with increasing oil addition ratio. However, the
average particle size of MCT walnut butter showed no significant
difference at different MCT addition ratios. As the addition of DG or
CLA increased from 60\% to 70\%, the average particle size of walnut
butter decreased by 36.23\% and 20.88\%, respectively (Fig. 1B). The
particle size of commercial walnut butter varied considerably as shown
in D (4,3) for SS1, SS2, and SS3. The particle size of MCT-WB did not
vary with the addition of MCT, but the particle size of DG-WB or CLA-WB
could be adjusted by adjusting the addition of DG or CLA, which was used
to prepare a product with a particle size more similar to that of
commercial walnut butter. The above results indicated that the particle
size data of FLWB could have similar characters with commercially walnut
butter after ball milling treatments.

\textbf{3.2 Color of walnut butter}

Color was usually an unappreciated physical parameter (Jose Moyano et
al., 2010). However, the study by Gambaro showed that color could
influence the preferences of consumers (Gambaro et al., 2014). In the
color analysis, L* represented lightness and darkness (black and white),
a* represented red-green, and b* represented yellow-blue. Table 1
represented the color difference results of different walnut butter.
There were significant differences (\emph{p\textless{}0.05} ) in the L*,
a*, and b* between the FLWB and commercial walnut butter. MCT-WB had
slightly higher L* than SS1 and SS2. The L*, a* and b* of DG-WB and
CLA-WB were lower than those of commercial walnut butter. As a result,
the color of the sauces showed different degrees of yellow color for
commercial walnut butter and FLWB. The b* of FLWB was significantly
lower than the commercial walnut butter. The oil in traditional walnut
butter was mainly derived from the walnut oil in the walnut kernels, and
its color was mainly influenced by the beta-carotene contained in the
walnut oil (Misawa, 2009). The carotenoid content in walnuts ranged from
0.08-0.49 mg/kg (Ozrenk et al., 2012), which was resulting in a higher
yellow value of walnut oil (Mart\selectlanguage{ngerman}ínez et al., 2008). As a result, walnut
oil had a more yellow color due to its highest carotenoid content, while
other oils appear lighter yellow or even colorless. Walnuts could lose
the carotenoids after the extraction of walnut oil, which caused that
the defatted walnut meal lost the original color of walnuts and took on
a grayish-yellow color. This could also affect the color of walnut
butter which could appeared light-yellow or grayish-yellow. It may also
be the reason why commercial walnut butter containing walnut oil is more
yellowish than walnut butter prepared with FL. Tables 2S also showed
differences in the color of the four oils. There is a correlation
between the prepared walnut butter and FL, which may account for the
differences in the color of the walnut butter.

\textbf{3.3 Microrheological characterization}

\textbf{3.3.1 Apparent viscosity of walnut butter}

During the ball milling process, MCT, DG and CLA formed different
emulsification structures with the defatted walnut powder, which
resulted in different textures of walnut butter. As the viscosity of the
oil increased, the stability and sensory acceptability of walnut butter
was improved. However, when the viscosity of oil beyond a certain range,
it could have a negative impact on the spreadability of low-fat walnut
butter (Fernandes and Salas Mellado, 2018). The viscosity of WO, MCT,
DG, and CLA does not vary with shear rate (Fig. 2A). The viscous of CLA
was the largest and was closer to walnut oil, while MCT and DG were less
viscous.

The rheological properties of walnut oil play a crucial role in food
processing. Fig. 2 showed the results of the apparent viscosity
measurements of commercial walnut butter and functional lipids walnut
butter at a temperature of 25°C. The results showed that the apparent
viscosity of all samples showed a gradual decrease with increasing shear
rate at the same temperature. This phenomenon indicated that walnut oil
has non-Newtonian shear thinning properties (Mostafa et al., 2019).
Similar phenomena have been found in sesame butter, peanut butter and
mayonnaise (Loncarevic et al., 2016; Muresan et al., 2014; Yang et al.,
2020). The presence of high molecular weight substances and aggregation
of polymers, such as xanthan gum, walnut proteins and polysaccharide
bonds, were also responsible for their high shear thinning behavior
(Vardhanabhuti and Ikeda, 2006). In addition, with the increase of
external shear force, the agglomerated particles in the emultion system
could continue to deform and break. This could reduce the flow
resistance of lotion, which also resulted in the reduction of its
apparent viscosity (Mun et al., 2009). The apparent viscosity of MCT-6.5
was significantly higher than that of MCT-6 and MCT-7 (Fig. 2D). It may
be due to the better stability of the formed emulsion agglomerate
structure at the ratio of oil: defatted walnut meal was 6.5:3.5,
exhibiting a higher apparent viscosity at low shear rates. The apparent
viscosity of DG-WB or CLA-WB decreased with the increase of oil addition
ratio (Fig. 2B and 2C). It may be due to that more oil acted as the
mobile phase of the system, which resulting in a more effective
arrangement of small particles in the flow direction and a lower degree
of intermolecular entanglement (Marti, 2004). Fig. 2 showed that, the
apparent viscosities of CLA-6.5, CLA-7, DG-6.5 and MCT-6.5 are closer to
those of commercial walnut butter.

