J Fluid Mech.2017 May;818:5-25

From red cells to soft lubrication, an experimental study of lift generation inside a compressible porous layer

Thomas Gacka,1,2 Robert Crawford,1,2 Zenghao Zhu,1,2 Rungun Nathan,1,3 and Qianhong Wu1,2*

1Villanova Cellular Biomechanics and Sports Science Laboratory, Villanova, Pennsylvania 19085, USA

2Department of Mechanical Engineering, Villanova University, Villanova, Pennsylvania 19085, USA

3Division of Engineering, Penn State Berks, Reading, Pennsylvania 19610, USA

*Address all correspondence to Qianhong Wu, E-mail: qianhong.wu@villanova.edu

 

Abstract

It is a new concept for porous media flow that hydrodynamic lifting force is generated inside a highly compressible porous layer as a planing surface glides over it. The concept was originated from the observation of the pop-out phenomena of red blood cells (RBCs) over the endothelial glycocalyx layer (EGL) lining the inner surface of our blood vessels (Feng and Weinbaum, J. Fluid Mech. 422, 282, 2000). In the current paper, we report an experimental study to examine this concept. A novel testing setup was developed that consists of a running conveyer belt covered with a soft porous sheet, and a fully instrumented upper planar board, i.e. planing surface. A fast generation of pore pressure was observed and captured by pressure transducers when the planing surface glides over the porous sheet. Its distribution strongly depends on the relative velocity between the planing surface and the running belt, the mechanical and transport properties of the porous sheet, as well as the compression ratios at the leading and trailing edges. The relative contribution of the transiently trapped air to the total lift was evaluated by comparing the pore pressure to the total lifting pressure measured by a load cell mounted between two adjacent two pressure transducers. For a typical running condition with a polyester porous material (k=h2/h1=5, λ=h2/h0=1, U=3.8 m/s, where h2, h1, are the porous layer thickness at the leading and trailing edges, respectively; h0 is the un-deformed porous layer thickness; and U is the velocity of the running belt), over 68% of the local lift is generated by the pore pressure. The results conclusively verified the validity of lift generation in a highly compressible porous layer as a planing surface glides over it. This study provides the foundation for the application of highly compressible porous media for soft lubrication with minimal frictional losses. It also sheds some lights on the biophysics study of the EGL.

 

Supplement:

Friction is a major contributor to the loss of energy and causes inefficiencies in mechanical systems. Anywhere moving parts exist in an assembly, friction will be present to scavenge energy. Therefore, methods to reduce friction can have major effects on a global scale. Through millions of years of evolution, nature has created a model for us to follow that may tremendously reduce friction. A new concept for lubrication was inspired by the outgrowth of the observation and related theoretical studies about the endothelial glycocalyx layer (EGL), which covers the inner surface of our blood vessels. Biologists have wondered why an 8 µm in diameter red blood cell is able to glide over the EGL and survive 105 passages through microcirculation during a typical lifetime of 120 days, without being damaged or undergoing hemolysis. This longevity is quite remarkable in that the red blood cell can travel at velocities that approach 100 times its diameter a second and can also pass, at much lower velocities, through muscular sphincters of a few µm diameters at the entrance to arterioles. In 2000, Feng and Weinbaum [1], attributed this low friction motion to the tremendously enhanced hydrodynamic lifting force as a red blood cell glides over the EGL and rapidly compresses this soft porous layer. A lubrication theory for highly compressible porous media was developed, which shows that: (a). The excess pore pressure generated by a planing surface moving on any compressible porous media, scales as α2 = h22/KP, where α is the Brinkman parameter, h2 is the porous layer thickness at the leading edge and KP is the local Darcy permeability; (b). α is of an order 102 or larger for red blood cells gliding on the EGL. Thus, the lift forces generated can be four or more orders of magnitude greater than the classical lubrication theory. Adhesive proteins in the opposing membranes of the red blood cells and endothelial cells would be in constant contact were it not for this large pressure (lift) forces generated within the EGL that prevent opposing membranes from touching; (c). The same mechanism applies to a human skiing or snowboarding on fresh snow powder, which has an unexpected, remarkable hydrodynamic similarity to the motion of a red blood cell gliding over the compressed EGL, even though their difference in mass is of the order 1015. Interestingly, α is of the same order for both cases; (d). The huge enhancement in the lift arises from the fact that as the matrix compresses there is a dramatic increase in the lubrication pressure because of the marked increase in hydraulic resistance that the fluid encounters as it escapes from the confining boundaries through the thin porous layer. Weinbaum et al. [2] also predicted that the elastic restoring force of the core proteins of the EGL is at most five percent of the pore pressure when the red cell is moving at velocities of even a few µm/s. Thus, the friction drag from the solid phase will be dramatically reduced.

The observations in the low friction movements of red cells on the EGL provided a new perspective on saving energy consumption by significantly reducing the friction in the mechanical systems. However, to apply the soft porous lubrication to a real mechanical system, further experimental study is needed for verifying the reliability of the theoretical model. To our knowledge, the experimental study for the scenario originally examined by Feng & Weinbuam [1] (a planing surface gliding over a soft porous layer, which is more related to the soft porous lubrication) remains purely theoretical [1,3-14]. Without studying the lift generation and lubrication effect inside a porous layer when a planing surface glides over, the feasibility for applying the soft porous lubrication into the real mechanical system is unknown.

 

 

Figure 1. The experimental setup of soft porous lubrication.

