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Publication# Two-dimensional modelling of transient capillary driven damped micro-oscillations and self-alignment of objects in microassembly

Abstract

In the fields of microgripping and microassembly, the self-alignment motion of a solid micro-object linked by a liquid meniscus to a substrate or a tool is an inexpensive way to overcome the current limitations of the assembly processes at microscale by getting rid of the positioning actuators. Original models providing a dynamical description of the capillary self-alignment of an chip are reported, as well as experimental results as evidence of their validity. The first two models describe the liquid and the solid physics in two dimensions. Both include nonlinearities and describe the coupling between a laminar flow and a solid structure. The fluid-solid coupling is ensured by the boundary conditions at their surface of contact and by the forces the liquid and the solid apply on each other. Both models yield the shift, lift and tilt modes of deformation of the liquid meniscus. Equations are first numerically solved by using a finite element method (model 1). By approximating the menisci with spherical caps, a geometrical model is then presented (model 2). Next, for small oscillations and thin liquid layers, the equations are linearised. The solution to the semianalytical three degrees of freedom (3-DOF) modal analysis is thus obtained (model 3). Finally, a semianalytical 1-DOF model is presented and numerically solved by considering a one-dimensional motion for the solid object (model 4). Solutions for models 1, 3 and 4 are computed and show good agreement with the experimental measurements. Yet, the remaining deviations are investigated to identify their origin.

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Solid

Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural rigidity (as in rigid bodies) and resistance to a force applied to the surface. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire available volume like a gas.

Solid-state physics

Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. Along with solid-state chemistry, it also has direct applications in the technology of transistors and semiconductors.

Spherical cap

In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere.

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