\textbf{3.3.2 Frequency scan of walnut butter}

The linear viscoelastic region (LVE) was the region where the elastic
modulus (G') and viscous modulus (G'') of all samples did not vary with
the oscillatory stress under the same conditions (Bi et al. 2020). The
LVE of walnut butter could be determined by strain scanning in the
dynamic rheological oscillation measurement mode. To ensure that all
samples were in the linear viscoelastic region, a strain value of 0.01\%
was selected for subsequent experiments (Fig. 1S).

Frequency scanning is a standard method for studying the viscoelastic
behavior of substances, which helped study the chemical composition and
physical structure of substances (Daubert, 2017; Steffe, 1996). The
results showed that the G' values of commercial walnut butter and three
groups of FLWB were always more significant than the G'' values in the
frequency range of 0.1-100 Hz (Fig. 3). There was no crossover between
G' and G'', which indicating that commercial walnut butter and FLWB were
dominated by elastic properties. There was a weak frequency dependence
of G' and G'' of the samples, suggesting that aggregation and
cross-linking between the components of walnut butter occurred. The G'
and G'' values of walnut butter decreased with the increase of FL
addition, indicating that the particle size of the samples decreased
with the increase of oil addition (Fig. 3B - D). The results showed the
trend of walnut butter from elasticity to viscosity was increased, the
distance between oil droplets was decreased, and the flocculating trend
appeared between microdroplets. This led to enhanced fluid interaction
and increased viscosity (Barnes, 1994; Sato et al., 2015). In all walnut
butter samples, the G' values were higher than the G'' values in all
frequency ranges. The G' values indicated strong interparticle
interactions and stable network structures within the samples, and the
same phenomenon was observed in sesame butter (Çiftçi et al., 2008).

\textbf{3.3.3 Thixotropy of walnut butter}

Thixotropy could reflect the phenomenon that the structure was disrupted
and the viscosity of the system decreases when shear was applied to a
system. After the removal of shear, the sample could gradually and
reversibly return to the initial stress and viscosity, which was typical
for non-Newtonian fluids (Hadjistamov, 2019). The thixotropic behavior
was related to the ``untangling-entanglement'' process of protein
molecules and the alignment of molecular protein chains in the shear
direction (Benchabane and Bekkour, 2008).

When the shear rate applied to commercially available walnut butter SS1,
SS2 and SS3 increased and then decreased, the viscosity curves of walnut
butter did not overlap while formed a closed loop region surrounded by
the upper and lower curves of viscosity, which could be called
thixotropic loop (Fig. 4A). The thixotropic ring area was negatively
correlated with the reversibility of viscosity, while the sample
recovered gradually when the shear rate was reduced (Ashok et al.,
2015). Firstly, the formation of the thixotropic ring could be due to
the non-covalent interaction between proteins in walnut butter at the
initial stage of shearing, which formed a three-dimensional network
structure with more intermolecular entanglement points and higher
shearing resistance. A linear increase in the applied shear rate during
the shearing process resulted in a gradual deformation between the
walnut butter particles and a disruption of the three-dimensional
network structure. This increased the number of broken structures and
decreasing the viscosity (Nikzade et al., 2012). During the shearing
process, the linear increase of applied shear rate led to gradual
deformation between walnut butter droplets. As a result, the protein
three-dimensional network structure was disrupted and the viscosity of
walnut butter was reduced (Reza et al., 2019). Secondly, the thixotropy
size was related to the intermolecular forces. Some researches about the
thixotropy of guar gum and papaya seed gum found that the stronger the
intermolecular interact ions, the greater the structural strength and
the longer the time required for structural rearrangement (Wang et al.,
2019). DG-7, CLA-6 and CLA-7 formed distinct thixotropic loops (Fig. 4B
- D). In addition to this, the initial viscosity values of CLA-6.5 and
CLA-7 were closer to those of commercial walnut butter. In summary, the
thixotropy of CLA-WB was more similar to that of commercial walnut
butter.