 

In this study, we report a biomimetic study to examine the lift generation inside a soft porous layer and its applications to soft porous lubrication. A unique experimental setup is developed to examine the lift generation as a planing surface glides over a macro-scale porous layer. Figure 1 shows an image of the actual experimental setup, where a fibrous porous layer (uniformed thickness of h0) is attached to a urethane tabletop conveyer belt. The conveyer belt rotates on two rollers at linear velocity, U. The rollers are driven by a DC electric motor via a pulley and connecting belt. The upper planing surface is fixed. The tilt angle of the planing surface is precisely adjusted by varying the heights at the leading edge (h1) and trialing edge (h2) to the belt surface. Two nylon sidewalls are mounted to the frame to allow a surface to seal along the edge of the planing surface. This arrangement allows for the elimination of any pressure leakage in the lateral direction, forming a one-dimensional pressure distribution, as described in Feng & Weinbaum [1] for the motion of red blood cells in a tightly fitting capillary. A foam sealing between the sidewalls and the planing surface is also applied to eliminate the pressure leakage though the gap.

 

 

MATLAB Handle Graphics

Figure 2. The data obtained from the pressure sensors mounted along the axial direction of the planing surface, P1, P2, P3, P8, P9 and P10. The running conditions for the results are carefully chosen, where the velocity of the running belt is 3.88m/s; the undeformed porous layer thickness, h0, is 19 mm, and the thickness of the porous layer at the leading and trailing edge are h2=19 mm and h1=6.3 mm respectively, making the pre-compression λ=h2/h0=1 and compression ratio k=h2/h1=3. The Brinkman parameter at the leading edge α=h2/(Kp(L) )0.5 = 98.

 

Time dependent pressure data taken from the pressure sensors along the centerline of the planing surface is shown in Figure 2. For showing the locations of the pressure sensors on the planing surface, the sensors’ arrangement is also attached to Figure 2. Pressure was immediately generated as the belt begins to move because the porous layer is continuously compressed by the upper planing surface. The data is noticeably cyclical, and not particularly smooth. This is due to a) slight non-uniformity of the porous sheet, b) the seam connecting the two ends of the porous sheet. As the two ends were glued together as one attached the porous sheet to the conveyer belt, the microstructure of the material is changed, and the local permeability decreases. The largest peaks in the data (t=0.4, 1, 1.5 sec) is found to be a result of the seam, as it passes underneath the planing surface cyclically. Therefore, the data taken between the peaks is of most interest. From Figure 2, it is evident that over 300Pa of pore air gage pressure is generated underneath the planing surface at the location near its trailing edge where pressure sensors 2 and 3 are located. The pressure relaxes toward the leading edge (P8, P9, and P10) and the trailing edge (P1).

 

 

Figure 3. The comparison between the theoretical result and experimental result. The initial conditions for the experiment and theoretical model is α(h2)=98, k=3.0, λ=1, and U=3.88m/s.

 

A better demonstration of this axial distribution is shown in Figure 3. The data points are generated by time averaging between two pressure peaks in Figure 2. Moreover, in order to examine the reliability of the theory in Feng & Weinbaum [1], the theoretical prediction is also plotted. Since both the leading edge, x/L=1, and the trailing edge x/L=0 are exposed to the atmosphere, the pressure values at these two positions are set to zero gage pressure. The highest pressure is registered around the location of sensor 3. It relaxes gradually towards the leading edge and sharply decreases toward the trailing edge, where zero gage pressure is achieved. Because the largest compression of the material occurs near the trailing edge, the local Darcy permeability decreases significantly and the fluid encounters more resistance as it escapes from the porous media. Thus higher pressure is generated towards the trailing edge. This behavior is consistent with theoretical predictions by Feng & Weinbaum [1], Wu et al. [7,8], and Wu and Sun [12]. Significantly, this is the first experimental demonstration of the pressure distribution inside a soft porous media as a planing surface glides over it. Excellent agreement is observed between the experimental result and the theoretical prediction. Therefore, the validity of the Feng & Weinbaum [1] theory for the pore pressure distribution underneath a planing surface as it glides over a soft porous media is conclusively demonstrated.

 

 

Figure 4. The pressure reading from pressure sensor P3, along with the local total pressure reading from the load cell. The experiment was run with material P at α=98, k=4.0, λ=1, and U=3.88m/s.

 

The pressure reading from pressure sensor 3, along with the local total pressure reading from the load cell is presented in Figure 4. The percentage of lift generation contributed by the pore air pressure is of particular interest. If we define f=Pair/Ptotal, where Pair is the local air pressure, and Ptotal is the local measurement of the total lifting pressure, obtained by dividing the load cell reading by its sensing area. It is clearly shown that at x/L=0.3, where pressure sensor P3 and the load cell are located, around 61% of the total lifting force comes from the pore pressure. This finding is extremely important for an application using highly compressible porous media for soft lubrication. Since sliding frictional force is proportional to the solid phase lifting force, reduction in the solid phase lifting force leads to a reduction in friction.

The work presented here provides the very first experimental study of lift generation inside a highly compressible porous layer when a planing surface glides over. The lubrication theory for a highly compressible porous media developed by Feng & Weinbaum [1] was conclusively verified with respect to the pore pressure distribution underneath a planing surface as it glides over a soft porous layer. It provides critical insight into the biophysics study of the EGL and other soft porous structures that are found in biological systems, e.g. cartilage and eyelid [15-24]. The study lays the foundation for employing highly compressible porous media for lubrication with a significantly higher pressure and longer life, which has a broad impact on energy conservation, and the reduction of greenhouse gas emissions.

 

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