  Sample preparation is an indispensable component of almost all biochemical
protocols, and it involves, among others, making dilutions and mixtures of
fluids in certain ratios. Recent microfluidic technologies offer suitable
platforms for automating dilutions on-chip, and typically on a digital
microfluidic biochip (DMFB), a sequence of (1:1) mix-split operations is
performed on fluid droplets to achieve the target concentration factor (CF) of
a sample. An (1:1) mixing model ideally comprises mixing of two unit-volume
droplets followed by a (balanced) splitting into two unit-volume
daughter-droplets. However, a major source of error in fluidic operations is
due to unbalanced splitting, where two unequal-volume droplets are produced
following a split. Such volumetric split-errors occurring in different
mix-split steps of the reaction path often cause a significant drift in the
target-CF of the sample, the precision of which cannot be compromised in
life-critical assays. In order to circumvent this problem, several
error-recovery or error-tolerant techniques have been proposed recently for
DMFBs. Unfortunately, the impact of such fluidic errors on a target-CF and the
dynamics of their behavior have not yet been rigorously analyzed. In this work,
we investigate the effect of multiple volumetric split-errors on various
target-CFs during sample preparation. We also perform a detailed analysis of
the worst-case scenario, i.e., the condition when the error in a target-CF is
maximized. This analysis may lead to the development of new techniques for
error-tolerant sample preparation with DMFBs without using any sensing
operation.