\textbf{3.4 Microrheological characterization}

Microrheological techniques could monitor the Brownian Motion of tracer
particles and track interparticle interactions (Mengjie et al., 2021).
The Brownian motion of the particles is described by the MSD versus time
curve, which reflects the viscoelastic characteristics of the sample.
The interaction forces between the model particles with viscoelasticity
limit their mean square displacement. Since the particles are not free
to move, they are trapped in a three-dimensional microstructural
network. These interactions make the samples viscoelastic, which is
manifested in the root mean square displacement versus de-correlation
time curves as non-linear MSD for all samples. Fig. 5 shows the results
for the root mean square displacement of walnut butter particles. The
MSD curves of commercial walnut butter and all three groups of FLWB were
nonlinear. It indicates that both commercial walnut butter and FLWB are
typical viscoelastic products (Fernandes and Salas Mellado, 2018;
Tisserand et al., 2012). MCT-WB and DG-WB had a long decorrelation time,
while commercial and CLA-WB had a shorter decorrelation time. The
samples with longer decorrelation times had higher viscoelasticity when
moved the same distance (Yun et al., 2018).

Fig. 6 showed the results of elasticity index (EI), solid-liquid balance
(SLB) and fluidity index (FI) of walnut butter. the EI value of FLWB
tended to decrease with increasing amount of grease addition and the
fluidity of walnut butter was enhanced, which was consistent with the
results of frequency scan in rheological experiments. the FI value of
FLWB increased with increasing amount of oil addition. This indicates
that the particle migration rate and fluidity of FLWB were enhanced with
the addition of oil. The FI of DG-WB was higher than that of commercial
walnut butter, and this phenomenon may be due to the relatively low
viscosity of DG, resulting in the higher fluidity of DG-WB. With the
increase of oil addition, the FI of MCT-WB or CLA-WB gradually
approached the FI of commercial walnut butter (Fig. 6C). Therefore, it
was feasible to prepare samples of MCT-WB or CLA-WB by adjusting the
amount of oil addition to make them closer to commercial walnut butter.
Fig. 6B showed that SLB \textless{} 0.5 for all walnut butter except for
the MCT-7 sample (which was mainly liquid behavior), indicating that the
samples were mainly gel behavior. In summary, the microscopic
rheological properties of CLA-WB are closer to those of commercial
walnut butter.

\textbf{3.5 Microstructure analysis}

In conclusion, among FLWB, CLA-WB were closer to the quality of
commercial walnut butter. Therefore, the walnut butter with CLA addition
was selected for further microstructural analysis. Image analysis
provided information on the pixel organization of the different regions
of the samples (Backes and Bruno, 2013). The walnut butter samples
prepared with CLA were further analyzed using optical microscopy Fig. 7
showed the optical microstructure of walnut butter prepared by CLA and
commercially available walnut butter. The results indicated that all
walnut butter showed a porous matrix structure encasing the oil
droplets. Proteins were adsorbed on the surface of the oil droplets
while some of them formed aggregates between the oil droplets and the
proteins. The aggregation of SS1 and SS2 was higher while the oil
droplet size of SS1 was more homogeneous. Emulsion droplets with smaller
average particle size may result in a larger total interfacial area of
emulsion droplets and more adsorbed proteins (Farshchi et al., 2013),
thus preventing aggregation between oil droplets. The formation of high
oil content and low interfacial adsorbed proteins may result in unstable
oil droplets that tended to form aggregated large oil droplets (Fig.
7F). Due to protein and oil droplet interactions, FLWB had a particle
size and emulsion structure, which was similar to that of commercial
products (Xu et al., 2020). The results showed that the quality of
CLA-WB was closer to that of commercial walnut butter. Further
microscopic results showed that the particle size, distribution and
aggregation of CLA-6.5 were closer to the microstructure of commercial
walnut butter.

