Many theoretical and experimental studies have been conducted to determine the factors critical for improving the filling performance in microinjection moulding。 Most studies tried to find the relationship between the process parameters and the achievable filling length, or the replication quality。 As a result, it has been found that injection speed, injection pressure, hold pressure and its duration, melt temperature, and mould temperature are competitive processes; however, the mould temperature appears to be the most critical factor in many studies [15–22]。

Despite the aforementioned studies, the filling mechanism of microinjection moulding is still poorly understood and a theoretical model and its validation are insufficient。 Most experimental investigations probably suffer from the fact that the melt delivery system (i。e。 sprue, runner, and gate) and cavity geometry are all different in each work, and thus, different results have often been obtained on the governing parameters。 Furthermore, engineers cannot predict whether the designed part containing microstructures could be moulded, nor can they know how  to  design  a  new  part  and  mould。  As  a  related

example, although many studies choose the machine parameters, such as injection pressure and injection speed (flow rate), as experimental factors, the influence of such parameters inevitably depends on the mould structures。 This is one of the reasons why the effect of each parameter is often different。

In addition, theoretical solutions to the flow  behaviour in microinjection moulding are highly demanding。 Because commercial simulation packages are inadequate in describing the filling process for microscale applications, multiscale simulations using in-house code, and/or commercial packages based on finite element modelling have been used by modelling separately the geometries of macrocavities and microcavities and applying different governing equations。 Recently, Lin et al。 and Kuhn et al。 used an analytical model on the filling process with three- dimensional nano/microsurface structures [23, 24]。 They showed reasonable trends and relationships between both experimental and theoretical results on the filling heights correlated withprocess parameters。 Such an analytical model is favourable for simple geometries, such as a cantilever, because it provides fast results and direct insights into the flow behaviour in microchannels。

The aims of this study were to understand the behaviour of the polymer melt filling through microchannels and to predict the filling length based on an analytical model。 For the experiment, a microcantilever beam array whose thickness was either 50 or 100 μm and length was 2 mm was designed with a main body, and the corresponding mould was fabricated。 Cavity pressure was measured to evaluate the effects of injection pressure and injection flow rate on the filling length。 Additionally, the effects of the melt and mould temperature were observed。 Using a dynamic mould temperature control system, the mould temperature was changed in a moulding cycle。 As a theoretical approach, the polymer melt in a microchannel was modelled as a non-Newtonian, power-law fluid, and a heat transfer model was also developed based on a quasi- steady-state assumption。 The measured data of the cavity pressure against time throughout the experiment were applied to the calculation of the melt flow solution。 The analytical model was verified by directly comparing the lengths of the moulded microcantilevers in the experiment。

2 Experiment

2。1 Moulding material

The material applied in this study was general-purpose polystyrene (GPPS 15NF(I), LG Chemicals)。 The melt flow index of the material is 10 g/10 min at 200 °C/5 kg, and the freeze temperature (glass transition temperature) is 117 °C。 The material was preconditioned for 4 h with a dryer, before injection moulding。 The detailed material properties are given in Section 3。