# Industrial Soldering Process Simulator
## 2 Basic Research--The Process of Measurement and Analysis of the Wetting Force  
The capillary wetting force is denoted as the difference between the force measured before and after immersion of the specimen in the liquid brage. Specifically, it is the difference between the maximum force measured just before immersion and the force measured when the liquid meniscus has wholly covered the specimen. This difference is caused by the surface tension of the liquid, which creates a force that pulls the fluid toward the model's surface. The Wilhelmy plate method is a precise technique utilized to quantify the force of wetting [7; 8]. To receive the shape of the meniscus formed around a vertical solid, the Laplace equation was used to analyze the weight changes (equal to the sum of capillary and buoyancy forces) versus the depth of immersion. With this method, it is possible to simultaneously measure the surface tension of the liquid and the contact angles. The weight changes during immersion and emerg, respectively, allow us to deduce both advancing and receding contact angles. To simplify the explanation, it is assumed that the vertical movement of the solid in the liquid is infinitely slow. The weight of the solid in the gas phase as the reference point for weight measurements is considered. Based on these conditions, the force exerted on the partially submerged solid, with its base located at the \(z_{b}\) level compared to the flat horizontal liquid surface, equals the sum of the weight of the meniscus \(F_{c}\) and the buoyancy force \(F_{w}\). Figure 1 shows the distribution of forces acting on a vertical plate and the measurement system before Figure1a and after partial immersion Figure1b. Before dipping:  
\[\sum_{i=n}^{i=1}F_{iy}=F_{g1}-F_{c}=0, \tag{1}\]  
* \(F_{g1}\)--weight registered by the measuring system before dipping.
* \(F_{c}\)--sample weight.  
After dipping:  
\[\sum_{i=n}^{i=1}F_{iy}=F_{\delta 2}-F_{\delta 1}+F_{w}-F_{\sigma}=0, \tag{2}\]  
* \(F_{\delta 2}\)--weight registered by the measuring system after dipping.
* \(F_{w}\)--buoyancy force.
* \(F_{\sigma}\)--surface tension force.  
There exist two potential models depending on the value of the contact angle \(\theta\) (Figure 1):  
* \(0\leq\theta\leq 90^{\circ}\)-- \(F_{\sigma}\)-- is directed downwards.
* \(90^{\circ}<\theta\leq 180^{\circ}\)-- \(F_{\sigma}\)--is directed upwards.  
The model selected for further examination involves summating all force projections on the OY axis shown in Figure1a,b. At the steady state, when the angle \(\theta\) reaches an equilibrium angle \(\theta_{0}\), and the head surface of the sample is located at a depth of \(z_{b}\) below the horizontal surface of the liquid, a force is exerted on the measuring system.  
\[F_{\delta 2}-F_{\delta 1}=F_{\sigma}-F_{w}, \tag{3}\]  
It was assumed that \(F_{\delta 2}-F_{\delta 1}=F_{M}\), The buoyancy force depends on the geometry of the sample and dipping depth:  
\[F_{w}=P_{p}\rho gz_{b}, \tag{4}\]  
where: \(P_{p}\)--cross-section area of a sample, \(\rho\)--density of the liquid metal, \(g\)--gravitational acceleration, \(z_{b}\)--dipping depth. The weight of meniscus \(F_{\sigma}\) can be represented by:  
\[F_{\sigma}=O_{p}\sigma_{LV}cos\theta_{0}, \tag{5}\]  
where: \(O_{p}\)--sample circuit, \(\sigma_{LV}\)--surface tension on the liquid-gas boundary, \(\theta_{0}\)--equilibrium wetting angle. Finally the wetting force \(F_{k}=\sigma_{LV}cos\theta_{0}\) is given by the equation:  
\[F_{k}=\frac{F_{M}+P_{p}\rho gz_{b}}{O_{p}}, \tag{6}\]  
Figure 1: Distribution of forces acting on a vertical plate and the measurement system. (**a**) Before immersion and (**b**) after partial immersion.