\textbf{Conclusion}

In this study, different types and additions of FL (MCT, DG, CLA) were
selected to prepare walnut butter. By measuring the physicochemical
properties of the three groups of samples, it was obtained that when the
addition ratio of CLA and defatted walnut meal was 6.5:3.5, the prepared
walnut butter had the similar properties to commercial walnut butter.
FLWB with similar processing physical properties and microscopic
morphology as commercial walnut butter could be obtained after vibratory
ball mill grinding. In addition, FLWB contained 65\% CLA had higher
bioactive functions. This study provided a new way for the comprehensive
development and utilization of defatted walnut meal, which could help
the development of functional lipids walnut butter. Vibratory ball
milling technology was used to grind walnut butter in a single process
to streamline the milling process. which provided a new method for the
preparation of functional lipids walnut butter.

\textbf{Conflict of Interest Statement}

The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to
influence the work reported in this paper.

\textbf{Acknowledgement}

This study was supported by the HZAU-AGIS Cooperation Fund
(SZYJY2022013) and the Fundamental Research Funds for the central
Universities Program (No.2662022JC003).

\textbf{Authorship:}

Y.X. Conceived and designed the study, and wrote the first draft of the
manuscript, N.J. Carried out the research, H.S. and F.T. Analyzed the
data, X.C. and J.W. Writing -- review \& editing. All authors
contributed to and approved the final draft of the manuscript.

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\textbf{Fig. 1 Particle size distribution of commercial walnut butter
and walnut butter prepared with MCT, DG and CLA(A).Effect of functional
fats on walnut butter D(4,3) (B): {[}SS1, SS2, SS3 (Three types of
commercial walnut butter); Amount of oil added: MCT-6(60\%MCT),
MCT-6.5(65\%MCT), MCT-7(70\%MCT); DG-6(60\%DG), DG-6.5(65\%DG),
DG-7(70\%DG); CLA-6(60\%CLA), CLA-6.5(65\%CLA), CLA-7(70\%CLA){]}}

\begin{CJK}{UTF8}{gbsn}\textbf{Fig. 2 Apparent viscosity of walnut oil, MCT, DG and
CLA(A).Apparent viscosity of walnut butter prepared by
CLA、DG、MCT(B、C、D); Apparent viscosity of commercial walnut
butter(E): {[}SS1, SS2, SS3 (Three types of commercial walnut butter);
Amount of oil added: MCT-6(60\%MCT), MCT-6.5(65\%MCT), MCT-7(70\%MCT);
DG-6(60\%DG), DG-6.5(65\%DG), DG-7(70\%DG); CLA-6(60\%CLA),
CLA-6.5(65\%CLA), CLA-7(70\%CLA){]}}\end{CJK}\selectlanguage{english}

\begin{CJK}{UTF8}{gbsn}\textbf{Fig. 3 Frequency scan of commercially available walnut butter(A)
Frequency scanning of walnut butter prepared by MCT, DG and
CLA(B、C、D): {[}SS1, SS2, SS3 (Three types of commercial walnut
butter); Amount of oil added: MCT-6 (60\%MCT), MCT-6.5 (65\%MCT), MCT-7
(70\%MCT); DG-6 (60\%DG), DG-6.5 (65\%DG), DG-7 (70\%DG); CLA-6
(60\%CLA), CLA-6.5 (65\%CLA), CLA-7 (70\%CLA){]}}\end{CJK}\selectlanguage{english}

\begin{CJK}{UTF8}{gbsn}\textbf{Fig. 4 Thixotropy of commercially available walnut butter(A)
Thixotropy of walnut butter prepared by MCT, DG and CLA(B、C、D):
{[}SS1, SS2, SS3 (Three types of commercial walnut butter); Amount of
oil added: MCT-6 (60\%MCT), MCT-6.5 (65\%MCT), MCT-7 (70\%MCT); DG-6
(60\%DG), DG-6.5 (65\%DG), DG-7 (70\%DG); CLA-6 (60\%CLA), CLA-6.5
(65\%CLA), CLA-7 (70\%CLA){]}}\end{CJK}\selectlanguage{english}

\textbf{Fig. 5 MSD curve of walnut butter: {[}SS1, SS2, SS3 (Three types
of commercial walnut butter); Amount of oil added: MCT-6 (60\%MCT),
MCT-6.5 (65\%MCT), MCT-7 (70\%MCT); DG-6 (60\%DG), DG-6.5 (65\%DG), DG-7
(70\%DG); CLA-6 (60\%CLA), CLA-6.5 (65\%CLA), CLA-7 (70\%CLA){]}}

