7-Mech - IJMPERD - Investigation - Ghassemi - Iran

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD ) ISSN 2249-6890 Vol.2, Issue 3 Sep 2012 67-75 © TJPRC Pvt. Ltd.,

INVESTIGATION OF NANOBIO MECHANICAL SYSTEMS WITH TWO MOST IMPORTANT COMPUTATIONAL METHODS 1 1

A.SHAHIDIAN ,2 N. MAFTOUNI & 3M.GHASSEMI

Professor Assistant Mechanical Engineering Department, Islamic Azad University, East Tehran Branch, Tehran, Iran 2 3

PhD candidate, Mechanical Engineering Department, University of Tehran, Tehran, Iran

Professor, Mechanical Engineering Department, K. N. Toosi University of Technology, Tehran, Iran

ABSTRACT To study nanobio systems is an important subject in recent decades. In this work two branches of these subjects are studied: i) pressure profile in cell nanobio membrane; ii) Bio-nanofluid flow Simulation. It is very essential to know mechanical properties in different regions of nanobio membrane as one of the most important parts of living systems. Here the coarse-grained molecular dynamics (CGMD) simulations method has been used to study the pressure profile in a system including nanobio membrane and water. This pressure data can be used to calculate many mechanical properties like tension and surface tension. Pressure profile calculation has been done via Virial pressure theorem for each case of standard MARTINI water and polarizable coarse-grained water model. Results indicate that using polarizable water model leads to higher picks in pressure profile in water region near surface of nanobio membrane. In this research also Bio-nanofluid (blood with suspension of nanoparticles) flow simulation is studied. A new effective thermal conductivity model for bio-nanofluid is used. Also the Einstein equation is used for prediction the effective viscosity of bio-nanofluid. A CFD code based on finite volume is used to solve the governing continuity and momentum equations. The proposed model agrees well with other researchers data. The simulation results show that thermophysical properties increase. But behavior of flow, velocity and pressure, is same for blood and bio-nanofluid. The results of both cases are presented and discussed.

KEYWORDS: Bio-Nanofluids, Nanobio Membrane, Virial Pressure, Momentum Equation, Computational Method

INTRODUCTION Investigating nanobio mechanical systems is one important subject in recent decades. Different computational methods are used to study these cases. Drug delivery is one of most popular cases in nanobiotechnology. Also cell engineering and investigating mechanical properties of living cell’s components is very important. In current work bio-nanofluid flow simulation for drug delivery application and also calculation of pressure profile in live cell’s nanomembrane with two water models are studied. The computational method used for studying mechanical properties of alive cell’s nanomembrane is molecular dynamics simulation (MD) and that for bio-nanofluid simulation is

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A.Shahidian, N. Maftouni & M.Ghassemi

computational fluid dynamics (CFD).

The virial pressure relation has been implemented to calculate pressure profile for nanobiomembrane [1].

The system including water and cell’s lipid membrane has been modeled for one microsecond to have enough data to calculate pressure. Several experimental studies have explained the reason behind the enhancement of effective thermal conductivity [2]. Most recent studies are about properties of nanofluid with water or ethylene glycol base fluid. Bio-Nanofluid is blood with suspended nanoparticles.

According to blood which is complex of different material with different size, the behavior of bionanofluid and the other nanofluid with usual base fluid such as water and ethylene glycol, is not similar.

So nanofluid properties models are not enough for bio-nanofluid study. Therefore obtain the bionanofluid thermo-physical properties is essential when flow and heat transfer study of blood in drug delivery and new cancer therapy is considered. In this study the effect of the nanoparticles in channel blood flow is investigated. A CFD code based on finite volume is used to solve the governing continuity and momentum equations.

METHODS Pressure Calculation in Cell Nanobio Membran A suitable tool for studying nanoscale biological phenomena is molecular dynamics simulation (MD). In all atoms MD each particle is treated as one particle. To access longer times and bigger systems coarse grained molecular dynamics (CG-MD) in which some atoms are treated like one bead, is used. In first models of CG-MD water is treated explicitly, at the same level of coarse-graining as all other molecules implying that four water molecules are making a single coarse-grained bead. MARTINI water beads, just as many other CG water models, do not bear charges and, consequently, are unable to detect electrostatic fields and effects. To compensate for the neglect of explicit polarization, screening of electrostatic interactions is done implicitly, assuming a uniform relative dielectric constant. While this is a reasonable approximation for bulk water, problems arise at the interfaces between water and other phases. Because of the implicit screening, the interaction strength of polar substances is underestimated in nonpolarizable solvents. Correct modeling of the partitioning of polar and charged compounds into a low dielectric medium, e.g. a lipid nanobio membrane, has proven a big challenge for CG models in general [3].

A new model named polarizable water has been introduced in which every CG water consists of three particles instead of one in the standard MARTINI water. The central particle W is neutral and interacts with other particles in the system by means of the Lennard-Jones interactions, just like the standard water particle. The additional particles WP and WM are bound to the central particle and have a positive and negative charge of +q and -q, respectively. They interact with other particles via a Coulomb function only [8].

