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The main objective of this study was to obtain the flow restricting capacity by determining their flow coefficients and to investigate the unsteady flow with low Reynolds number in the flow‐restricting devices such as orifices and capillary tubes having small diameters.

There is an enormous literature on the flow of Newtonian fluids through capillaries and orifices particularly in many application fields of the mechanical and chemical engineering. But most of the experimental results in literature are given for steady flows at moderate and high Reynolds numbers (Re>500). In this study, the unsteady flow at low Reynolds number (10<Re<650) through flow‐restricting devices such as orifices and capillary tubes having very small diameters between 0.35 and 0.70 mm were experimentally investigated.

The capillary tubes have much more capillarity property with respect to equal diameter orifices. Increasing the ratio of capillary tube length to tube diameter and decreasing the ratio of orifice diameter to pipe diameter before orifice increase the throttling or restricting property of the orifices and the capillary tubes. The orifices can be preferred to the capillary tubes having the same diameter at the same system pressure for the hydraulic systems or circuits requiring small velocity variations. The capillary tubes provide higher pressure losses and they can be also used as hydraulic accumulators in hydraulic control devices to attenuate flow‐induced vibrations because of their large pressure coefficients. An important feature of the results obtained for capillary tubes and small orifices is that as the d/D for orifices increases and the L/d reduces for capillary tubes, higher values C are obtained and the transition from viscous to inertia‐controlled flow appears to take place at lower Reynolds numbers. This may be explained by the fact that for small orifices with high d/D ratios and for capillary tubes with small L/d ratios, the losses due to viscous shear are small. Another important feature of the results is that the least variations in C for small orifices and the higher variations in C for capillary tubes occur when the d/D and L/d ratios are smallest. This has favourable implications in hydraulic control devices since a constant value for the C may be assumed even at relatively low values of Re.

To the authors' knowledge, there is not enough information in the literature about the flow coefficients of unsteady flows through capillary tubes and small orifices at low Reynolds numbers. This paper fulfils this gap.

The purpose of this paper is to develop a general numerical solution for the wetting fluid spread into porous media that can be used in solving of droplet spread into soils, printing applications, fuel cells, composite processing.

A discrete capillary network model based on micro‐force balance is numerically implemented and the flow for an arbitrary capillary number can be solved. At the fluid interface, the boundary condition that accounts for the capillary pressure jump is used.

The wetting fluid spread into porous medium starts as a single‐phase flow, and after some particular number of the porous medium characteristic length scales, the multi‐phase flow pattern occurs. Hence, in the principal flow direction, the phase content (saturation) decreases, and in the lower limit for the capillary number sufficiently small, the saturation should become constant. This qualitative saturation behavior is observed irrespective of the flow dimensionality, whereas the quantitative results vary for different flow systems.

The numerical solution has to be expanded to solve the spread of the fluid in the porous medium after there is no free fluid left at the porous medium surface.

It is shown that the multi‐phase flow can develop even on a small domain due to the porous medium heterogeneity. Neglecting the medium heterogeneity and flow type can lead to a large error as shown for the droplet spread time in the porous medium.

This is believe to be the only paper relating to solving the droplet spread into porous medium as a multi‐phase flow problem.

This paper aims to present experimental and finite volume method (FVM)-based simulation studies on the scaling effect on the capillary contact angle and entrant pressure for a three-dimensional encapsulation process of ball-grid array (BGA).

With the development of various sizes of BGA packages, the scaling effect of BGA model on capillary underfill (CUF) process is investigated together with the influences of different industrial standard solder bump arrangements and dispensing methods used as case study.

The experimental results agree well to the simulation findings with minimal deviation in filling time and similar flow front profiles for all setups. The results revealed that the capillary contact angle of flow front decreases in scale-up model with larger gap height observed and lengthens the encapsulation process. Statistical correlation studies are conducted and accurate regression equations are obtained to relate the gap height to the completion filling time and contact angle. CUF threshold capillary pressures were computed based on Leverett-J function and found to be increasing with the scale size of the package.

