Investigation of flows in nano-ribbed and nano-grooved channels

Filippos SOFOS,

T. E. KARAKASIDIS, A.E. GIANNAKOPOULOS, A. LIAKOPOULOS

Department of Civil Engineering, School of Engineering, University of Thessaly

Preface• Investigate flow conditions at the nanoscale.

• Describe micro/nano-bleeding under certain conditions during a vascular surgery process, where the addition of patches applies.

• We present molecular dynamics simulation results on fluid and transport properties for nanochannel flows.

• We believe that the proposed channels are able to simulate the rough-wall and interaction potentials inside a patched artery nanochannel.

• We show that groove orientation (ribs and grooves) has a primitive effect on flow mainly due to slip length increase in a ribbed-wall channel.

• The transport properties of the fluid are significantly affected by wall wettability

2

What we do

3

Model duct flows in nanochannels with flat, ribbed andgrooved walls.

Various hydrophobicity/hydrophilicity degrees Argue on each channel effect on flow parameters, such as

density profiles, velocity profiles and slip length calculation We present detailed transport properties calculation

(diffusion coefficients, shear viscosity and thermalconductivity) along the channel, both in layer and channelaverage values

We incorporate microscopic relations in conjunction withrelations from the continuum theory.

Flow system

• Liquid monoatomic flow in channels with flat, grooved and ribbed walls

• Wall separation for the flat-wall channel is h=18.58σ, while groove height and length are gh=1.9σ and gl=5.3σ, respectively.

• Distinction between a grooved and a ribbed channel is made by the flow direction.

• Fluid/fluid, wall/fluid and wall/wall interactions are described by Lennard-Jones (LJ) 12-6 potential.

4

Simulation details

• The system is simulated for two different wall/fluid interaction energy ratios ew/ef =0.5 and 1.5 (w: wall and f: fluid)

• A means of estimating the slippage of fluid atoms close to the channels walls.

• Simulations are held under constant temperature Τ=1, with the application of Nosé-Hoover thermostats.

• The simulation step for is Δt=0.005τ• Simulation begins with fluid atoms given appropriate initial

velocities in order to reach the desired temperature• The system reaches equilibrium after an equilibrium run of 2x106

time steps. • Then, a number of NEMD simulations for each channel type are

performed, each with duration of 5x105 time steps.

Calculations

• Number densityf

binbin

N

hzzNzN

),()(

)(

),()(

/

zN

hzzuzu

binyx

w

weffsdz

dL

,

2

1

)0()(2

1lim

N

j

jjt

ch tdNt

D rr

2

1

2

1

| | )0()()0()(2

1lim

2

1

2

N

j

yj

yj

N

j

xj

xj

t

yx

ttNt

DDD rrrr

2

1

)0()(2

1lim

N

j

zj

zj

t

zT tNt

DD rr

• Velocity profile

• Slip length

• Diffusion coefficient

Calculations

• Shear viscosity

• Thermal conductivity

0

2)0()(

1 xq

xq

B

JtJdtTVk

2

1 1 1

( )1( ) : ( )

2

NN Nijx x x x

q i i i ij ij ixi i j ij

uJ m r u

r

rI r

σπη

ΤkD

s,ch

Βch

4

8

Number density

9

Velocity profile

10

Slip length

11

Diffusion coefficient - layer

12

Diffusion coefficient - parallel

13

Diffusion coefficient - transverse

14

Shear viscosity - layer

15

Thermal conductivity- layer

Conclusions

16

Fluid number density for ribbed- and grooved-wall channels presents similar ordering, indicating that groove orientation does not affect number density.

The presence of grooves on channel walls slows down velocity values, however, flows over a ribbed-wall channel present greater velocity values compared to the grooved-wall channel, which, furthermore, present velocity profile asymmetry.

Surface slippage is maximized by fluid flow in longitudinal compared to transverse direction of the grooves and increased wall wettability ratio .

A hydrophobic surface adds anisotropy in diffusion coefficient values, no matter if the upper wall is flat or rough. This anisotropy is calculated about 7-8% for hydrophobic walls and 3-4% for hydrophilic ones. Diffusion coefficients do not differ significantly either in ribbed- or in grooved-wall channel flows.

Conclusions

17

Due to small values on shear viscosity calculations, we conclude that flat, hydrophobic walls facilitate fluid flow, but, in contradistinction, hydrophobic grooved or ribbed walls present larger shear viscosity values. Maximum shear viscosity values are obtained near the rough wall in grooved, hydrophilic nanochannels.

Thermal conductivity calculations reveal small values near the channel walls and wall grooves or ribbs and significantly larger near the channel centerline. Wall ribs also seem to enhance heat transfer, as depicted by the increased λlay values, while thermal conductivity is decreased in a grooved-wall channel due to fluid atom sticking inside and near the grooves. In bulk channel values, flows over hydrophobic walls present greater λch values compared to flows over hydrophilic walls.

All above findings can be encapsulated in fluid dynamics theory, for both fundamental research and technological guidance, in order to be able to describe in detail fluid behavior at the nanoscale.

Thank you…