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Investigation of Nanobio Mechanical Systems with Two Most Important Computational Methods

WP W

W

WM

Fig. 1. MARTINI water models: standard water with one bead(left), polarizable water with three beads(right). W in left model represents the only bead of standard water. In polarizable model(left) PW represents the charges of water molecule In current work nanobio membrane has been simulated with CG simulations twice, one with standard MARTINI water and the other with polarizable water. Then the pressure profile of each system has been calculated and results have been compared.

In this study the system has been simulated with GROMACS 4.0.7. package. The system includes a nanobio membrane containing phospholipids and also water molecules. The height of POPC nanobio membrane is 2.2 nm. Two systems are simulated separately: i) nanobio membrane and standard MARTINI water molecules; ii) nanobio membrane and polarizable water molecules. One microsecond coarse-grained molecular dynamics simulation is done for each of systems. Then a special version of GROMCAS [1] is used to calculate the pressure profiles of systems.

Bio-Nanofluid Flow Simulation Fluids Al2O3 with suspended nanoparticles are called nanofluids, a term first proposed by Choi in 1995 of the Argonne National Laboratory, U.S.A. [5]. Mixing nanoparticles in blood results bionanofluid.

As known blood is a combination of plasma and blood cells including red blood cells (RBC), white blood cells (WBC) and plackets.Table 1 shows the number of concentration and size of blood cells [6,7].

A new model for effective thermal conductivity for bio-nanofluid is developed [8]. In this model first Leong, et al. equation [8] is used with plasma as base fluid (kf) and Al2O3 as nanoparticles (kp).

The Leong, et al. relationship is shown as equation (1):

Keff = +

(k p − klayer)φ Klayer (2β13 − β23 +1)

(1)

β13 (k p + 2klayer) −(k p − klayer)φ (β13 + β23 −1)

(k p + 2klayer) β13 (φβ23 (klayer − k f ) + k f )

β13 (k p + 2klayer) −(k p − klayer)φ (β13 + β23 −1)

Maxwell equation is then used to calculate the thermal conductivity of bio-nanofluid. The blood cells are as particles (kp), and the mixture of plasma and Al2O3 is the base fluid (kf).

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K eff =

k p + 2k f + 2(k p − k f )φ k p + 2k f − (k p − k f )φ

(2)

kf

Also Keff and Φ are the effective thermal conductivity and Nanoparticles volume fraction respectively.

For bio-nanofluid effective viscosity [9] and effective density [10] below equations are used.

µeff =1+ 2.5φ µf

(3)

ρ eff

(4)

( Einstein equation ) = (1 − φ ) ρ f + φ ρ p

Where ρeff ,ρf ,ρp ,µ eff and µ f are effective density, base fluid density ,nanoparticle density, effective viscosity and base fluid viscosity.

GOVERNING EQUATIONS Pressure calculation in cell Nanobio membran The base of molecular dynamics simulation is Newton’s second law and the base of pressure profile calculation is virial pressure. Different suitable potentials are defined for different particles and then the acceleration of each particle is obtained as derivative of the potentials. In the next step velocities and coordinates of each particle can be found by time derivatives of the acceleration. The pressure for an inhomogenous system is represented as a tensor P(r) that depends on the location r. For a system consisting of pointwise particles with n-body potentials Un the local pressure can be defined as a sum of kinetic and configurational contribution [1]:

pαβ (r ) = ∑ mi viα viβ δ (r − ri ) − i

1

∑ n ∑∑ ( ∇α U n

< j > < kl >

jk

n

− ∇αjlU n )

∫

c jljk

dl β δ (r − 1) (5)

Where Cjljk is a contour from the particle jl to the particle jk, <j> stands for summation over all n clusters in the system, <k,l> describes summation over all pairs of particles within a given n cluster, and mi, vi, and ri refer to the mass, velocity, and location of atom i, respectively, and α and β refer to the components.

Equation (5) gives a continuous pressure field. To find the pressure tensor PV for a volume element V, we have to take an average over the volume element finds the pressure tensor for volume V

. Together with Eq. (5) one

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Investigation of Nanobio Mechanical Systems with Two Most Important Computational Methods

Al2O3 Nanoparticle

Human Blood

3900

1060

35

0.492

-

3

Density (kg/m3) Thermal Conductivity (W/m.K) Viscosity (cp)

Where fv(r) =1, if r Є V, and zero in other cases.

Each vector rjljk = rjk-rjl is divided in N parts and the contribution of a given part λ is added only if the contour goes through V, i.e., if fV =1. PV(r) has been called as pressure field [1].

Bio-Nanofluid Flow Simulation The bio-nanofluid flow in two dimensional channels is studied. Blood and Al2O3 nanoparticles thermo physical properties are given in Table 1.

TABLE 1 THERMO PHYSICAL PROPERTIES OF BLOOD AND Al2O3 NANOPARTICLES [7] The bio-nanofluid thermophysical properties are calculated from equations 1 to 4 and data which recorded in Table 1.

Flow is assumed to be steady, laminar, incompressible and Newtonian. According to these assumptions the continuity and momentum equations are as follows, respectively. Where V (u,v) and P are flow velocity and pressure respectively.