These statistical data provide accurate insights into the impact of BGA’s scale sizes to the CUF process that will be benefiting the future design of BGA package. This study provided electronic designers with profound understanding on the scaling effect in CUF process of BGA, which may be extended to the future development of miniature-sized BGA and multi-stack device.

This study relates the flow behaviour of encapsulant to its capillary contact angle and Leverett-J pressure threshold, in the CUF process of different BGA and dispensing conditions. To date, no research has been found to predict the threshold pressure on the gap between the chip and substrate.

The paper aims to determine whether the type selection and parameters determination of the compensation are most important for yielding the acceptable or optimized characteristics in design of hydrostatic bearings.

This paper utilizes the equations of flow equilibrium to determine the film thickness or displacement of worktable with respect to the recess pressure.

The stiffness due to compensation of constant‐flow pump increases monotonically as recess pressure increases. Also, the paper considers which is larger than that due to orifice compensation and capillary compensation at the same recess pressure ratio.

The findings show that the usage range of recess pressure and compensation parameters can be selected to correspond to the smallest gradient in variations of worktable displacement or film thickness.

The underfilling of flip chip components with the encapsulant is based on the principles of capillary flow. A reasonable understanding of capillary flow and an effective estimate of the encapsulant's flow time will help develop a robust process. Factors which may influence the encapsulant's flow rate and its variation include the material type (viscosity, wetting characteristics, silicon particle size, etc.), the aging of the material, the substrate preheat temperature, the chemical composition and texture of the flow surface, standoff height, and the presence of obstructions (solder bumps).A screening experiment through the use of orthogonal array was conducted to determine the factors which would have a significant effect on the encapsulant's flow rate. The screening experiments served as a precursor to subsequent process modeling and the identification of a robust process design. Comprehensive experiments were then performed to further investigate the flow behavior of the underfill materials with realistic properties.

The purpose of this paper is to apply negative thermal coefficient (NTC) thick film segmented thermistors (TFSTs) in a micro‐flow sensor for water.

A TFST is printed using NTC paste based on nickel manganite. The resistance of this thermistor is measured in a climatic chamber and the resulting curves are calibrated. A micro‐flow sensor is designed using a self‐heated segmented thermistor. The sensing principle is based on heat loss depending on the water flow intensity through the capillary. Water flow calibration is performed. The sensor sensitivity, inertia, and stability are analyzed.

The micro‐flow sensor exhibits good stability, suitable sensitivity, and inertia for integral measurements of water flow.

Advantages of a micro‐flow sensor using a TFST include low energy consumption, simple measuring procedure, and passive electronics.

This paper describes initial work on a micro‐flow sensor for water using TFSTs.

Laser sintering kinetics and part reliability are critically dependent on the melt viscosity of materials, including polyamide 12 (PA‐12). The purpose of this paper is to characterise the viscosity of PA‐12 powders using alternative scientific methods: constrained boundary flows (capillary rheometry) and rotational rheometry.

Various PA‐12 powders were selected and characterised by both techniques. Measurement of molecular weight was also carried out to interpret the viscosity data.

Results demonstrate conventional pseudoplastic flow in all PA‐12 materials. Zero‐shear viscosity has been quantified by rotational rheometry; a notable observation is the striking difference between virgin/used PA‐12. This is interpreted in terms of molecular weight and chain structure modifications, arising from polycondensation of PA‐12 held at the bed temperature during laser sintering.

Accurate zero‐shear viscosity data provide scope for use in predictive computational models for laser sintering processes. Careful sample preparation and equipment operation are critical prerequisites for accurate rheological characterisation of PA‐12 powders.

Differences in flow behaviour and molecular structure allow prediction and deeper understanding of process‐property relationships in laser sintering, giving potential for further optimisation of material specification and in‐process machine parameter control.

This is believed to be the first time that techniques other than melt flow rate (MFR) have been reported to measure the viscosity of PA‐12 in a laser sintering context, noting the effects of pre‐drying and molecular weight, then predicting differences between virgin/used powders in practical sintering behaviour.

