# Capillary Forces between Concave Gripper and Spherical Particle for Micro-Objects Gripping

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## Abstract

**:**

## 1. Introduction

## 2. Modeling the Capillary Bridge and Capillary Force

#### 2.1. Geometry of the Capillary Bridge

#### 2.2. Capillary Force Based on Young–Laplace Equation

## 3. Numerical Solution of Capillary Forces

## 4. Results and Discussion

#### 4.1. Capillary Bridge Rupture

#### 4.2. Capillary Forces

^{−6}, as illustrated Figure 7d.

#### 4.3. Experimantal Measurements

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Double iterative processes of meniscus profiles: (

**a**) stable solution; (

**b**) unstable solution.

**Figure 3.**Various parameters changing with dimensionless separation distance variation at three contact angles: (

**a**) dimensionless neck radius, (

**b**) dimensionless pressure difference, (

**c**) half-filling angle, and (

**d**) dimensionless capillary force.

**Figure 7.**Evolution processes of the capillary bridge: (

**a**) initial definition, (

**b**,

**c**) evolution processes, and (

**d**) after evolution.

**Figure 9.**Processes of capillary force measurements: (

**a**) geometrical representation of a stable liquid bridge, (

**b**) separation distance of 0.36 mm, and (

**c**) separation distance of 0.4 mm. The scale bar is 0.5 mm.

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**MDPI and ACS Style**

Fan, Z.; Liu, Z.; Huang, C.; Zhang, W.; Lv, Z.; Wang, L.
Capillary Forces between Concave Gripper and Spherical Particle for Micro-Objects Gripping. *Micromachines* **2021**, *12*, 285.
https://doi.org/10.3390/mi12030285

**AMA Style**

Fan Z, Liu Z, Huang C, Zhang W, Lv Z, Wang L.
Capillary Forces between Concave Gripper and Spherical Particle for Micro-Objects Gripping. *Micromachines*. 2021; 12(3):285.
https://doi.org/10.3390/mi12030285

**Chicago/Turabian Style**

Fan, Zenghua, Zixiao Liu, Congcong Huang, Wei Zhang, Zhe Lv, and Lefeng Wang.
2021. "Capillary Forces between Concave Gripper and Spherical Particle for Micro-Objects Gripping" *Micromachines* 12, no. 3: 285.
https://doi.org/10.3390/mi12030285