Continuity equation ∂u ∂v + =0 ∂x ∂y

(7)

Momentum equation u

 ∂ 2u ∂ 2u  ∂p ∂u ∂u +v + µ  2 + 2  =− ∂x ∂y ∂x ∂y   ∂x

(8)

u

 ∂ 2v ∂ 2v  ∂v ∂v ∂p + v = − + µ  2 + 2  ∂x ∂y ∂y  ∂x ∂y 

(9)

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A finite volume based method is used to solve the non-linear governing equations. A FORTRAN code with a structured grid is used. . The 1100*50 grid is used. Alsothese boundary conditions are used; i) The velocity inlet is set to fixed velocity such as 0.05 m/s. ii) The first derivative of velocity is zero for the channel outlet.

RESULTS AND DISCUSSIONS Pressure Calculation in Cell Nanobio Membran The pressure profile is sketched comparatively for these two systems in figure2. The vertical axis represents pressure (bar) and the horizontal one represents the position(nm) according to size of the defined voxel. It should be mentioned that for calculation of pressure profile the simulation box has been divided to some voxels in any direction. Size of each voxel is 0.2 nm so for example value of 24 in this

Pressure (bar)

graph’s horizontal axis means z position of 4.8 nm.

½ z position (nm)

Fig. 2. Pressure profile for systems of nanobio membrane and both of standard and polarizable water. It is observable that picks of the pressure profile for polarizable water are higher than global pick of system with standard MARTINI water.

As it is obvious pressure profile of system including polarizable water has higher picks relative to that of system with standard MARTINI water. The heights of interfaces between nanobio membrane and water molecules are 4.8 nm at bottom and 9.2 nm at top. These values are the average heights of most external atoms of phosppholipids’ head groups. In system with plorizable water there are two global picks with magnitude of 152 bar. There is also a local pick in the middle of nanobio membrane with magnitude of 137 bar. The first global pick of nanobio membrane and polarizable pressure profile appears at 4.4 nm and the second one appears at 9.8 nm. Both of these picks are outside of nanobio membrane and are located in water region. In the system including standard MARTINI water there is one global pick in the middle of nanobio membrane with magnitude of 137 bar and also there are two local

Investigation of Nanobio Mechanical Systems with Two Most Important Computational Methods

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picks (90 bar) in water region that are closer to the interface of water and nanobio membrane relative to two global picks of polarizable water system.

Bio-Nanofluid Flow Simulation Bio-Nanofluid (Blood with 0.1% Al2O3 Nanoparticle) velocity contour is shown in figure 3.

Fig. 3. Bio-Nanofluid velocity contour As shown there is not significant different between blood velocity contours (figure1) and bionanofluid velocity contour (figure 3).

Velocity distribution for different volume fraction of Al2O3 nanoparticles at y = 0.00036 m from bottom edge of the channel is shown in figure 4.

Fig. 4. Velocity distribution in channel for different volume fraction of Al2O3 nanoparticle Figure 5 depicts part of figure 4.

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Fig. 5. Large scale velocity distribution for different volume fraction of Al2O3 nanoparticle As shown in figures 4 and 5, although nanoparticle volume fraction is changes from 0.001% to 2%, velocity is constant in channel.

This means that, for biomedical application, nano drug delivery is achieved without changes in velocity trend.

CONCLUSIONS In this work two of most important computational methods are investigated with one of their significant applications. The area of importance of the computational methods is problems that are very hard or expensive to be experimented.

In the part of cell membrane mechanical properties study, using a three-bead model to represent four water molecules in coarse-grained molecular dynamics simulation as a polarizable water molecule, a new system of nanobio membrane and water has been made in addition of a model including standard water molecules. The pressure profile has been calculated for cell membrane. It is observable that including charges of water moleculeâ&#x20AC;&#x2122;s components has an effect in interaction of nanobio membrane with any other probable biological components like proteins, peptides and so on. This effect is also dependent on charges of the other components.

The new model for bio-nanofluid effective thermal conductivity is introduced. Also the bioNanofluid (Blood with 0.1% Al2O3 Nanoparticle) flow simulation for drug delivery is studied. A CFD code based on finite volume is used to solve the governing continuity and momentum equations. The velocity distribution for different volume fraction of Al2O3 nanoparticle is studied. As shown there is not significant different between blood velocity contour and bio-nanofluid velocity contour. Also nanoparticle volume fraction is changes from 0.001% to 2%, velocity is constant in channel. This means that, for biomedical application, nano drug delivery is achieved without changes in velocity trend.

Investigation of Nanobio Mechanical Systems with Two Most Important Computational Methods

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ACKNOWLEDGEMENTS We here acknowledge the financial support of research department of Islamic Azad University, East Tehran branch and also helps of Prof. S. J. Marrink the head of molecular dynamics group in university of Groningen, the Netherlands.

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[8] K.C. Leong, C. Yang, S.M.S. Murshed., A model of the thermal conductivity of nanofluids the effect of interfacial layer”. Journal of Nanoparticle Research 8, 245–254, 2006.

[9] Einstein, A., Eine neue bestimmung der molekuldimensionen", Annalen der Physik, Leipzig, 19, pages 289–306,1906.

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