This paper aims to provide a comprehensive literature review on modelling electro-osmotic flow in porous media.

Modelling electro-osmosis in fluid systems without solid particles has been first introduced. Then, after a brief description of the existing approaches for porous media modelling, electro-osmotic flow in porous media has been considered by analysing the main contributions to the development of this topic.

The analysis of literature has highlighted the absence of a universal model to analyse electro-osmosis in porous media, whereas many different methods and assumptions are used.

For the first time, the existing approaches for modelling electro-osmotic flow in porous have been collected and analysed to provide detailed indications for future works concerning this topic.

This paper aims to present new analytical model for the filling times prediction in flip-chip underfill encapsulation process that is based on the surface energetic for post-bump flow.

The current model was formulated based on the modified regional segregation approach that consists of bump and post-bump regions. Both the expansion flow and the subsequent bumpless flow as integrated in the post-bump region were modelled considering the surface energy–work balance.

Upon validated with the past underfill experiment, the current model has the lowest root mean square deviation of 4.94 s and maximum individual deviation of 26.07%, upon compared to the six other past analytical models. Additionally, the current analytically predicted flow isolines at post-bump region are in line with the experimental observation. Furthermore, the current analytical filling times in post-bump region are in better consensus with the experimental times as compared to the previous model. Therefore, this model is regarded as an improvised version of the past filling time models.

The proposed analytical model enables the filling time determination for flip-chip underfill process at higher accuracy, while providing more precise and realistic post-bump flow visualization. This model could benefit the future underfill process enhancement and package design optimization works, to resolve the productivity issue of prolonged filling process.

The analytical underfill studies are scarce, with only seven independent analytical filling time models being developed to date. In particular, the expansion flow of detachment jump was being considered in only two previous works. Nonetheless, to the best of the authors’ knowledge, there is no analytical model that considered the surface energies during the underfill flow or based on its energy–work balance. Instead, the previous modelling on post-bump flow was based on either kinematic or geometrical that is coupled with major assumptions.

The purpose of the study is to investigate the spatial aspects of underfill flow during the flip-chip encapsulation process, for instance, meniscus evolution and contact line jump (CLJ). Furthermore, a spatial-based void formation mechanism during the underfill flow was formulated.

The meniscus evolution of underfill fluid subtended between the bump array and the CLJ phenomenon were visualized numerically using the micro-mesh unit cell approach. Additionally, the meniscus evolution and CLJ phenomenon were modelled analytically based on the formulation of capillary physics. Meanwhile, the mechanism of void formation was explained numerically and analytically.

Both the proposed analytical and current numerical findings achieved great consensus and were well-validated experimentally. The variation effects of bump pitch on the spatial aspects were analyzed and found that the meniscus arc radius and filling distance increase with the pitch, while the subtended angle of meniscus arc is invariant with the pitch size. For larger pitch, the jump occurs further away from the bump entrance and takes longer time to attain the equilibrium meniscus. This inferred that the concavity of meniscus arc was influenced by the bump pitch. On the voiding mechanism, air void was formed from the air entrapment because of the fluid-bump interaction. Smaller voids tend to merge into a bigger void through necking and, subsequently, propagate along the underfill flow.

The microscopic spatial analysis of underfill flow would explain fundamentally how the bump design will affect the macroscopic filling time. This not only provides alternative visualization tool to analyze flow pattern in the industry but also enables the development of accurate analytical filling time model. Moreover, the void formation mechanism gave substantial insights to understand the root causes of void defects and allow possible solutions to be formulated to tackle this issue. Additionally, the microfluidics sector could also benefit from these spatial analysis insights.

Spatial analysis on underfill flow is scarcely conducted, as the past research studies mainly emphasized on the temporal aspects. Additionally, this work presented a new mechanism on the void formation based on the fluid-bump interaction, in which the formation and propagation of micro-voids were numerically visualized for the first time. The findings from current work provided fundamental information on the flow interaction between underfill fluid and solder bump to the package designers for optimization work and process enhancement.