## 1 Introduction
In most LoaD systems, these valves retain the liquid during so-called laboratory unit operations (\"LUOs\"), such as metering and mixing, which are extensively covered in the literature [45; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69], and briefly in a subsequent section within the context of LSL. Furthermore, while essential ingredients for full-fledged LoaD applications, we refer to the numerous specialized publications regarding the many, primarily optical or electrochemical, techniques for downstream detection [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34]. In traditional valving mechanisms, the spinning-induced pressure head, which simultaneously acts on all disc-based liquid volumes, is opposed by different sources of counterpressure. For instance, interfacial tension is at the root of capillary burst valves; liquids are retained in siphon valves until the capillary pressure exceeds the centrifugal pressure by lifting [14], lowering [9] or accelerating [72] the spin rate across critical frequency thresholds, or overflow prompted by volume addition under prevalent artificial gravity conditions. This work runs along the example of centrifuge-pneumatic (CP) dissolvable-film (DF) siphon valving that has shown to offer wide tunability, configurability, and operational robustness compared to other rotationally controlled valving schemes [29; 33; 55; 72; 73]. Yet, the portrayed digital twin method [74; 75; 76], i.e., the model-based virtual representation of a physical object or process, can readily be extended to characterize and refine other flow control mechanisms over their multidimensional parameter spaces. This paper investigates systematic design optimization of rotationally actuated valves to facilitate fluidic large(r)-scale integration (LSI). The notion of microfluidic LSI was first elaborated in the early 2000s in the context of pneumatically controlled elastomeric systems [77]. Based on previous publications on \"digital twin\" [76] modeling of fluidic performance and operational robustness on LoaD systems [73; 78], valve retention frequencies and their band widths were identified as key performance indicators. They can directly be calculated, either algebraically of numerically, from the standard deviation of elementary input parameters, such as general (linear) machining and pipetting tolerances [79; 80]. These statistical spreads can either be found in manuals or the literature, and are determined by low-complexity test structures; importantly, these basic parameters are broadly independent of the specific layout of a specific LoaD cartridge. This method is, therefore, essential to predict and optimize the device performance and its operational robustness _in silico_, prior to the time- and resource-consumption and, thus, the risky and costly development of manufacturing and assembly. Such facilities are rarely available in academic labs, not even during early-stage research and development projects in common industrial environments. At first, the principles of centrifugal flow control are modeled to support a digital twin of LoaD systems orchestrated by a group of CP-DF siphon valves. Then, fundamental requirements underlying rotational valving for fluidic LSI in real and frequency space are elaborated. In the next section, a set of performance metrics supporting the initial, knowledge-based qualitative design and its subsequent, computational optimization are defined. Examples for typical tasks in multiplexing and resulting valve geometries are given before compiling general rules guiding the layout and rotational automation of multi-step/multi-reagent bioanalytical assay panels.