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Figure below shows a micro gripper used for conveying very small objects (i.e. the spherical object in Figure) and putting them in desired place using capillary force principal in a liquid bridge.

To calculate the maximum weight that this capillary gripper can pull up, considering both "Laplace pressure term" applied to wet section in top of the sphere and "surface tension force" applied to the interface of liquid and air, one can write:

$F=F_L+F_T$

$F_L=(2\gamma/R)A$

$F_T=\gamma . (contact\ line\ length)$

$(2\gamma/R) \pi R_a^2+2\pi R_a\gamma sin(\theta+\alpha)=4/3(\pi R^3\rho g)$

What condition should we apply to this equation in order to determine the maximum weight of sphere that gripper can pull up before the bridge breaks up.

enter image description here

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  • $\begingroup$ I think you need to look at the relationship between $r_0$ and $h$ - obviously, the force is a function of distance between the plate and the object. When that function no longer has a minimum, the bridge will break. $\endgroup$ – Floris Feb 15 '15 at 19:47
  • $\begingroup$ The bridge will break when the internal pressure is insufficient to support the weight. $r_1$ is a function of the volume of the drop and $h$. As $r_1$ gets bigger, the contact angle grows but the internal pressure gets less. There is an equilibrium somewhere. I suspect it is hard to write an equation for it. May I ask what the context of your question is? $\endgroup$ – Floris Feb 15 '15 at 19:56
  • $\begingroup$ @Floris Thanks for your comment. I think you mean that the bridge will break when we have a vertical interfacial i.e. $r_1=$infinity, however, since contact angle is a property of material, shouldn't change in different states. But, it seems that $\alpha$ would be larger in case of a vertical interfacial line. What do you think? $\endgroup$ – vorujak Feb 15 '15 at 19:56
  • $\begingroup$ @Floris I encountered this question by reviewing this paper. $\endgroup$ – vorujak Feb 15 '15 at 20:09

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