\textbf{Fig. 6 Texture characteristics of walnut butter
(p\textless{}0.05): {[}SS1, SS2, SS3 (Three types of commercial walnut
butter); Amount of oil added: MCT-6 (60\%MCT), MCT-6.5 (65\%MCT), MCT-7
(70\%MCT); DG-6 (60\%DG), DG-6.5 (65\%DG), DG-7 (70\%DG); CLA-6
(60\%CLA), CLA-6.5 (65\%CLA), CLA-7 (70\%CLA){]}}

\textbf{Fig. 7 Microstructure of walnut butter prepared by CLA compared
with commercial walnut butter {[}SS1, SS2, SS3 (Three types of
commercial walnut butter); Amount of oil added: CLA-6 (60\%CLA), CLA-6.5
(65\%CLA), CLA-7 (70\%CLA){]}}

Table 1 Marketable and homemade walnut butter color difference results\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Walnut butter types & L* & a* & b*\tabularnewline
\midrule
\endhead
SS1 & 57.19\selectlanguage{ngerman}±0.30\textsuperscript{c} & 3.97\selectlanguage{ngerman}±0.07\textsuperscript{ab} &
22.91\selectlanguage{ngerman}±0.21\textsuperscript{a}\tabularnewline
SS2 & 57.31\selectlanguage{ngerman}±0.19\textsuperscript{c} & 4.00\selectlanguage{ngerman}±0.20\textsuperscript{a} &
23.38\selectlanguage{ngerman}±0.77\textsuperscript{a}\tabularnewline
SS3 & 59.43\selectlanguage{ngerman}±0.62\textsuperscript{a} & 3.34\selectlanguage{ngerman}±0.15\textsuperscript{d} &
22.80\selectlanguage{ngerman}±0.52\textsuperscript{a}\tabularnewline
MCT-6 & 57.60\selectlanguage{ngerman}±0.60\textsuperscript{bc} & 3.15\selectlanguage{ngerman}±0.17\textsuperscript{de} &
16.70\selectlanguage{ngerman}±0.37\textsuperscript{ef}\tabularnewline
MCT-6.5 & 58.21\selectlanguage{ngerman}±0.40\textsuperscript{b} & 3.15\selectlanguage{ngerman}±0.14\textsuperscript{de}
& 16.39\selectlanguage{ngerman}±0.24\textsuperscript{f}\tabularnewline
MCT-7 & 58.23\selectlanguage{ngerman}±0.49\textsuperscript{b} & 3.02\selectlanguage{ngerman}±0.09\textsuperscript{e} &
16.17\selectlanguage{ngerman}±0.47\textsuperscript{f}\tabularnewline
DG-6 & 52.91\selectlanguage{ngerman}±0.17\textsuperscript{d} & 3.71\selectlanguage{ngerman}±0.06\textsuperscript{c} &
18.77\selectlanguage{ngerman}±0.44\textsuperscript{b}\tabularnewline
DG-6.5 & 52.94\selectlanguage{ngerman}±0.58\textsuperscript{d} & 3.61\selectlanguage{ngerman}±0.14\textsuperscript{c} &
18.40\selectlanguage{ngerman}±0.50\textsuperscript{bc}\tabularnewline
DG-7 & 52.54\selectlanguage{ngerman}±0.34\textsuperscript{d} & 3.60\selectlanguage{ngerman}±0.14\textsuperscript{c} &
18.12\selectlanguage{ngerman}±0.81\textsuperscript{c}\tabularnewline
CLA-6 & 46.74\selectlanguage{ngerman}±0.22\textsuperscript{e} & 3.94\selectlanguage{ngerman}±0.09\textsuperscript{ab} &
17.42\selectlanguage{ngerman}±0.29\textsuperscript{d}\tabularnewline
CLA-6.5 & 45.10\selectlanguage{ngerman}±0.60\textsuperscript{g} & 3.77\selectlanguage{ngerman}±0.06\textsuperscript{bc}
& 16.82\selectlanguage{ngerman}±0.22\textsuperscript{def}\tabularnewline
CLA-7 & 45.98\selectlanguage{ngerman}±0.45\textsuperscript{f} & 3.56\selectlanguage{ngerman}±0.20\textsuperscript{c} &
17.24\selectlanguage{ngerman}±0.12\textsuperscript{de}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{ngerman}

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