ABSTRACT (original article): Unlike human intestines, which are long, hollow tubes, the intestines of sharks and rays contain interior helical structures surrounding a cylindrical hole. One function of these structures may be to create asymmetric flow, favoring passage of fluid down the digestive tract, from anterior to posterior. Here, we design and 3D print biomimetic models of shark intestines, in both rigid and deformable materials. We use the rigid models to test which physical parameters of the interior helices (the pitch, the hole radius, the tilt angle, and the number of turns) yield the largest flow asymmetries. These asymmetries exceed those of traditional Tesla valves, structures specifically designed to create flow asymmetry without any moving parts. When we print the biomimetic models in elastomeric materials so that flow can couple to the structure’s shape, flow asymmetry is significantly amplified; it is sevenfold larger in deformable structures than in rigid structures. Last, we 3D-print deformable versions of the intestine of a dogfish shark, based on a tomogram of a biological sample. This biomimic produces flow asymmetry comparable to traditional Tesla valves. The ability to influence the direction of a flow through a structure has applications in biological tissues and artificial devices across many scales, from large industrial pipelines to small microfluidic devices. CITATION (original article): Ido Levin, Naroa Sadaba, Alshakim Nelson & Sarah L. Keller, (2024), Asymmetric fluid flow in helical pipes inspired by shark intestines, Applied Physical Sciences 121 (40) e2406481121. https://doi.org/10.1073/pnas.2406481121
PRESS: These 3D-printed pipes inspired by shark intestines outperform Tesla valves
PRESS: These 3D-printed pipes inspired by shark intestines outperform Tesla valves
Render a Helical Pipe
Render a Helical Pipe
This code renders a Helical Pipe - a tube with radius and a thickness with an inner helical blade with pitch , inner-hole radius , slope (tangent of the cone’s angle ), and number of turns .Generated structures can be exported to separate STL files and printed.For 3D printing purposes, the thickness of the helical blade can be increased at its contact with the outer tube. This is performed by introducing an exponential thickness profile using the function. It has extra pare meters - the extra thickness at the connection, the length scale of the exponential decay and the thickness of each layer. The thickness is given by . For simplicity, these assumed to be fixed (, =1, ).Resolution is defined via nPtAz and nPtRad - the number of azimuthal and radial plot points, respectively.Opacity of 0.8 is added for the outer tube for visualization.For the experiment - all measures are assumed to be in mm.
R
t
tube
p
r
hole
tanα
α
n
turns
reinforcedHelicalBlade
t
extra
ρ
δr
t(r)=t+
t
extra
r-R
ρ
δr=0.25
t
extra
ρ=2
Outer tube
Outer tube
In[]:=
outerTube[R_,tTube_,L_,zOffset_]:=BlockrEff=R+,nPtAz=72,nPtRad=25,αTube=0.75,ParametricPlot3D[{rEffCos[u],rEffSin[u],v},{u,0,2.01π},{v,zOffset-tTube,L+zOffset+tTube},PlotStyleDirective[LightBlue,Thickness[tTube],Opacity[1-αTube]],MeshNone,Axes->False,Boxed->False,PlotPoints{nPtAz,nPtRad}]
tTube
2
Test
Test
In[]:=
Block[{R=10,tTube=2,L=50,zOffset=0},outerTube[R,tTube,L,0]]
Out[]=
Simple Helical Blade
Simple Helical Blade
In[]:=
helicalBlade[R_,t_,p_,rHole_,tanα_,nTurns_]:=Block{nPtAz=72,nPtRad=25},ParametricPlot3DvCos[u],vSin[u],+tanαv,{u,0,2πnTurns},{v,rHole,R},PlotStyleDirective[Thickness[t],LightOrange],PlotPoints{Max[10,Round[nTurnsnPtAz]],nPtRad},Mesh->None,Boxed->False,Axes->False
pu
2π
Test
Test
In[]:=
Block[{R=10,t=0.2,p=5,rHole=5,tanα=1,nTurns=3},helicalBlade[R,t,p,rHole,tanα,nTurns]]
Out[]=
Simple Helical Pipe
Simple Helical Pipe
In[]:=
helicalPipe[R_,tTube_,t_,p_,rHole_,tanα_,nTurns_]:=BlockzOffset=tanαrHole,Show[outerTube[R,tTube,pnTurns+tanαR,zOffset],helicalBlade[R,t,p,rHole,tanα,nTurns]]
1
2
Test
Test
In[]:=
Block[{R=10,tTube=2,t=0.2,p=12,rHole=1,tanα=2,nTurns=4},helicalPipe[R,tTube,t,p,rHole,tanα,nTurns]]
Out[]=
Reinforced Helical Blade
Reinforced Helical Blade
reinforcedHelicalBlade[R_,t_,p_,rHole_,tanα_,nTurns_]:=Block{nPtAz=72,nPtRad=25,dr=0.25,ρ=1,tExtra=1,r0List},r0List=Table[r0,{r0,rHole,R-dr,dr}];tVar[r0_]:=t+tExtraExp[-(R-r0)/ρ];ShowTableParametricPlot3D(v+r0List[[r0Ind]])Cos[u],(v+r0List[[r0Ind]])Sin[u],+tanα(v+r0List[[r0Ind]]),{u,0,nTurns2π},{v,0,dr},BoxedFalse,AxesFalse,PlotStyleDirective[Thickness[tVar[r0List[[r0Ind]]]],ColorData[97][r0Ind]],MeshNone,PlotPointsMax[10,Round[2nPtAz]],Max3,Round,{r0Ind,1,Length[r0List]},PlotRange->{1.25{-R,R},1.25{-R,R},1.25{0,pnTurns+tanαR}}
pu
2π
drnPtRad
R
Test
Test
In[]:=
Block[{R=10,t=0.2,p=5,rHole=5,tanα=1,nTurns=3},reinforcedHelicalBlade[R,t,p,rHole,tanα,nTurns]]
Out[]=
Reinforced Helical Pipe
Reinforced Helical Pipe
Test
Test
Batch rendering and export
Batch rendering and export
CITE THIS NOTEBOOK
CITE THIS NOTEBOOK
Asymmetric fluid flow in helical pipes inspired by shark intestines
by Ido Levin, Naroa Sadaba, Alshakim Nelson & Sarah L. Keller
Wolfram Community, STAFF PICKS, October 15, 2024
https://community.wolfram.com/groups/-/m/t/3299162
by Ido Levin, Naroa Sadaba, Alshakim Nelson & Sarah L. Keller
Wolfram Community, STAFF PICKS, October 15, 2024
https://community.wolfram.com/groups/-/m/t/3299162